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Dymola User's Manual - Department of Computer Science

1. 0 0 0 00 0 cece eee 262 Constructing anti symmetric expressions 0 0 0 0 eee 264 Equality comparison of real values ir ox eee aba fe oe eal EVER SEE EE 266 Aveo vartables idas proa ns a cut t part ebat 266 Trigger events Tor equality os voee e Secr Den eL RH es ES ERN DERE is 266 Locking when equal ss s erronee bb Ege ERO SLE ob Een 267 Guarding against division by zero iilis 267 Appendix Migration 1 ss 271 Migrating to newer libraries ax 4x oe b E A ATE EUM 271 QW IOAN A ON ot 2o Ed Pe oed bie A eae ne ieee aa 271 Basic commands to specify translation 2 0 0 0 00 0000 cee ee 272 How to build a convert Scr pls 3o 2t et pito Sales eae ut pa ra bet 275 Appendix Installation 1 s 281 Installation on Windows x utet as a vitam ean Yeu Raab eee ruse deeds 281 Installing Dymola ee Pops Dem do use ee Erb SUERTE a 281 Dongl installation ue eked as ir eruere bua sr it Mu S I Mo erm EE 283 Additional A c cto ase sick E EASE e pur SS RE eL LENA TR FIO 284 Installing mpdates Das oe iN ebus te aaa ODIT 285 Removing Dymola rda dt a ai ts bs bud de set cuftos oe ad 285 Installation UNES susi rra ts ele aa A ded adiens 285 Installing Dymola eslora a ti 285 PIO E AMA NO 286 Removi o Dymola s oem es ER AI e ia Potuit 287 Dymola License Server Sala dioi ae id sde eto CES 287 Backoround citadas A a E Behan eee psa 287 Installing the licen
2. Drag a resistor from Basic to the Motor window and place it as shown above The compo nent browser displays that Motor has a component Resistorl 52 Inserting a resistor El Motor DriveLib Motor Diagram component File Edit Simulation Plot Animation Window Help 8i xi Ie El amp N2 C o C7 A 2 dr Zle 3 28 1 Bio i E Ground Resistor gt Conductor o Capacitor e nductor Resistor1 IE Transformer EJDriveLib Motor Resistorl When inserting a component is given an automatically generated name The name may be changed in the parameter window Double click on the component to get its parameter win dow The parameter window can also be reached by pointing on the component and press ing the right mouse button and select Parameters The parameter window of a resistor with de fault settings E Resistor1 in Motor aixi Add Modifiers r Component Name JResistort Comment m Model Path Modelica Electrical Analog Basic Resistor Comment Ideal linear electrical resistor m Parameters RI Ohm Resistance OK Cancel Change the component name to Ra The parameter window allows setting of parameter val ues To set the resistance parameter R select the value field of parameter R and input 0 5 GETTING STARTED WITH DYMOLA 53 The parameter window of a resistor with new settings Add Modifies r
3. xIsPositive if if level gt eventLimit then x gt 0 else noEvent x gt 0 then Bl else 1 der x if noEvent xIsPositive 0 then cpos x else cneg x Tif time gt 1 then y else 0 Note the noEvent on the last line Without it we would always have an event when x changed sign If level gt eventLimit the expression x gt 0 will introduce events and thus xIsPos itive need not introduce an additional event Constructing anti symmetric expressions Quite a few expressions are naturally anti symmetric in some variable In most cases this requires no extra thought and only requires one to write the expression in the natural form and it will be anti symmetric 264 However in some cases it 1s known that a formula 1s anti symmetric and it straightforward to give a formula for positive values but more difficult to give a simple formula valid for both positive and negative values The natural idea in these cases 1s to extend the expression for positive values to an anti symmetric formula valid for all values As a generic example consider zum g x p x20 g x p x lt 0 As a model this 1s written as Real x parameter Real p equation der x noEvent if x gt 0 then g x p else g x p assert noEvent abs g 0 p lt le 10 Formula requires g 0 p 0 In most cases the assert statement would be removed for efficiency reasons and the func tion g replaced by an expression involving x p and perhap
4. Hybrid modeling in Modelica Realistic physical models often contain discontinuities discrete events or changes of struc ture Examples are relays switches friction impact sampled data systems etc Modelica has introduced special language constructs allowing a simulator to introduce efficient han dling of such events Special design emphasis was given to synchronization and propaga tion of events and the possibility to find consistent restarting conditions after an event A hybrid Modelica model 1s described by a set of synchronous differential algebraic and discrete equations leading to deterministic behaviour and automatic synchronization of the continuous and discrete parts of a model The consequences of this view are discussed and demonstrated at hand of a new method to model ideal switch elements such as ideal diodes ideal thyristors or friction At event instants this leads to mixed continuous discrete systems of equations that have to be solved by appropriate algorithms For modeling of continuous time systems Modelica provides DAEs to mathematically describe model components For discrete event systems this 1s different because there does not exist a single widely accept ed description form Instead many formalisms are available e g finite automata Petri nets statecharts sequential function charts DEVS logical circuits difference equations CSP process oriented languages that are all suited for particular application a
5. Description C Custom Apply Cancel Titles tab The user may enter a heading to be displayed above the active diagram An empty heading is not shown the space is used for the diagram instead Vertical axis title specifies the title for the vertical axis of the diagram None No title 15 shown by the vertical axis Description The title is extracted from the descriptions and units of plotted signals Custom The title 1s specified by the user in the input field Horizontal axis title specifies the title for the horizontal axis of the diagram None No title 15 shown by the horizontal axis Description The title is extracted from the independent variable if other than time Custom The title 1s specified by the user in the input field Examples of user defined heading and custom axis titles are shown on page 156 162 Legend tab of the plot window setup Signals Titles Legend Options Bange r Appearance Y Show units Show variable descriptions Use line styles instead of color Do not use markers r Layout IV Show variable legend v Arrange legend horizontally Draw frame around legend m Location Above Top Left Right TopRight C Below Bottom Left Bottom Right Cancel Legend tab The legend displays names and other properties about plotted signals The ap pearance of the signals 1s set as follows Show units of variables in the vert
6. These commands in the graphical editor DDE Command Corresponding command in graphical editor open filename File Open clear File Clear All All Modelica script features are also supported Explorer file type associations It is possible to associate new commands with the mo file type These commands are ac cessible through the right mouse button menu in Explorer We suggest this setup 1 Start Windows Explorer and select View Options Select the File Type tab 2 Click on New Type to create a new association Enter the following general informa tion a Change icon browse for the Dymola program typically C Dymola bin dymola exe b Description of type Modelica model c Associated extension mo d Content type MIME text plain e Default extension for content type txt 3 Associate new menu commands with the file type Click on New then enter a Action Open b Application used to perform action browse for the Dymola program typically C Dy mola bin dymola exe c Use DDE check d DDE message open 1 e Application dymola OTHER SIMULATION ENVIRONMENTS 233 Leave the remaining fields empty In a similar way you can associate several commands with the extensions mo and mos Action Application to perform action DDE message File extension Edit C windows notepad exe 961 all or C winnt notepad exe 1 Open C Dymola bin dymola exe open 1 m
7. APPENDIX MIGRATION 277 278 APPENDIX INSTALLATION Appendix Installation Installation on Windows This section refers only to the Windows version of Dymola Following installation the user may do additional setup The installation of updates and re moval of Dymola is also described below Holders of a floating Dymola license should install Dymola on the server first and then proceed with the installation of the license server After that Dymola can be installed on all client computers see Installing on client computers on page 290 Installing Dymola The installation normally starts when you insert the distribution CD If autostart has been disabled please start D setup exe assuming your CD drive is labeled D from Win dows Explorer or Start Run The first choice in the installation procedure is the name of the Dymola distribution directo ry The default is C NDymola The second choice is to select optional components of the distribution By unselecting com ponents some space can be saved The first three alternatives are related to compiler sup port see below Creating a desktop shortcut 1s a convenient way to access Dymola without using the Start Programs menu APPENDIX INSTALLATION 281 Component selection Japanese translation requires special fonts 2 Select Components E xj In the options list below select the checkboxes for the options that you would like to have
8. Edit Combined Edits an array of calls to functions or record constructors 118 Editor for array of records Editor for matrices 2 Table Editor for setup tuners View Parameter Settings Shows where the default originates from and all modifiers ap plied between the original declaration and the current one Propagate Inserts a parameter declaration in the enclosing model and binds the compo nent s parameter to it by introducing a modifier of the type p p Default values are not propagated to the new parameter declaration Class Reference Inserts a reference to a class in the model Component Reference Inserts a reference to a component in the model at the insertion point of the input field Select Class Provides a class selector for redeclarations with all matching classes Select Record Selects a record constructor or constant among suitable candidates Any changes become effective when pressing the OK button and are discarded by pressing the Cancel button If the shown model is read only no changes are possible and only a Close button appears Array and matrix editor The array and matrix editor allows editing of both elements and array size A context menu available to insert rows before the selected entry and delete rows and columns Insertion after the last entry 1s performed by increasing the size E Matrix Editor for table BEN 7i xl Rows Columns 2 Edit Text Copy Default Delete
9. Modelica Math sin 0 0 5 1 5 0 0 479425538604203 0 841470984807897 0 997494986604054 1 2 3 4 1 2 3 4 7 10 T5 22 1 e the tool completes the equation with an equal sign and the result The semicolon at the end may be omitted The character denotes a prompt Itis possible to continue a statement on several input lines 1 2 3 4 1 2 3 4 Continue line transpose 1 2 3 4 1 2 3 4 Continue line Modelica Math sin 1 2 3 4 1 2 3 4 309 234551260163 83 9358210418974 674 574723255002 183 082439325942 by ending a line before a complete assignment or expression has been entered This rule al lows omitting the semicolon at the end of a statement and or using a continuation symbol A tool might enlarge input window to show all pending input lines Several expressions are also allowed if separated by semicolon SIMULATING A MODEL 173 2 3 4 5 6 20 Diagnostics 1s given immediately when errors are encountered transpose 1 2 3 4 5 Error The parts of 1 2 3 4 5 are not of equal sizes 2 3 Assignments It 1s possible to use a Modelica assignment For convenience the operator 1s used below to denote assignment Comments can be written as usual using or model pl 5 update model pl model 3 q model p1 Modelica Math sin 6 Interactive variables The result might be stored in a variable The vari
10. Real x pattern equation pattern 0 end M Full documentation Match search pattern against the full documentation of classes It is also possible to match the search pattern against specific details of the model This group 1s disabled if the Modelica text 1s searched Class name Match search pattern against names of classes Description Match search pattern against the description string of classes or components Component name Match search pattern against the names of components Example model M CompType pattern end M Use of class Match search pattern against uses of class as the type of components and in extends clauses Matches in redeclarations and extends are marked with a special icons Ex amples DEVELOPING A MODEL 135 Changing directory model M extends pattern pattern comp name CompType cl redeclare pattern c2 end M The search options control how the matching 1s done for each searched item Complete match Match the complete contents of topics If not checked the search pattern will match parts of the topics Match case Match upper and lower case exactly If checked the search pattern a will not match A The search result at the bottom of the search dialog displays the name of the class or com ponent matching where the matching item 1s located and the short description of the matching item The results can be sorted by clicking on the corresponding heading Two operations are ava
11. Real x sign x parameter Real p equation sign x noEvent if x 0 then 1 else 1 der x sign x g sign x x p assert noEvent abs g 0 p amp 1e 10 Formula requires g 0 p 0 APPENDIX ADVANCED MODELICA 265 Similar remarks as for the first example apply to this example Equality comparison of real values Following the Modelica specification Dymola does not allow you to compare two real val ues for equality The reason 1s not that it would be difficult to allow it but that the desired result depends on circumstances and there 1s not one correct way of re writing 1t as legal code Instead of automatically generating a result that would only work for some cases you are required to manually select the desired result Type of variables In many cases it does not matter whether variables are declared as Integer or Real Howev er only integers may be used as indices and compared for equality Thus some equality comparisons between real expression can be removed by replacing Real variables by Inte ger variables and perhaps a fixed scaling In some cases all variables and constants appearing in the expression are integers but some operations generates a real valued result e g division If the result is known to be an integer one can replace these by integer division div or use integer to convert a real valued ex pression to an integer valued one Trigger events for equality In some cases one want t
12. row 1 elements separated by blanks may span several lines row 2 last row Blank lines are ignored as well as all characters which are present after the comment char acter The first matrix on every file is a char matrix with name class The first row of this matrix contains the class name of the data on file This name allows the identifi cation of the type of data stored in the file The second row contains a class specific version number Finally the third row contains a description text of the data which 1s an arbitrary string provided by the program which generated the file If desired the ASCII form of files can be directly generated by hand With the provided program alist the ASCII and binary form can be transformed into each other E g al ist file lists file file on standard output in ASCII format independent of the previ ous format of the file Command alist h produces the following short description Usage alist options files transform Dymosim files and write them to standard output Options a write in ASCII format default b write in Matlab binary format h help list this description d transform single precision matrices into double precision 5 transform double precision matrices into single precision Example alist as dsres mat gt dsres txt transform file dsres mat from binary into ASCII format change the precision to float and store the
13. Modelica s normal vectorization applies for convertClass which means that it 1s possible to let the arguments be vectors of Strings For example convertClass oldClass1 oldClass2 newClass1 newClass2 1s equivalent to 272 convertClass oldClass1 newClass1 convertClass oldClass2 newClass2 convertElement The command convertElement oldClass oldElement newElement converts references to elements connectors parameters and local variables of classes in equations connections modifier lists etc The class name of the component is still convert ed according to convertClass The conversion uses the model structure after conversion thus it correctly detects base classes among the models you convert However only the new library is used thus any in heritance used in the old library 1s lost It means for example if a connector was renamed in base class conversion of that connector name must be specified for all models in the old library extending from base class By using vector arguments to the conversion functions it 1s only necessary to list the classes once for each renamed element Let us illustrate by an example Assume that we have a drive train library where there 1s a partial class DriveTwoCut specifying two connectors pDrive and nDrive The new library has a similar class TwoFlanges defining two connectors flange a and flange b We thus give the commands convertCl
14. The controller of an axis gets references for the angular position and speed from the path planning module as well as measurements of the actual values of them The controller out puts a reference for the current of the motor which drives the gearbox The motor model consists of the electromotorical force three operational amplifiers resis tors inductors and sensors for the feedback loop 30 The robot motor Rp2 R 50 c Rp1 o bee R 200 0 004 D Rd2 Ri power 4 D I R 100 ets le CN S SA D a gt T C H R 100 ud 93 g1 zieu Em e A wey sh T n 3 3 aal 2 9 o Co a S g S 2 S E c o y 10 53 p i 4 no 3 o g o ae m o Q g2 ce o o uv 3 2 View the component gear in a similar way as for the other components It shows the gear box and the model of friction of the bearings and elasticity of the shafts The robot gearbox flange of joint flange of motor axis Sins gear i bearingFriction Ar flange b flange a GETTING STARTED WITH DYMOLA 31 Modeling y Simulation Herz Animated 3D view of the robot Animation toolbar Simulation Let us simulate the robot model To enter the Simulation mode click on the tab at the bot tom right When you selected the robot the Commands menu became active to indicate that robot contains a Command for simulating it select this B fullRobot MultiBody Exa
15. Under Windows 95 98 and ME Dymola may under exceptional circumstances generate the error message Out of environment space during compilation The remedy 1s to modify two system configuration files to increase environment space sys tem ini and config sys 1 Open windows system ini with notepad Search for a variable called CommandEn vSize This variable should be set to at least 6000 If it does not exist in system ini add the following two lines NonWindowsApp CommandEnvSize 6000 2 On Windows 95 and 98 open config sys with notepad The command environment space must also be set to 6000 Locate the line defining SHELL The E switch is used to define command environment space for example SHELL C NCOMMAND COM C P E 6000 Please keep other switches on the line unchanged Windows must be restarted after these changes 294 Symbols 174 149 176 A about 143 absolute tolerance 201 acausal modeling 76 algorithm 81 animated GIF 137 animation 166 menu 169 visual shapes 166 arrow keys 115 143 assignment 81 interactive 174 automatic manhattanize 121 143 AVI Audio Video Interleaved 137 Index B backstep animation 169 base class 110 112 113 BMP graphical object 124 bound parameter 61 bring to front 139 browser component 109 package 109 c chattering 184 check 109 139 checkModel 179 class description 76 113 doc
16. h list command summary d file use input defaults from file i e read first all input data from file and afterwards read a subset of the input data from the Dymosim input file dsin txt or from file_1n i generate Dymosim input file containing e g the names and default initial values of all parameters and state variables ib generate Dymosim input file in Matlab binary format mat file it generate Dymosim input file using timer defaults for realtime Dymosim p precede Dymosim output lines by program name for realtime Dymosim in order to identify the process which prints the line DYNAMIC MODEL SIMULATOR 207 v verify input 1 e store complete input in file dsinver txt cemd execute command cmd after simulation end This can be useful if dymosim is started as a separate process in the background Basic file format The input file as well as the result file of Dymosim have the same format The data may be given in ASCII human readable or binary format The binary format 1s 1dentical to the Matlab binary format i e the Dymosim input file can be generated by the Matlab save command whereas the Dymosim result file can be loaded into Matlab by the Matlab load command The contents of a file consists of a set of named matrices of type char int float or double In ASCII format a matrix has the following structure type name row dimension column dimension
17. 130 setup 137 hybrid modeling 81 hybrid system 183 1con layer 111 142 if expression 85 information window 116 initialization of models 90 over specified 182 inline integration 190 InlineIntegration 192 InlineIntegrationExplicit 192 instability 183 installation clients of server 290 dongle 283 environment variables 286 license daemon 287 license server 287 multiple compiler support 282 troubleshooting 290 UNIX 285 windows 281 integration method 148 190 integrator DASSL 203 205 DEABM 203 204 DOPRIS 203 204 DOPRIS 203 205 GRKAT 203 205 LSODAR 203 204 LSODEI 203 204 LSODE2 203 204 MEXX 203 205 ODASSL 203 205 J JPEG graphical object 124 K keyboard commands 143 298 L layer 108 111 diagram 111 documentation 111 icon 111 Modelica text 111 library 48 documentation 113 shortcut to 134 library annotation 255 library menu 134 library migration 271 library window 110 license file error message 291 license server 287 line 123 color 124 style 125 linearize 150 list 180 listfunctions 176 logging events 183 LogVariable 205 M manhattanize 121 139 141 material visual objects 167 Matlab mex 219 path 219 using Dymola models 224 see also Simulink matrix equations 79 menu animation 169 diagram 160 m file 205 206 tcomp 207 tcut 207 tder 207 tdiff
18. Arete 05 10 Simulation menu Run Script i Translate YW Simulate Continue x Stop Linearize oo Setup fa Visualize Show Log The simulation menu includes commands to setup and run simulations The most common simulation commands are available in the tool bar IBe O iv g Simulation Run Script Executes the commands in the script file The scripting facilities are described in more de tail in Scripting language on page 173 SIMULATING A MODEL 149 4 General tab of Simula tion Setup Simulation Translate Translates the active model to simulation code Error messages and warnings are shown in the message window After successful translation the class 1s ready for simulation Simulation Simulate Simulates the model for one simulation period according to the specified experiment setup If the active model has not been translated or an editing operation has invalidated the previ ous translation then the model is automatically translated before simulation Simulation Continue Continues the simulation for one simulation period start time to stop time from the previ ous stop time Simulation Stop Interrupts the execution of a translation command script or simulation An active stop but ton indicates that one of these operations 1s 1n progress Simulation Linearize The command Simulate Linearize calculates a linearized model at the initial values The linearized model is
19. Within the controller the discrete states x are needed both at the actual sample instant x and at the previous sample instant x 7 which is determined by using the pre operator Formally the left limit x f of a variable x at a time instant f is characterized by pre x whereas x itself characterizes the right limit x t Since x is only discontinuous at sample instants the left limit of x at sample instant f is identical to the right limit of x t T at the previous sample instant and therefore pre x characterizes this value The synchronous principle basically states that at every time instant the active equations express relations between variables which have to be fulfilled concurrently As a conse quence during continuous integration the equations of the plant have to be fulfilled where as at sample instants the equations of the plant and of the digital controller hold concurrently In order to efficiently solve such types of models all equations are by block lower triangular partitioning the standard algorithm of object oriented modeling for contin uous systems now applied to a mixture of continuous and discrete equations under the as sumption that all equations are active In other words the order of the equations is determined by data flow analysis resulting in an automatic synchronization of continuous and discrete equations For the example above sorting results in an ordered set of assign
20. end SiSOController model MotorDrive3 replaceable block ControllerModel SISOController protected ControllerModel controller then same as MotorDrive end MotorDrive3 where the replaceable model ControllerModel 1s declared to be of type SISOController which means that it will be enforced that the actual class will have the inputs ref and inp and the output out but it may be parameterized in any way Setting ControllerModel to for example PID 1s done as 80 model PIDDrive MotorDrive3 redeclare block ControllerModel PID The use of model class parameters to support machine medium decomposition 1s illustrated in Mattsson ef al 1998 Ernst et al 1997 and Tummescheit and Eborn 1998 Algorithms and functions Algorithms and functions are supported in Modelica for modeling parts of a system in pro cedural programming style Modelica functions have a syntax similar to other Modelica classes and matrix expressions can be used Assignment statements if statements and loops are available in the usual way A function for polynomial multiplication 1s given as an ex ample It takes two coefficient vectors as inputs and returns the coefficient vector for the product function polynomialMultiply input Real a b output Real c zeros size a 1 size b 1 1 algorithm for i in l size a 1 loop for j in l size b 1 loop c i tj 1 c i j 1 a il b jl end for end for end polynomialMultiply
21. v v MEA 1 x R 2 i 191 ds i dt C The first 5 equations are coupled and build a system of equations in the 5 unknowns off s ae _ dv u v and ig The remaining equations are used to compute i i and the state derivative During continuous integration the Boolean variables i e off are fixed and the Boolean equations are not evaluated In this situation the first equation is not touched and the next 4 equations form a linear system of equations in the 4 unknowns s u v4 ig which can be solved by Gaussian elimination An event occurs if one of the relations here s lt 0 chang es its value At an event instant the first 5 equations are a mixed system of discrete and continuous equations which cannot be solved by say Gaussian elimination since there are Real and Boolean unknowns However appropriate algorithms can be constructed 1 Make an as sumption about the values of the relations 1n the system of equations 2 Compute the dis crete variables 3 Compute the continuous variables by Gaussian elimination discrete variables are fixed 4 Compute the relations based on the solution of 2 and 3 If the re lation values agree with the assumptions in 1 the iteration is finished and the mixed set of equations 1s solved Otherwise new assumptions on the relations are necessary and the iter ation continues Useful assumptions on relation values are for example a Usethe relation values computed
22. 05 r Description Radius ofload Modelica parameter Modelica Slunits Radius r 0 5 Radius of load Click OK and the text appearing in the bottom row is inserted into the Modelica text win dow The parameter m is defined in an analogue way Parameter declara tions added to motor drive El MotorDrive DriveLib MotorDrive Modelica Text E Eile Edit Simulation Plot Animation Window Help x lu S NV m o y A2 tin Zle y SSR Bho hodel MotorDrive parameter Modelica SIunits Radius r 0 5 Radius of load t Modelica parameter Modelica SIunits Mass m 80 Mass of load 7 Modelica dditions selon Unnamed E end MotorDrive FJ DriveLib In Modelica Text representation above the components and connections are indicated by icons It 1s possible have them expanded textually Click the right mouse button and select Expand Show components and connect ElMotorDrive DriveLib MotorDrive Modelica Text Editing H File Edit Simulation Plot Animation Window Help l x m gt ld Ni mova 2 Hne gt aneno model MotorDrive parameter Modelica SIunits Radius r 0 5 Radius of load E Modelica parameter Modelica SIunits Mass m 80 Mass of load deed a JModelica dditions DriveLib Motor motor a Unnamed Modelica Mechanics Rotational IdealGear gearbox ratio 100 a JDiveLib Modelica Mechanics Rotational
23. 3 pp 213 234 1991 Kaps P and Rentrop P Generalized Runge Kutta Methods of Order Four with Step size Control for Stiff Ordinary Differential Equations Numer Math 33 pp 55 68 1979 Otter M and Gaus N ANDECS DSSIM Modular Dynamic Simulation with Data base Integration User s Guide Version 2 1 Technical Report TR R51 91 DLR In stitut f r Robotik und Systemdynamik June 1991 Petzold L R A description of DASSL A differential algebraic system solver Proc 10th IMACS World Congress Montreal August 8 13 1982 Shampine L F and Gordon M K Computer Solution of Ordinary Differential Equa tions Freeman San Francisco 1975 Shampine L F and Watts H A DEPAC Design of a User Oriented Package of ODE Solvers Sandia National Laboratories Albuquerque New Mexiko SAND79 2374 1980 DYNAMIC MODEL SIMULATOR 215 216 OTHER SIMULATION ENVIRONMENTS Other simulation environments Using the Dymola Simulink interface Before starting make sure to have a working Matlab mex configuration by trying to compile and link an example Mex file e g matlab extern examples mex yprime c Please include dymola mfiles e dymola mfiles traj in the Matlab path These must be present every time you want to use blocks constructed with Dymola a good idea is to do it once and then store the path 1n Matlab Graphical interface between Simulink and Dymola Dymola has a new interface to Simulink You find it in Simulin
24. Directories Hardware configuration Before Opening Model After pening Model m Local settings r Extra Fil Transfer files to target C Retrieve files from target File name c util dymola source c Ascii 7 c NutildymolaNsource S h Ascii Edit vehicledynamics_dy9501 guppd c Ascii Remove Remove All m Debug amp Command Line Templates gAl OSM_MASTER FEES Update Cancel OK Cancel Change Global settings Apply The first two lines describe required files from the Dymola distribution note the use of wildcards Also compilation of the DymolaBlock creates a model source file with a ma chine generated name this file can be found using Windows Explorer in this case 1t was vehicledynamics_dy9501guppd c and the filename must be recorded Compilation options Experiments have shown that for large models moderate optimization O1 yields faster codes than maximum optimization O2 on the QNX platform Under the Compilation options tab the field for User compiler option should contain the optimization option Ol 232 DDE communication Dymola DDE commands Dymola accepts commands through a Windows DDE connection The DDE connection should be opened with an application name of dymola the topic name is not used The following commands are recognized All Dymola commands as entered in the command input or read from a script file
25. For details see also Eich Soellner and F hrer 1998 In general it 1s not possible to determine by source inspection whether a specific relation will lead to a discontinuity or not Therefore by default it 1s assumed that every relation po tentially will introduce a discontinuity or a non differentiable point in the model Conse quently relations in Modelica automatically trigger state events or time events for relations depending only on time at the time instants where their value 1s changed This means e g that model TwoPoint is treated in a numerical sound way the if expression u gt O is not taken literally but triggers a state event In some situations relations do not introduce discontinuities or non differentiable points Even if such points are present their effect may be small and 1t may not affect the integra tion by just integrating over these points Finally there may be situations where a literal INTRODUCTION TO MODELICA 85 Real and ideal diode characteristic evaluation of a relation is required since otherwise an outside domain error occurs such as in the following example where the argument of function sqrt to compute the square root of its argument is not allowed to be negative y if u gt 0 then sqrt u else 0 This equation will lead to a run time error because u has to become small and negative be fore the then branch can be changed to the else branch and the square root of a negativ
26. Hybrid modeling in Modelica A A ges hee Gee Sek pet ES 81 Synchronous equations of 5 Hoc ELEC doe bt ib eet tA Sth abe i shee RET did 82 Relation triggered AAA I eode rep UI HeLa Geld ee a eae 85 Variable structure systems n on t adc reo ta edt es arte xao cfe a 86 Initialization of models 1 22 eade plas FRE EDU cubes danse bet 90 Basis ois eda Kehoe Re US ieu es oia c pones Pe bate et ms 90 Continuous time problems C e ss s Nee evt Spip tete pape 9 Parameter Values ore oe dax Ao Su denso v Y er TRO ES ae In PUER RISO 95 Discrete and hybrid problems cura ti od kb eet e deh s 96 Example Initialization of discrete controllers llli 0020000 c eee 97 Standard DESI qe en Ge a dere o eorr eti ug aot Es de ee Nas petet det rds 100 A aad daddies Do no oe PL ak bod ok ees 101 References yous ces ues ROC pe as taies yh uer Usted VL MC etta 101 Developing a model 1 1 1 1 s isses 107 General concepts ac uod vifo beh nash te pU bua DEUS obtu Vitro p 107 Window LYDOS s as hace ons dar aequius cn d auk REANO es da Re ER SE 107 Clas layers a car e ad el e Guth ed e n A gf 111 Class documentation 00 eee bebe teen ees 112 C cordinate system Letto echte gcd es hited ot eda toe side ei a ne ia dea 113 Model editi tac li dt ob tos LT a i Lor aes TL 114 Basic Opera tons o lA EI IQ MESES m AIR EC Gl ee oe A 114 Components and connectors 2 2 eee 115 CONMECHONS preci bare tete ie IUL
27. If you want to learn the basics first you can skip to a smaller example in the next section Solving a non linear differential equation We will study a model of an industrial robot Start Dymola The Dymola window appears in Modeling mode as displayed above To view the industrial robot model use the File Demos menu and select Robot 24 Opening a demo exam ple The robot demo E Dymola Dynamic Modeling Laboratory Diagram al Fie Edit Simulation Plot Animation Commands Window Help lex File Edit Simulation Plot Animation Commands Window Help jus i Q amp N m e Ams 9 ttin sS gt mE EI 00 B Systems e fRobotR3 j mechanics mechanics path axis1 amp axis2 axis3 The package browser in the upper left sub window displays the package hierarchy and it is now opened up with the robot model selected and highlighted The model diagram in the right sub window opens up and shows the top level structure of the model The model dia gram has an icon for the model of the robot with connected drive lines for the joints The GETTING STARTED WITH DYMOLA 25 About to view the me chanical structure of the robot reference angles to the drive lines are calculated by a path planing module giving the fastest kinematic movement under given constraints The component browser in the lower left sub window also shows the components of the ro bo
28. Load NewLibrary 3 In the Dymola main window select File Run File Script to run Convert mos 4 Load myModel mo 5 In the model window myModel select File Check 6 Hopefully there 1s no error message and the model can be saved The conversion 1s done 7 n case of error message consult the next two subsections on specifying translation and building a script file After a migration the model shall of course be tested and it shall be checked that it gives the same simulation result as the old one Basic commands to specify translation The command to build the translation tables are convertClass oldClass newClass convertElement oldClass oldElement newElement convertModifiers oldClass oldParameterBindings newParameterBindings convertClear convertClass The command convertClass oldClass newClass builds conversion tables to be applied on extends clauses and type declarations As an ex ample consider convertClass DriveTwoCut Modelica Mechanics Rotational Interface Compliant All components of type DriveTwoCut or classes that contain extends DriveTwoCut will be converted such that they refer to class Modelica Mechanics Rotational Interface Compliant instead Conversion 1s also applied on hierarchical names For example convertClass Modelica RotationallD Modelica Rotational will take effect on Modelica Rotational1D Clutch and give Modelica Rotational Clutch
29. MultiBo name 0 0 1 B vodeno B8 v A A 108 E 7 Math EJ Mechanics E E Rotational JExamples Ln First o Friction CY CoupledClutches amp Interfaces 4Zplnertia E E M Example Modelica Icons Ex dt torque E clutch1 H sint Estepl m2 clutch 53 Ei clutch3 amp J4 Hsin fH step2 Open Library Window Open Class in This Window Open Class in New Window Edit gt Info Lu What s this Package and component browsers The Dymola window contains two browsers along the left edge of the window The package browser top displays the hierarchy of several packages and it 1s possible to drag a compo nent model from the tree into the graphical editor in order to add a component to a model The component browser bottom provides a tree representation of the current model s com ponent structure The diagram window and the component browser are synchronized to give a consistent view When you select a component in the diagram window it 1s also highlighted in the component browser and vice versa The diagram window gives the top level component structure of a component while the component browser gives the entire hierarchical com ponent structure When a model is chosen in the package browser it becomes the root model of the graphical editor The check translate and simulate commands operate on the root model Navigation into i
30. MultiBody Examples Systems RobotR3 fullRobot Read Only Plot 1 zl x E File Edit Simulation Plot Animation Commands Window Help la x E Q S N2 Soc E amp ro 3 ola Ear EAH Wo M 4 Ui path bus axis 3 speed ref path bus axis 3 speed fullRobot 1 rad s Advanced 0 1 2 Other demo examples Other demo examples can be found under the File Demos menu After selecting an exam ple it can be simulated by running a corresponding script file as was done for the robot ex ample Solving a non linear differential equation This example will show how to define a simple model given by an ordinary differential equation We will simulate a planar mathematical pendulum as shown in the figure GETTING STARTED WITH DYMOLA 33 A pendulum The first step to create a new model mg The variable m is the mass and L 1s the distance from the support to the center of mass Let us assume the string 1s inextensible and massless and further let us neglect the resistance of the air and assume the gravitational field to be constant with g as the acceleration of gravity The equation of motion for the pendulum is given by the torque balance around the origin as J der w m g L sin phi where J 1s the moment of inertia with respect to the origin Assuming a point mass gives J m L 2 The variable w 1s the angular velocity and der w denotes the ti
31. Provided you have Matlab 6 1 or later it is possible to map hierarchical connectors in Modelica to buses in Simulink This is accomplished by checking hierarchical Connectors as Buses and recompiling In order to get an understanding of the structure an easy way 1s to construct hierarchical out put connectors in Modelica and examine the corresponding bus signals in Simulink The tules for the buses are All hierarchical input outputs components are transformed into buses except the signal element of block connectors Connector members of simple types Real Integer Boolean are mapped to real signals in Simulink with the same name as in Dymola Non scalar elements are mapped into non scalar signals in Simulink Connector members that are scalar records connectors are mapped to buses in Simulink with the same name as in Dymola For connector members that are arrays of records connectors each element 1s mapped to buses in Simulink with the same name as in Dymola except that Simulink requires that any for matrix elements is replaced by The mapping is fully hierarchical i e connectors can contain sub connectors that contain sub connectors etc and applied to all input outputs Result files Sometimes it useful to generate result files in Dymola s standard format when running in Matlab Simulink e g to OTHER SIMULATION ENVIRONMENTS 223 Animate 3d objects Investigate intermediate variables in
32. being prefer default or avoid The value never forbids the variable to be used as a state and it solves the sensor problem Real r stateSelect StateStateSelect never Real v der r The value prefer indicates that the variable should be used as a state when possible The am biguity lies 1n that there may be several candidates with prefer when selecting states It solves the problem of giving preference to relative positions in mechanical problems It 1s also useful for thermodynamic problems to avoid nonlinear equation systems However here the value never may be useful to rule out other candidates as well The value default means never for algebraic variables of the model The index reduction procedure may introduce derivatives of algebraic variables when differentiating equations However this should not make them candidates for being state variables Neither should higher order derivatives make derivatives candidates for being state variables For example in mechanics we have der r v m der v F The index procedure may introduce the second order derivative of r but we should then not consider der r as candidate for being state variable The priorities for state selection are thus always prefer default and avoid for variables ap pearing differentiated Using noEvent Note that this is an advanced section and in most cases one should not use noEvent This section describes the exceptions and how to correctly use
33. element list public element list protected element list equation clause algorithm clause external language specification external function call annotation language specification STRING external function call component reference IDENT expression expression 240 element list element annotation element inner outer replaceable class definition extends clause replaceable component clause Extends extends clause extends name class modification Component clause component clause type prefix type specifier array subscripts component list type prefix flow discrete nondiscrete parameter constant input output type specifier name component list wow component declaration 2 component declaration component declaration declaration comment declaration IDENT array subscripts modification Modification modification class modification expression z expression expression class modification Lh argument list jJ argument list argument argument APPENDIX MODELICA 241 argument element_modification element redeclaration element modification final component reference modification element redeclaration redeclare replaceable class definition extends clause replaceable component clausel co
34. it needs to be translated The translation 1s initiated by pressing the Translate button in the toolbar Setting parameters and initial conditions After translation new values for parameters and initial values can be entered using the vari able selector which displays a tree of all variables Variables vales jUnt Description zi A phi 98 rad Absolute rotation angle of component flange_a phi flange_b phi der phi rad s der Absolute rotation angle of component flange_a phi flange b phi der phi 2 rad s 2 der Absolute rotation angle of component flange a phi flange b phi 2 lange a lange b J 1 kg m2 Moment of inertia Ww HO rad s Absolute angular velocity of component der w rad s s der amp bsolute angular velocity of component a rad s2 Absolute angular acceleration of component torque clutch Hsin Gistepl phi rad Absolute rotation angle of component flange a phi flange b phi der phi rad s der amp bsolute rotation angle of component flange a phi flange b phi der phi 2 rad s 2 der Absolute rotation angle of component flange_a phi flange b phi 2 lange lange b J 1 kg m2 Moment of inertia Y 0 tad s Absolute angular velocity of component der w rad s s der amp bsolute angular velocity of component zi For parameters such as J1 J there
35. lowing discussion an overall description of the system in one model 1s used model SampledSystem parameter Real Ts 0 1 sample interval parameter Real A size A 1 B size A 1 C size A 2 D size C 1 size B 2 constant Integer nx 5 input Real r size B 2 reference output Real y size B 2 measurement Real u size C 1 control Real xc size A 1 discrete state 82 Real xp nx plant state equation der xp f xp u plant y g xp when sample 0 Ts then controller xc A pre xc B r y C pre xc D r y end when end SampledSystem This Modelica model consists of the continuous equations of the plant and of the discrete equations of the controller within the when clause Note that der x defines the time de rivative of x During continuous integration the equations within the when clause are deac tivated When the condition of the when clause becomes true an event is triggered the integration 1s halted and the equations within the when clause are active at this event 1n stant The operator sample triggers events at sample instants with sample time 7 and returns true at these event instants At other time instants it returns false The values of vari ables are kept until they are explicitly changed For example u is computed only at sample instants Still u 1s available at all time instants and consists of the value calculated at the last event instant
36. ment statements known variables r xp pre xc y g xp when sample 0 Ts then XC A pre xc B r y u 7 C pre xc D r y end when der xp f xp u INTRODUCTION TO MODELICA 83 Note that the evaluation order of the equations is correct both when the controller equations are active at sample instants and when they are not active The synchronous principle has several consequences First the evaluation of the discrete equations 1s performed in zero simulated time In other words time is abstracted from the computations and communications see also Gautier ef al 1994 Second in order that the unknown variables can be uniquely computed it 1s necessary that the number of active equations and the number of unknown variables in the active equations at every time instant are identical This requirement 1s violated in the following example equation incorrect model fragment when h1 lt 3 then close true end when when h2 1 then close false end when If by accident or by purpose the relation h1 3 and h2 1 becomes true at the same event instant we have two conflicting equations for close and it 1s not defined which equation should be used In general it is not possible to detect by source inspection whether condi tions becomes true at the same event instant or not Therefore in Modelica the assumption 1s used that all equations in a model may potentially be active at the same time
37. quires an update This section applies only if you received a dongle with Dymola change the compiler Dymola uses to translate the model select Simulation Setup and the Compiler tab see page 154 Users of WATCOM C C 11 0 should download an updated runtime library the file you need is called rt1_d11 zip Please contact Dynasim if you have problems obtaining it The updated library is required 1f you use WATCOM C C with MATLAB Do not forget to delete the files in DymolaXmp before you recompile Mex files because various object files are incompatible Microsoft compilers Dymola supports several Microsoft compilers The Dymola installation script tries to find which Microsoft compilers are installed and prefers the latest compiler Supported are Microsoft Visual Studio 6 e Microsoft Visual Studio NET 2002 and 2003 Microsoft Visual C Toolkit 2003 This is a free compiler for Windows 2000 and Win dows XP which can be downloaded from http msdn microsoft com visualc vctoolkit2003 If additional compilers are installed after Dymola or to use a different compiler a setup file must be edited by hand Examples of typical installation paths are shown 1n the comments in the file In file dymolaNbinNsetvcdir bat modify the line set MSvCDir to the right path The environment variable MSvcDir should point to the compiler s installation directory To find the right directory search for the file vevars32 bat e
38. troubleshooting 292 xPC 228 special keyboard commands 143 stability boundary 203 starting Dymola 23 state event 85 259 state selection 257 StateSelect 257 step animation 169 stiff e 203 204 stop 138 150 store as one file 127 in model 151 152 string manipulation 175 syntax of Modelica 239 T terminate 138 text editor 125 126 text strings 124 toolbar 123 124 tooltips plot window 159 translate model 37 148 150 translateModel 179 U undo 138 unit display 74 of measure 74 Unix compiler 154 installation 285 V variable in Modelica 74 interactive 174 predefined 175 variable order 202 variable step size 202 variable structure systems 86 view menu diagram layer 142 documentation layer 142 equation layer 142 icon layer 142 visual modeling 166 visual reference 170 VisualShape 166 VRML 137 WwW WATCOM C C e 154 what s this 142 window edit 108 grid 113 library 110 modifier 110 113 116 plot 156 window menu diagram layer 142 301 documentation layer 142 icon layer 142 Modelica text 142 modeling 141 new Dymola window 142 new library window 142 next 142 previous 142 simulation 141 window types 107 Windows environment space 294 WriteMatrix 206 X xPC 228 xscale 201 Z zooming 142 302
39. 127 Q quantity 74 quit 138 R RandomNormal 206 RandomSeed 206 RandomUniform 206 ReadMatrix 206 real time simulation 190 225 Real Time Workshop 228 recent files 137 recent models 141 rectangles 123 redeclare keyword 80 redo 138 relative tic mark 159 relative tolerance 201 rename 110 replaceable model 80 reshaping objects 113 115 reverse animation 169 rewind animation 169 robot demo 24 root finder 203 204 root model 109 rotate 139 RT LAB 229 run animation 169 run script 32 137 149 S save all 134 save as 134 results 199 save log 137 save model 138 save total 134 scaling 201 script 32 create 137 files 176 functions 181 run 149 search class or component 109 134 text 126 127 129 selecting objects 114 138 send to back 139 setting parameters 40 S function MEX block 220 shell command alist 208 300 dymosim 200 207 shift key 114 143 shortcut to library 134 Show Log 155 simulate 150 simulateModel 179 simulation 32 147 efficiency 184 time 148 simulation menu continue 150 linearize 150 run script 149 setup 150 simulate 150 stop 150 translate 150 simulation mode 107 Simulink DymolaBlock 220 external input and output 221 graphical interface 219 implementation notes 224 parameters and initial values 221 Real Time Workshop 228 simulation 222
40. 1s an input field in the value column New values are set by clicking 1n the corresponding value cell and entering the new value The description strings are extracted from the model classes For time varying variables having active start values 1 e fixed true and the start value be ing a literal there are also input fields to change their start values Above J1 phi and J1 w are examples of such variables Setting parameters may of course also influence an active start value bound to a parameter expression Specify simulation run To set up the experiment click on the Setup Experiment button to get a menu for setting simulation time output interval and specifying integration method etc 148 A plot window active in the variable selector Perform simulation To run the simulation click on the Simulate button Plot results Dymola supports plotting of any variable Multiple plot windows may be created Each plot window may contain several diagrams Multiple curves in each diagram are allowed Multi ple diagrams in a plot window allow the user to lay out the curves nicely with aligned time axis and different heights and y scales of the diagrams Variables to be plotted are selected by clicking in the variable selector When a variable is selected the square in front of the name is ticked The variable selector above has J1 w and J2 w selected for plotting Plot lolx w 2w Bw J4 w rad s
41. 1s integrated with a non stiff integration method and the integrator step size 1s limited by the stability boundary and not by the maximum lo cal error the system 1s stiff This usually means that the step size chosen from the non stiff method becomes very small and the efficiency of the integration degrades considerably However note that the stiffness depends on the chosen error tolerances If the error toler ances are decreased the system may become non stiff since the step size 1s now limited by the maximum local error and no longer by the stability boundary Dymosim integrators At present Dymosim provides ten different variable step size integration methods The most important characteristics of these methods are given 1n the following table alg method model order stiff dense root author s type output finder ae DEABM ODE 1 12 no yes no Shampine Gordon Watts Sham75 Sham8 0 2 LSODE1 ODE 1 12 no yes no Hindmarsh Hind80 3 LSODE2 ODE 1 5 yes yes no Hindmarsh Hind80 4 LSODAR ODE 1 12 both yes yes Petzold Hindmarsh Hind83 1 5 5 DOPRI5 ODE 5 no no no Kraft Hair87 6 DOPRI8 ODE 8 no no no Kraft Hair87 7 GRK4T ODE 4 no no no Arnold Kaps79 8 DASSL DAE 1 5 yes yes yes Petzold Petz82 Bren89 9 ODASSL ODAE 1 5 yes yes yes F hrer Fueh88 10 MEXX ODAE 2 24 no yes no Lubich Lubi91 There are also four different fixed step size integration methods
42. Additional information If there 1s some error in the license file or with the license server Dymola presents a short error message by default A more detailed description including FLEXIm error codes is produced 1f Dymola 1s started with the command line option FLEX1mDiag Start a com mand DOS window and issue the following commands cd dymola bin dymola5 exe FLEXlmDiag The additional information will in many cases be helpful in correspondence with support License server Correct operation of the license server should be verified with 1mtools exe see Install ing the license server on page 288 The FLEXIm logfile provides additional information about the day to day operation of the server Always using the latest version of the FLEXIm license daemon 1mgrd exe is strongly rec ommended It is guaranteed to be compatible with all earlier versions of FLEXIm Compiler problems The compiler used to compile the C code generated by Dymola into executable code for simulation 1s set in the Compiler tab see Simulation Setup on page 150 Several potential problems can be found by pressing the Verify compiler setup button Any warning messages indicate problems that need to be resolved before translating a mod el APPENDIX INSTALLATION 291 Compiler not found If you have setup your system to use Microsoft Visual C you may get the following error message E Experiment Setup xi Microsoft Visu
43. HTML 137 image 136 160 to clipboard 136 expression interactive 173 external function 253 annotations 255 including 254 linking to library 254 F file menu check 139 clear all 134 clear log 137 copy to clipboard 136 demos 134 duplicate class 133 exit 137 138 export animation 137 export HTML 137 export image 136 export to clipboard 136 libraries 134 new 131 132 open 133 print 136 recent files 137 save 134 save all 134 save as 134 save log 137 save total 134 search 134 setup HTML 137 file type associations 233 fill color 124 297 find class or component 109 134 text 126 127 129 FLEXIm 287 flow prefix 75 function 81 derivative 249 external 253 Furuta pendulum 65 G gccbuild 198 GenerateBlockTimers 187 GenerateTimers 189 GIF export of image 160 graphical object 124 GIF Construction Set 137 global error 201 GNU C Compiler 255 GNU C compiler 154 graphical attributes 124 graphical objects 123 default 124 grid 113 115 121 123 140 gridlines 115 139 H handles 114 hardware in the loop 225 help 176 help menu about 143 documentation 142 Dymola support 143 Dynasim website 143 what s this 142 high index DAE 78 HTML 137 documentation 113 129 escape sequence 128 export 137 external references 129 hyperlinks 129 online documentation 130 options
44. The model window now contains an empty Motor model The diagram window has a gray frame and grid to indicate that the component is not write protected It 1s possible to toggle the grid using the toolbar button We will now start building the motor model To make it easier to follow the instructions the result 1s displayed below GETTING STARTED WITH DYMOLA 51 We need a model component for a resistor It can be found in Modelica Electrical Ana log Basic The basic approach is to use drag and drop You can drag and drop from the package browser or from a library window To drag from package browser open in turn Modelica Electrical Analog and Basic Note that title of the Dymola window is still DriveLib Motor and also the component browser has DriveLib Motor as top level to indicate that we are editing the motor model About to drag a resis EI Motor DriveLib Motor Diagram AA tor from the package G File Edit Simulation Plot Animation Window Help la x browser qe Do C A mh Basic gt Conductor link lt Capacitor You can also drag from a library window If you do not have a library window for it then open one Go to Modelica Electrical Analog Basic The basic analog ail El Basic package Modelica Electrical Analog Basic ponents library win dow Ground Resistor Conductor Capacitor Inductor Transformer EN aL AE e EMF VCV VEC ccv ccc Gyrator
45. This gives the same dialogue as File New Model but with several fields filled out It extends from MotorDrive and is inserted in the same package DriveLib Enter MotorDriveTest as the name of the model Click OK The result is a model window where the diagram layer looks exactly like that of MotorDrive However the components cannot be edited Try to move or delete a component It has no effect Drag over a component Step from Modelica Blocks Sources and connect it Save the model A model can be used for different tasks One 1s tuning the controller manually Click on the tab for Simulate Translate the model MotorDriveTest The PID controller has four parame ters k Ti Td and Nd 60 Tuning the controller E MotorDriveTest MotorDriveTest Plot 1 i 1 File Edit Simulation Plot Animation Window Help m gj xi jw El amp NP ES amp ve te l SR LIRE WO 4 00 9 5 MotorDriveT est 1 motor amp iload 0 94 Elcontraller El 0 84 0 74 0 64 m 055 0 54 i 0 4 4 gearbox phiload positionerror 0 34 0 24 0 14 Advanced 0 02 0 4 0 6 D 8 1 Modeling Y Simulation WZ There are many ways to tune a PID controller One 1s to disable the integrator part by setting a large vale for Ti say 1000 here Disable also the derivative part by setting Td small say 0 001 Simulate for 10 seconds The step respons
46. WM 4D gt Animation Run function key F3 Starts an animation The animation runs from the current frame until the last frame If Dy mola 1s in continuous mode the animation automatically restarts with the first frame Animation Pause function key F4 Stops a running animation This command has no effect if no animation 1s running Animation Rewind function key F7 Rewinds the animation to the first frame A running animation 1s stopped Animation Reverse function key Shift F6 Moves the animation backward at high speed Animation Backstep function key F6 Displays the previous frame of the animation If the animation 1s at the first frame this command steps to the last frame A running animation 1s stopped Animation Step Forward function key F5 Displays the next frame of the animation If the animation 1s at the last frame this command steps to the first frame A running animation 1s stopped SIMULATING A MODEL 169 The animation setup dialog Animation Forward function key Shift F5 Moves the animation forward at high speed Animation Setup Changes several options that control animation and viewing of animated objects BS Animation Setup fx Frames Vectors Animation Run animation continuously Appearance Unit cube reference Axis reference View visual reference for cylinders Highlight selected object XY Grid reference X Grid reference Y Z Grid reference Per
47. and the start value being a literal Setting parame ters may of course influence an active start value bound to a parameter expression When setting variables from scripts Dymola generates a warning 1f setting the variable has no effect what so ever e g if it 1s a structural parameter Non linear algebraic loops A non linear algebraic problem may have several solutions During simulation a numerical DAE solver tends to give the smoothest solution A DAE solver 1s assumed to start at a con sistent point and its task 1s to calculate a new point along the trajectory By taking a suffi ciently small step and assuming the existence of a Jacobian that 1s non singular there 1s a local well defined solution INTRODUCTION TO MODELICA 93 A planar pendulum The initialization task 1s much harder and precautions must be taken to assure that the cor rect solution 1s obtained The means to guide the solver include min and max values as well as start values for the unknowns As a simple example consider a planar pendulum with fixed length L mg The position of the pendulum can be given in polar coordinates Introduce an angle phi that 1s zero when the pendulum is hanging downward in its rest position The model can be given as Xe co p e parameter Real g parameter Real m parameter Real L 1 Real phi w ll n equation der phi w m der w m g L sin phi Assume that we want to specify the initial c
48. during continuous integration and 1s thus evaluated only four times One should remember to reset the switch Advanced GenerateBlockTimers false in order to avoid the overhead for the next model This switch is not cleared by clear or Clear All commands The timer overhead also affects the total simulation time as well and that the accurate tim ers measure wall clock time and not CPU time in the simulation process Thus simple state ments can have large maximum times if some other process interrupts them between the start of the timer and the stop of the timer This should not affect the average and minimum times 188 Fine grained profiling In some cases the profiling indicates that one non equation block 1s the cause of the prob lem In order to determine what is the cause within that block In that case it 1s possible to turn on a more fine grained profiling by writing the following at Dymola s command input Advanced GenerateTimers true Then translate the model and run the simulation At the end of the log file a large table con tains the profiling information Note that it might be necessary to open the log file dslog txt in an editor to view the entire table By running e g Kinematic loop of an engine demo takes about 5s without profiling one gets results such as Profiling information for the blocks Estimated overhead per call 4 us total 9 930 s the estimated overhead has be
49. editing the Modelica model click on Edit Model after selecting the correct current directory at the Matlab prompt This launches Dymola and cd s to the correct directory in Dymola and opens a window with the model Edit the model in Dymola and verify it by making a test simulation in Dymola After that click on Compile Model Ignore the check boxes Allow multiple copies of block and Hierarchical Connectors as Buses only available in Matlab 6 1 and later and the boxes for results for now The form 1s now rebuilt as shown with parameters and start values for states depending on the model If the numbers of parameters or states 1f sufficiently large a scrollbar 1s added 220 Model dialog for a Dymola model in Simulink Parameters for Simulink block untitled DymolaBlock OF E File Edit View Insert Tools Window Help 4 Dymola model is a compiled block allowing acausal physical modeling see Dymola manual Dymola blocks must be compiled before the simulation is started or you get an error message Model Settings Model Name CoupledClutches Select from Dymola gt Select rom Dymola gt File Name C My Documents CoupledClutches mo Edit model Compile model Reset Parameters Generate result Advanced L7 Allow multiple copies of block 7 Hierarchical Connector as Bus Auto load Parameter Settings Minimum Dt freqHz NN 12 r s Y COCA clutch w small nn _ _
50. error Exceeds 10 of error estimate Component Name of the state number State number Hopefully a few states will dominate this statistics and this should have localized the prob lem to those few variables By plotting those variables one can see if it 1s caused by un damped oscillations in which case extra damping can 1s a solution or merely due to highly complex behavior in which case a simplified model can be more appropriate 186 Profiling The previous sections makes it possible to determine why the code 1s using too many steps in some cases the number of steps seems correct but the cost per step 1s too large If the time per step is too large one must determine where the time 1s spent in evaluating the mod el equations This can be accomplished under Windows by first selecting the Microsoft Visual C com piler with DDE support since it has access to highly accurate timers accuracy in micro seconds or nano seconds see Compiler tab on page 154 Selecting other compilers will only generate timers with milli second resolution which often 1s too inaccurate Basic profiling To turn on profiling write the following at Dymola s command input Advanced GenerateBlockTimers true Then translate the model and run the simulation At the end of the log file a table contains the profiling information Note that it might be necessary to open the log file dslog txt in an editor to view the entire t
51. for a top level package using Save As and not changing the name see File Save As on page 134 132 iia ai dai aix age Name of new package m Description S Partial Extends optional p Insert in package optional zj Y Save contents of package in one file Cancel File New Duplicate Class Creates a new class with the same definition as the current class The user must give the new class a unique name in the scope where it 1s inserted If the package name 1s empty the the duplicate class is inserted in the global scope 1 e outside of any packages Duplicating a class aixi Name of new model MotorDriveTes Insert in package zl Cancel File Open Reads the contents of a Modelica file The names of all read classes is shown in the status bar errors found when parsing the Modelica model are shown in the message window The number of read classes and the number of errors and warnings are shown after the file has been opened If any referenced classes used as base class or the class of a component cannot be found Dymola will search for additional packages defined in the directories of DYMOLAPATH or MODELICAPATH Dymola will automatically change the current working directory to the directory of the opened file DEVELOPING A MODEL 133 The libraries menu is extended when option al libraries are in stalled F
52. for matrices end recordFunction d Thus if APPENDIX ADVANCED MODELICA 251 y t recordFunction x t we have der y t recordFunction_d x t der x t Second and higher order derivatives If the Modelica function 1s a nth derivative n gt 1 the derivative annotation indicates the n 1 th derivative and order n 1 The input arguments are amended by the n 1 th derivatives which are constructed in order from the nth order derivatives The output arguments are similar to the output argument for the nth derivative but each out put 1s one higher in derivative order Continue the example above with function fool annotation derivative order 2 fo002 end fool function foo2 input Real x input Boolean linear input Real z input Real der x input Real der z input Real der 2 x input Real der 2 z output Real der 2 y algorithm der 2 y der 2 z if linear then der 2 x else cos x der 2 x sin x der x 2 end fool This allows us to conclude that y t foo2 x t b z t x t z t X t Z t Restrictions An input or output to the function may be any predefined type Real Boolean Integer and String or a record provided the record does not contain both reals and non reals predefined types Allowing mixed records would require that we automatically constructed a new record from the parts containing reals which would be difficult to describe The function must have at leas
53. found during event iterations can vary between off line and real time simulation The only guard 1s to perform several simulations with different values To debug this procedure a number of output variables are automatical ly generated to indicate which mode we are in and the size of the system of equations These are outputs and can thus be accessed even on real time hardware such as dSPACE Known Limitations e The automatically collected modes are limited to 100 in numbers There should be some possibility to automatically generate code for all modes The switches should have names starting with Advanced instead of Hidden Theoriginal model cannot appear inside a package create a new model Ifthe mode variables are changed but their number is constant you must remove the mat file in order to avoid additional modes with extra code erasing model Modes mat and only redoing Table 7 on page 193 gives a new mod el ModeValues that does not contain modes present in the model References Mattsson S E M Otter H Elmqvist 1999 Modelica Hybrid Modeling and Efficient Simulation 1n Proceedings of 38th IEEE Conference on Decision and Control Phoenix Arizona Also available as http www modelica org papers ModelicaCDC99 pdf SIMULATING A MODEL 193 194 DYNAMIC MODEL SIMULATOR Dynamic Model Simulator Overview What is Dymosim Dymosim stands for Dynamic model simulator and 1s the executable gen
54. function skew skew matrix constructed from 3 vector function cat concatenate arrays function array construct array of arrays function max computes max of an array function min computes min of an array function sum computes sum of an array function product computes product of an array function readMatrix read a matrix from a file function readMatrixSize read size of a matrix from a file function writeMatrix write a matrix to a file function interpolateTrajectory interpolates a trajectory on a file function readTrajectory return all output points of trajectory function readTrajectorySize return number of output points of trajectory function linspace vector of linearly spaced values function assert assert that a condition is true function terminate terminate simulation function help List help commands function list list variables on screen function listfunctions list builtin functions on screen function document write calling syntax for named function function realString Convert a real to a string function integerString Convert an integer to a string function cardinality cardinality of connector function direction direction of connector function constrain a special operator for kinematic loop constraints function initialized start of result from initializer function cos function sin function tan function exp function ln function sqrt SI
55. gearbox Fphiload E positionerror 0 47 J 05 m 80 kg 0 34 0 24 D 14 Ad d D vance aS S E Modeling V Simulation A The parameters r and m can be set interactively between simulation runs but not load J be cause it 1s no longer a free parameter because there 1s an expression binding it to r and m Building a mechanical model We will now develop a more complex model a 3D mechanical model of a pendulum called a Furuta pendulum It has an arm rotating in a horizontal plane with a single or double pen dulum attached to it see below GETTING STARTED WITH DYMOLA 65 The Furuta pendulum The MBS library win dow Start Dymola The package browser shows the library MultiBody This library includes 3D mechanical components such as joints and bodies which can be used to build a model of the Furuta pendulum Use the package browser to open MultiBody You may also create a new library window Select MultiBody in the package browser and click the right mouse button and select Open Library Window E MultiBody package MultiBody I lo x 1500050 El UsersGuide World Examples Forces Frames Interfaces te fue f m B Joints Parts Sensors Types Visualizers E ES K To build the Furuta pendulum you will need to use the Parts and Joints sub libraries Open them by double clicking 66 The MBS parts library B Parts package MultiBody Parts nil xl
56. in variant 1 equation der x x u when initial sample 0 TS then xd pre xd Ts T xref x u k xd xref x end when initial equation pre xd 0 pre u 0 leads to the following equations during initialization x x start 2 pre xd 0 pre u 0 xd pre xd Ts T xref x u k xd xref x der x x u Variant 4 Steady state initialization Assume that the system 1s to start in steady state For continuous time state x 1t means that its derivative shall be zero der x 0 While for the discrete state xd it means pre xd xd and the when clause shall be active during initialization Real x start 2 discrete Real xd discrete Real u Remaining declarations as in Variant 1 equation Plant model der x x u Discrete PID controller when initial sample 0 Ts then xd pre xd Ts T x xref u k xd x xref end when initial equation der x 0 pre xd xd INTRODUCTION TO MODELICA 99 The initialization problem becomes der x 0 Linear system of equations in the unknowns xd pre xd u x pre xd xd xd pre xd Ts T x xref u k xd xref x der x X tu Solving the system of equations leads to der x 0 x xref u xref xd xref k pre xd xd Standard libraries In order that Modelica is useful for model exchange it is important that libraries of
57. ini tial conditions than setting state variables 1s needed In many cases we would like to start at steady state implying that the user specifies dx dt O as initial condition to get the initial values of x calculated automatically by solving f x t 0 Besides the states a model has also other variables and in many cases it 1s natural to specify initial conditions in terms of these variables Modelica provides powerful language constructs for specifying initial conditions They per mit flexible specification of initial conditions as well as the correct solution of difficult non standard initialization problems occurring in industrial applications Modelica provides a mathematically rigid specification of the initialization of hybrid differential algebraic equations Dymola manipulates symbolically the initialization problem and generates analytic Jacobi ans for nonlinear subproblems to make the solution of the initialization problem more ro bust and reliable Moreover the special analysis of the initialization problem allows Dymola to give diagnosis and user guidance when the initialization problem turns out not to be well posed Basics Before any operation is carried out with a Modelica model especially simulation initializa tion takes place to assign consistent values for all variables present in the model During this phase also the derivatives der and the pre variables pre are interpreted as unknown algebraic varia
58. installed The disk space fields reflect the requirements of the options you have selected M Support for optional Microsoft Visual C 2757 k IV Support for optional Microsoft Visual C with DDE 4975k T Support for optional WATCOM C C 10 5 or 11 0 1091 k I Create desktop shortcut to Dymola 5 Ok TF Japanese translation of menus and dialogs k Disk Space Required 4975 k Disk Space Remaining 13010507 k The Japanese translation of menus and dialogs requires fonts that support all symbols For that reason the installation program will ask for confirmation before installing Japanese translations 774X 0D MRD T Eaip Lzsi Q suas voor Am Z dr seModel amp 3774 LeEBA lt o Big O Model ica 7 7 4 ode VERN CASE SUR Multiple compiler support Dymola uses a C compiler to translate the C code of the model into an executable simula tion program During the installation of Dymola the user is given the chance to install li braries that support several different compilers under Windows 1 Default compiler shipped with Dymola minimum distribution gcc 2 Microsoft Visual C C 3 Microsoft Visual C C with Dymosim DDE support 4 WATCOM C C 10 5 or 11 0 Dymola will start using the default compiler even 1f support for other compilers has been installed The Microsoft compiler is faster and allows bigger models to be simulated To 282 WATCOM C C re
59. intended for real time sim DYNAMIC MODEL SIMULATOR 203 ulations DEABM alg method model order stiff dense root author s type output finder 11 Euler ODE dl no no yes Dynasim 12 Rkfix2 ODE 2 no no no 13 Rkfix3 ODE 3 no no no 14 Rkfix4 ODE 4 no no no The three supported model types are abbreviated as ODE Ordinary Differential Equations DAE Differential Algebraic Equations of perturbation index 1 ODAE Overdetermined Differential Algebraic Equations In the following table some hints are given when to use a specific integration method If you don t know much about your problem or you don t want to think much about it use method DEABM DEABM is a robust code with conservative heuristics Other codes like LSODE1 may be faster in some situations however DEABM will often be more reliable Furthermore DEABM is the only code in Dymosim which will give you a warning 1f your problem appears to be stiff If the calculation of the right hand side of the differential equation 1s relatively expensive and your problem is non stiff or moderately stiff and or you want a great many output points use DEABM or LSODEI LSODEI LSODEI 1s similar to DEABM It 1s also a multi step method using the Adams Bashforth Moulton formula However some important details are realized differently You can use LSODEL1 in the same situations as DEABM LSODE2 If your system 1s stiff use method LSO
60. is available in dymola readme unix txt Please read this file for new information on the installation of Dymola Installing Dymola Dymola for UNIX 1s normally distributed as a compressed tar file Extracting the file with tar xvzf dymola tar gz will create a subdirectory dymola with the entire distribution The license file is normally copied from the distribution CD to dymola insert dymola lic APPENDIX INSTALLATION 285 The Linux distribution of Dymola 1s configured for RedHat Linux 7 x to run Dymola under other versions of Linux with incompatible C compilers another library 1s required to run simulations For example to compile on RedHat 6 2 execute the following commands cd dymola bin rm libds a cp p libds rh62 a libds a To perform a simulation Dymola will create temporary files in the directory of the model In order to test the examples shipped with Dymola we strongly recommend that users copy the examples directories to a private area If there is only one user the Dymola distribution directory can be made writable Environment variables and setup The following environment variables must be defined in order to run Dymola DYMOLA Directory root of the distribution DYMOLAPATH Search path for additional Dymola libraries and the license file The di rectories of the path may be separated by blanks or colon DYMOLAPATH is optional if the li cense file is in DYMOLA insert PATH Search path for executable progr
61. m SL dpt s ux toties e dum ums guest 198 R nnme Dy most Sue Ue iuf o dev dus atte senec dirt GEO e A LEE TECTA 198 Dymosim as a stand alone program 1 lel ees 199 Dymosim and Matlab eas cape shee II uie Ru er eee and a SES IM EU MG 200 Selecting the integration method cc LES LLRLESERE RP RUPEM RD P ROI bsegees 201 Integrator properties ros eee La dog List em reorum is e 201 Dy MOST MLC AA hehe sd rte etd ei LE xi Se Foc at 203 Dym sim reference 5 eua solados a du peter ace esas E A 205 Model functions for Dymosim 0 aoaaa aaaea ee 205 Dyinosim le eure prec Sha ctetu ho pdt S coetui rr dec 206 Dymosim command line arguments E A Spt Xe eee ee ees Be 207 Basic fue Format o oda ao e She TELE AS RA uU 208 Dymosim input file dsdxt one AS ie LS d 209 Simulation result file dsres mat usse ne ee ea ee ee ee ee 213 BIDHOBEADHy eo 55 Lr Lux daria At od Pee Baten Dao WEE eee 215 Other simulation environments 00 0 219 Using the Dymola Simulink interface 219 Graphical interface between Simulink and Dymola 219 Simulation in Matlab S s oai cep eae bees aes with apa as Edu ceca RR ep 224 Real time simulation 2554 5 acide fetataecabetes sus sbuts desire ieitegeds 225 ASPACE Systems oou eremi Ll dence Dos b dt ie de See ent Pass Ue aos 225 xPC and Real Time Workshop 00000 ERI eb eU ES 228 Real time simulation using RT LAB 00 00 00000000 e ele 229 DDE communication S
62. model TwoFlange Flange a b end TwoFlange A model of a rotating inertia 1s given by model Shaft extends TwoFlange parameter Inertia J 1 AngularVelocity w equation a r b r der a r w J der w a t b t end Shaft where der w means the time derivative of w Acausal modeling In order to allow reuse of component models the equations should be stated in a neutral form without consideration of computational order 1 e acausal modeling Background Most of the general purpose simulation software on the market such as ACSL Simulink and SystemBuild assume that a system can be decomposed into block diagram structures with causal interactions Astr m et al 1998 This means that the models are expressed as an interconnection of submodels on explicit state space form dx _ de f x u y gG u 76 A Simulink model for the motor drive A Simulink model for the motor where u is input y is output and x is the state It is rare that a natural decomposition into subsystems leads to such a model Often a significant effort in terms of analysis and analyt ical transformations 1s needed to obtain a problem in this form It requires a lot of engineer ing skills and manpower and it is error prone To illustrate the difficulties a Simulink model for the simple motor drive see page 73 1s shown below The structure of the block diagram does not reflect the topology of the physi cal system It 1s easy to
63. noEvent APPENDIX ADVANCED MODELICA 259 Background How events are generated By default Dymola generates events for the relational operators gt gt lt lt and certain built in functions abs sign ceil floor div mod and rem A simple optimization ensures that events are only generated if the arguments are varying continuously Events are gener ated after the boolean expression have changed value and it 1s thus necessary that expres sions involving relations are valid and smooth a certain amount past the actual event Events are generated for code for equations and algorithms outside of functions For algo rithms there are currently some minor limitations for events in for loops and severe limita tions inside while loops The problem of using events for a relations is that one cannot use an expression to guard against errors e g square root of a negative number since the boolean guard would keep the value from the previous event Furthermore the events can lead to undesirable degration of performance if the derivatives are sufficiently smooth On the other hand if the deriva tives are not smooth removing events would degrade performance even more Guarding expressions against evaluation Certain numerical operations have a limited range of allowed input values e g one cannot divide by zero and one cannot take the square root of a negative number To guard against this one must use noEvent sorrounding the gu
64. oio lso on Sih bo let et oT sd Deka 233 Dymola DDE commands lio kl Peed oes eee pede ces sheen eee eek as 233 Explorer file type associations oo pi eae VI E I S4 RE RECTE 233 Dymosim Windows application 0 000 eee 234 Appendix Modelica ooo 239 Modelica syntax specification o 239 Lexical conventions ss coercere Reno ahead utu Es vate Cree t Secreta prende 239 AA E E 2A alata a D drags 240 Appendix Advanced Modelica 249 Declatine functions aris enen cula ERI DSi Re UA IET RI a tae OM 249 User defined derivatives 26 cd oco e bob var Petite ae eet oe 249 How to declare a derivative yu vel ee Lou Rc IR ee Lee ee ak ee UE 250 Externa functions oos onere ts Day Enea en eet de ix 253 Including external functions vc Wins ctae eda este nbi dod 254 Linking to external library oos see vc resur tra y og ate 254 Other languages reper aenar Casinos tini LR Eoi nA rp RS asit DES Ep ira ie 256 Means to control the selection of states 0 0 eese 257 IMGT AIO te eos aes rede ra Eu d Stent eu Balle Paden ete 257 The state select attribute Less meos tb aae ae ex el rues tele Denes 258 sme DOR verius Costes pee A Lot eee E SN 259 Background How events are generated 260 Guarding expressions against evaluation 0 lel less 260 How to use noEvent to improve performance 00 0 0 000000 261 Combined example for noEvent o 261 Mixing noEvent and events in one equation
65. on several platforms dSPACE Real Time Workshop and RT LAB dSPACE systems The DymolaBlock allows you to run your Dymola models on dSPACE systems The Sim ulink model 1s created as described in the dSPACE documentation In many cases offline simulation in Simulink can be used to verify correct operation vehicle glx File Edit View Simulation Format Tools Help Dies i BBel a r Normal Heo m m sideAcceleration Alocity alSpeed lateral Speed side acceleration DymolaBlock 100 There can be only one DymolaBlock when generating code for a multi processor dSPACE system RTI MP If you have checked Allow multiple copies of block you will get a waming about the block not being up to date In the DymolaBlock model dialog in Sim ulink uncheck Allow multiple copies of block See Implementation notes on page 224 for reasons The appropriate target configuration must be selected in Tools Real Time Workshop Options OTHER SIMULATION ENVIRONMENTS 225 Target configuration for DS1005 Initial failed build to create makefile Simulation Parameters vehicle E c x Solver Workspace vo Diagnostics Advanced Real Time Workshop Category Target configuration v Build Configuration System target file ET Browse Template makefile ri10054mf Make command make ni Generate code only Stateflow options OK Cancel Help Agply In o
66. positionerror peowyd As when building a real system there are several approaches One extreme approach is to build the system from scratch However it is often a difficult and time consuming task An other approach is to investigate if the system already 1s available on the market or if there 1s some product that easily can be adapted or modified If not build the system from compo nents available when possible and develop only when necessary The idea of object oriented modeling 1s to support easy and flexible reuse of model know ledge Modelica has been designed to support reuse of model components as parts in differ ent models and to support easy adaptation of model components to make them describe similar physical components The design of Modelica has also been accompanied by the de velopment of model libraries The Modelica Standard Library We will now have a look at the Modelica Standard Library to see what is available and how we access the model components and their documentation To open the library double click on Modelica in the Package browser Dymola Dynamic Modeling Laboratory Modelica Text a _ 10 xi EB Eile Edit Simulation Plot Animation Window Help x Sas Ni moy AL gt 4h 2 gt 88 Blo model Unnamed equation pi a O Modelicadd Modelica Not yet opened gt lt Not yet opened gt end Unnamed Dymola reads in the library The Mod
67. random generator functions should only be used within instantaneous equa tions The integration routines do not support stochastic differential equations RandomUniform Time Uniformly distributed random number range 0 1 RandomNormal Time Normally distrubuted random number with mean 0 and variance 1 status RandomSeed seed Initializes the random number generator with another seed Dymosim m files Together with Dymosim some Matlab m files are shipped to ease the usage of Dymosim within Matlab In order to use the m files the Matlab path has to be extended by directory DYMOLA mfiles traj on Unix machines and by directory sDYMOLA mfiles traj on PC Windows The Dymosim m files are based on a trajectory datastructure A trajectory 1s defined by two matrices S A numeric matrix where column 1 1s the time vector 7 monotonically increasing values and the other columns are the corresponding signal values Intermediate values are obtained by linear interpolation If a trajectory 1s discontinuous two suc cessive time instants are identical Example s 00 0 qd 2 244 3 9 6 n A string matrix where row J of n is the name of the signal of column j of s Example n time t t 2 Le 206 The following m functions are provided as usual you get detailed help for an m file com mand within Matlab by command help lt name gt Functions on traj
68. recognize the controller in the Simulink model for the motor drive but the gearbox and the inertias of the motor and the load are no longer visible They appear combined into a gain coefficient 1 Jj Jpn Inertia T2wdot emf2 There 1s a fundamental limitation of block diagram modeling The blocks have a unidirec tional data flow from inputs to outputs This 1s the reason why an object like a gearbox in the simple motor drive cannot be dealt with directly It 1s also the reason why motor and load inertia appear in the mixed expression in the Simulink model If it is attempted to sim ulate the basic equations directly there will be a loop which only contains algebraic equa tions Several manual steps including differentiation are required to transform the equations to the form required by Simulink The need for manual transformations imply that it is cum bersome to build physics based model libraries in the block diagram languages A general solution to this problem requires a paradigm shift INTRODUCTION TO MODELICA 71 Differential algebraic equations In Modelica it 1s possible to write balance and other equations in their natural form as a sys tem of differential algebraic equations DAE 0 RS xy o where x 1s the vector of unknowns that appear differentiated 1n the equation and y 1s the vector of unknowns that do not appear differentiated Modelica has been carefully designed in such a way that compute
69. rotating elements and gear boxes which are useful for our modeling of the electrical motor drive 46 The rotational mechan E Rotational package Modelica Mechanics Rotational UN Examples Interfaces Inertia IdealGear IdealPlanetary IdealGearR2T ics library window ewe mE dU ithe ER FE Damper SpringDamper ElastoBacklash BearingFriction Clutch CE a ae o bi phn a m phi UE a ES OneWayClutch Brake GearEfficiency Gear Position Accelerate pI di B 0 PE tau phiw a Move i Torque RelativeStates Sensors 2 3 gt The Info for Modelica Mechanics Rotational contains important information on design principles behind the library and a list of components A quick scan of the list indicates that the model Inertia may be of interest for us Select Inertia and press the nght mouse button for a context menu Select Info to get docu mentation for the model The context menu for a E Rotational package Modelica Mechanics Rotational component z mN j 1 um e Hnnc j a bre Lr Open Class in New Window Examples Interfaces Info y Ideal amp earR2T To get a model window for Inertia select its icon in the library window and once again press the right mouse button select Show in New Window and a window for the model In ertia 1s created GETTING STARTED WITH DYMOLA 47 Mathematical defini tion of a rotational in ertia Creating a new Modeli ca package S
70. start 0 1 amp 7 MultiBody Real w Unnamed equation Pendulum der phi w J der w m g L sin phi end Pendulum amp X 9 nx J The model 1s ready to be saved Select File Save Call the file pendulum mo and place it in a working directory Simulation Now 1t 1s time to simulate To enter the Simulation mode click on the tab at the bottom right The simulation menu 1s now activated and new tool bar buttons appear To set up the simulation select Simulation Setup or click directly on the Setup toolbar but ton 36 Selecting Setup in the Simulation menu The Simulation Setup pene ES menu Translation Output Debug Compiler Realtime Experiment Experiment name Prenda m Simulation Interval Start time o Stop time fi M Output Interval Interval length fo Number of intervals 500 Integration Algorithm nas El Tolerance onn Fixed Integrator Step Lo Store in model Cancel Set the stop time to 10 seconds Click either OK or Store in model additionally this store some information in the model E To run the simulation select Simulation Simulate or click directly on the Simulate toolbar E button Selecting Simulate in Run Script the Simulation menu oo Setup Visualize Show Log Dymola first translates and manipulates the model and model equations to a form suitable for efficient simul
71. steady State and fixed are false then there 1s no initial equation The approach as outlined above allows x0 to be any expression When x0 is a parameter expression the specification above can also be given shorter as parameter Real x0 parameter Boolean fixed parameter Boolean steadyState Real x start x0 fixed fixed and not steadyState initial equation if steadyState then der x 0 end if Mixed Conditions Due to the flexibility in defining initialization equations in Modelica it is possible to for mulate more general initial conditions For example an aircraft needs a certain minimum velocity in order that it can fly Since this velocity is a state a useful initialization scheme 1s to provide an initial velocity 1 e an initial value for a state and to set all other state deriv atives to zero This means that a mixture of initial states and initial state derivatives 1s de fined How many initial conditions How many initial conditions are needed for a continuous time problem 92 For an ordinary differential equation ODE in state space form dx dt f x t exactly dim x additional conditions are needed in order to arrive at 2 dim x equations for the 2 dim x unknowns x to and dx dt tg The situation 1s more complex for a system of differential algebraic equations DAE 0 g dx dt x y t where x t are variables appearing differentiated y t are algebraic variables and dim g dim
72. stored in Matlab format and can be loaded into Matlab with the m file tloadlin Simulation Setup Opens a dialogue for specifying experiment name simulation interval integration method etc H Experiment Setup BEI Translation Output Debug Compiler Realtime Experiment Experiment name Unnamed Simulation Interval Start time fo Stop time fi m Output Interval C Interval length o Number of intervals 500 Integration Algorithm fost l Tolerance por Fixed Integrator Step a ns General tab includes Experiment name to specify the name of the experiment It is used to name the result file 150 Model translation tab of Simulation Setup Simulation Interval to specify Start time and Stop time for the simulation Output Interval to specify how often results shall be stored It can be specified in terms of Interval length or Number of Intervals for the simulation By default the results are also stored at discrete events Integration specifies Algorithm to be used to solve the differential equations and Toler ance specifies required accuracy Fixed integrator step 1s specified for fixed step integra tors such as Euler The information from this tab can also be stored in the model by selecting store in model Model translation tab includes H Experiment Setup BEI Output Debug Compier Realtime Evaluate parameters to reduce m
73. the most commonly used components are available ready to use and sharable between applications For this reason an extensive base library 1s developed together with the Modelica language from the Modelica Association see http www Modelica org It 1s called Modelica Stan dard Library and it is an intrinsic part of Modelica It provides constants types connectors partial models and model components in various disciplines Predefined quantity types and connectors are useful for standardization of the interfaces between components and achieve model compatibility without having to resort to explicit co ordination of modeling activi ties Component libraries are mainly derived from already existing model libraries from various object oriented modeling systems They are realized by specialists in the respective area taking advantage of the new features of Modelica not available in the original model ing system The Modelica Standard Library consists currently of the following sublibraries Constant Mathematical and physical constants p1 eps h Icons Icon definitions of general interest Math Mathematical functions such as sin cos SIunits SI unit type definitions such as Voltage Torque Blocks Input output blocks Electrical Electric and electronic components 100 Summary References Mechanics 1D rotational and 1D translational mechanical components Thermal Components for Thermal
74. time In realtime mode the simulator will maintain the relationship real time tscale simulated time abstol Absolute tolerance for hot linked variables default 0 reltol_ Relative tolerance for hot linked variables default 0 MATLAB example ddepoke channel tscale_ 2 0 Requesting variables The value of variables at the last accepted output point are available by sending a WM_DDE_REQUEST message with the name of the variable Dymosim will then return a message with a current value of the variable the string representation of the number or zero 1f no such variable exists It is also possible to request the value of the following special variables delayed_ Returns the time the simulation was delayed at the last accepted output point status _ Returns the state of the DDE server The state 1s composed of the following parts 1 Simulation started running 10 Simulation paused 100 Current simulation time 0 time Returns the current simulation time tscale_ Returns the current simulation time scale factor OTHER SIMULATION ENVIRONMENTS 235 abstol_ Absolute tolerance for hot linked variables reltol_ Relative tolerance for hot linked variables MATLAB example ddereq channel time Hot linking variables Variables can be hot linked using message WM DDE ADVISE The linked variables will be sent to the client at output points when a significant change h
75. to create additional shortcuts to the Dymola program typically to make Dymola start in the appropriate working directory 1 Click the right mouse button on the desktop 1 Select New Shortcut from the popup menu 2 Browse for the Dymola program C Dymola bin dymola5 exe by default 3 Enter a suitable name and finish the creation of the shortcut 4 Click the right mouse button on the newly created shortcut 5 Select Properties from the popup menu 6 Select the Shortcut tab of the dialog window 7 Specify a working directory in the Start in field Shortcuts for Dymola language The Dymola 4 program supports both the Modelica language and the Dymola language The appropriate mode 1s chosen from the Start Programs Dymola menu under Microsoft Windows However if you create your own shortcuts the switch Dymola must be speci fied to start Dymola 4 1n Dymola language mode 1 Click the right mouse button on the shortcut to Dymola 4 2 Select Properties from the popup menu 3 Select the Shortcut tab of the dialog window 4 Add Dymola to the Target field Adding libraries and demos to the File menu You can add your own libraries or demo examples to the File Libraries menu This 1s done by editing the file dymola insert dymodraw ini which contains further instructions 284 HTML viewer for online help Some alternatives of the Help menu display information stored in HTML Under some cir cumstances Dymola wi
76. window FixedTranslati FixedRotation Body BodyShape BodyBox L E ES c om ial ri BodyCylinder Mounting1D RotoriD BevelGeariD E ES K Hesg joints library Joints package MultiBody Joints E ol x window ActuatedPrism Revolute ActuatedRevol Cylindrical pi r 1 o woods ie Universal Planar Spherical FreeMotion SphericalSphe da 4M E E UniversalSphe GearConstraint Assemblies Internal E Select File New Model and give the name Furuta The first step in building an MBS model is to define an inertial system Drag the World icon onto the Furuta window The default parameters need not be changed The gravity of accel eration 1s set to 9 81 and pointing in the negative direction of the y axis We then need a revolute joint Drag the model Joints Revolute onto the Furuta window You can either drag from the library window but it is also convenient to drag from the package browser Select Edit Rotate 90 This just changes the appearance of the icon Double click on the icon GETTING STARTED WITH DYMOLA 67 LT zx General Animation Advanced Add modifiers Component Icon Name Ri Comment TET Revolute Path MultiBody Joints Revolute Comment Revolute joint 1 rotational degree of freedom 2 potential states r Parameters animation y true if animation shall be enabled show axis as cylinder n 0 1 0 gt Axis of rotation resolved in fram
77. window Alternatively the keyboard shortcuts Ctrl F1 and Ctrl F2 or the Window Mode menu can be used see Window menu on page 142 Modeling y Simulation Modeling Changes the window to modeling mode This mode 1s used to browse models compose new models or to change existing models Simulation Changes the window to simulation mode This mode is used to set up an exper iment and simulate a model The results can be plotted and visualized with 3D animation Edit window An edit window 1s used to compose models from existing classes models and connectors connections between connectors and graphical information An edit window by default shows a single layer of a class each layer represents a different aspect of the class see Class layers on page 111 The edit window has a toolbar with buttons to select layer and to start drawing operations There are browsers for packages and the component structure along the left side The user may insert components into a model by dragging components from the package browser E Revolute ModelicaAdditions MultiBody Joints Revolute Read Only Icon 4 E Bi x File Edit Simulation Plot Animation Window Help la x js M S NIX m e AZ 2 th 2 gt SHE J Interfaces E Joints Tt Prismatic E Screw x a g elj n Components g gt ilModelicaddditions MultiBody Joints Revolute M TreeJoint Modelica dditions
78. x dim y Here it can only be stated that at most dim x additional conditions h are needed in order to arrive at 2 dim x dim y equations for the same number of un knowns dx dt to x to y to 0 hee X to y to e h X to x to y to to The reason 1s that the DAE problem may be a higher index DAE problem implying that the number of continuous time states 1s less than dim x It may be difficult for a user of a large model to figure out how many initial conditions have to be added especially if the system has higher index At translation Dymola performs an index reduction and selects state variables Thus Dymola establishes how many states there are If there are too many initial conditions Dymola outputs an error message indicating a set of initial equations or fixed start values from which initial equations must be removed or start values inactivated by setting fixed false If initial conditions are missing Dymola makes automatic default selection of initial condi tions The approach is to select continuous time states with inactive start values and make their start values active by turning their fixed attribute to true to get a structurally well posed initialization problem A message informing about the result of such a selection can be obtained Interactive setting of start values The initial value dialogue of the Dymola window includes the continuous time variables having active start values 1 e fixed true
79. 0 peak 11 gt peak mue_pos 1 2 maximum value of mue for w_rel 0 cgeo Geometry constant containing friction distribution assumption n max J 20 gt N Maximum normal force ww small J rad s Relative angular velocity near to zero see model info text OK Info Cancel When multiple components have been selected the modifier window contains the intersec tion of all parameters If the selected components do not use the same value for a parameter then the symbol lt lt gt gt is shown instead of a value changing this field sets the parameter for all selected components E clutch1 clutch2 in CoupledClutches i x Add modifiers iponent Name Jelutcht clutch2 Comment Multiple components m Model Path Modelica Mechanics Rotational Clutch Comment Clutch based on Coulomb friction r Parameters mue pos 0 05 w mue positive sliding friction coefficient w rel 0 peak n peak mue_pos 1 2 maximum value of mue for w_rel 0 cgeo TT Geometry constant containing friction distribution assumption n max DN Maximum normal force ww small J rad s Relative angular velocity near to zero see model info text OK Info Cancel Component and connector modifiers Component modifiers are displayed in a table with columns for name value unit and de scription of the variables The list of variables 1s extracted from de
80. 0 0 1 0 Shape cone Extra 0 5 Material 1 1 0 0 5 SIMULATING A MODEL 167 r0 r 0 4 0 1 0 1 Shape pipe VisualShape v5 Extra 0 5 Material 0 1 1 0 75 VisualShape v6 r0 r 0 8 0 1 0 2 Shape beam Material 1 0 1 1 equation vl S identity 3 vl r 0 0 0 end shapes model VisualTest shapes sl r 0 0 2 0 shapes s2 r 0 0 6 0 Length 0 3 Width 0 2 Height 0 1 LengthDirection 1 1 0 WidthDirection 1 1 0 Rotated 45 degrees counter clockwise end VisualTest Overview of available shapes 727 d 9 7 a M9 gt File menu In the File menu the commands Export Image and Export Animation provide export of the animation window in several file formats see page 136 168 Animation menu The animation toolbar dl I gt Animation menu Open Result New Animation Window b Bun F3 Il Pause F4 I4 Rewind F 44 Reverse Shift FB 4l Backstep Fb I gt Step Forward F5 gt gt Forward Shift F5 Setup 3D View Control Animation Open Result Reads the result file from a simulation made with Dymola The 3D view 1s replaced by the the rendering of the new result file The result file 1s by default automatically opened after simulation and if it contains animation data the animation window 1s opened automatically Animation New Animation Window Creates a new animation window gt
81. 207 tfigure 207 tinteg 207 tload 199 207 tnhead 207 tnindex 207 tnlist 199 207 tplot 199 200 207 tplotm 207 trajectory 206 trange 207 tsame 207 tsave 200 207 tzoom 207 Microsoft Visual C 154 283 292 migration to a new library 271 mixed mode integration 190 mode modeling 107 simulation 107 model 73 documentation 113 126 replaceable 80 model debugging 182 model editor 73 Modelica 73 syntax 239 Modelica Standard Library 42 43 75 100 Modelica text 111 125 142 modeling 73 hybrid 81 modeling mode 107 modifier window 110 113 116 modifiers 116 117 mouse button left 114 right 114 moving class 110 objects 114 nested connectors 122 new model connector etc 131 package 132 noEvent operator 86 190 259 299 0 ODAE 204 ODE 78 204 Open result 169 openModel 178 ordering of objects 139 output interval 148 P package browser 109 parameter 118 class 79 118 declaration 76 propagation 61 partial models 75 paste 138 pause animation 169 pendulum 33 picking objects 114 plot 180 plot menu delete diagram 160 new diagram 160 new plot window 160 open result 160 rescale 160 plot window 156 plotArray 180 PNG graphical object 124 polygons 123 pre operator 83 print 136 printPlot 180 profiling 187 propagation of parameters 61 protected
82. ACE release 3 4 Additional compiler definitions The MATLAB option defines MATLAB 5 1 or later OPTS O5 D INLINE DDYMOLA DSPACE DMatlab51 For dSPACE release 4 0 compiler options are set in the options dialog of Real Time Work shop The following definitions are needed to compile Dymola models on dSPACE Simulation Parameters vehicle lu x Solver Workspace vo Diagnostics Advanced Real Time Workshop Category ATI general build options y Build Options Compiler options DDYMOLA DSPACE DMatlab51 Compiler optimizations Default O5 D INLINE Y User defined optimizations RTI Help OK Cancel Help Apply This completes the setup required to build for simulation on dSPACE The remaining setup issue is handling of overruns see page 228 Simulation After completion of the build step the model has been downloaded to the dSPACE hard ware Starting the simulation runs in realtime but signals are plotted in the Simulink scopes A more extensive user interface can be built using dSPACE ControlDesk which provides a range of tools for both input and output ControlDesk also allows plotting of important sys tem variables such as the models turnaround time model calculation time plus overhead and the number of overruns OTHER SIMULATION ENVIRONMENTS 227 Simulation using dSPACE ControlDesk RTI task configuration overrun strategy Vehicle yaw maneuver Co
83. Component Name Ra Comment m Model Path Modelica Electrical Analog Basic Resistor Comment Ideal linear electrical resistor r Parameters R 0 5 Ohm Resistance OK Cancel Click OK Similarly drag an inductor to the Motor window Name it La and set the inductance L to 0 05 Drag a ground component into the motor model Name it G The ground component is as important as in real electrical circuits It defines the electrical potential to be zero at its con nection point As in the real world never forget to ground an electrical circuit Drag an electromotive force EMF component into the motor model Name it emf A voltage source is to be found in Modelica Electrical Analog Sources Use a library win dow or package browser to locate it Select Signal Voltage and drag it to the model window of Motor Name it Vs Let Vs be selected and use Edit Rotate 90 to turn the signal input Vs inPort from a top position to a left position SignalVoltage produces between its two electrical pins p and n a voltage difference p v n v that is equal to the signal input Get the Info for Signal Voltage displayed in your web browser point on the icon and use the right mouse button menu The documentation shows that Signal Voltage extends the model Mod elica Electrical Analog Interfaces OnePort Click on that link The documentation shows that the pin p 1s a filled blue square To get the proper sign we
84. DE2 This integrator uses a multi step method with the BDF formula the so called Gear method LSODAR If you need a root finder to handle state events or 1f your system 1s stiff on some time intervals and non stiff on other time intervals use method LSODAR LSODAR 1s a combination of LSODEI and LSODE2 It starts with the algorithm of LSODE1 and switches between the algorithms of LSODE1 and LSODE2 depending on the stiffness of the system If your system is non stiff over the integration period you should get nearly the same results with respect to the number of function evaluations and computing time as with method LSODE1 DOPRI5 If the calculation of the right hand side of the differential equation 1s relatively cheap and your problem is non stiff use method DOPRIS This method works well for moderate relative error tol erance requirements of about tolre1 10 For higher precision computations a higher order method like DOPRI8 might be more effective with respect to computing time If you need a great many output points DOPRI5 and DOPRIS are not well suited Use instead a dense output integra tor for example DEABM Integrator DOPRIS uses a Runge Kutta method with the order comparing step size formulae of Prince and Dormand 204 DOPRIS Method DOPRIS 1s similar to DOPRIS The main difference lies in the different orders of the methods DOPRIS uses a Runge Kutta method of order 8 DOPRI8 may be used in t
85. DEVELOPING A MODEL 127 ave Graphics Description Jldeal planetary gear box m Restricted class Class C Block Model Function Connector C Package C Record Properties Encapsulated T Partial Protected Replaceable JV Store as one file m Dynamic typing Normal C Inner C Outer Editing documentation text Choosing Edit Source from the context menu switches the documentation layer to editing mode In this mode the unformatted HTML code of the documentation 1s shown and can be edited Documentation layer of amp iRevolute ModelicaAdditions MultiBody Joints Revolute Read Only Documentation E a model editing File Edit Simulation Plot Animation Window Help 18 xi ar SN moy A ith Pad a DJ Interfaces Joint where frame b rotates around axis n which is fixed in f Joints ransa ER Revolute The joint axis has an additional flange where it can be 7 Prismatic driven with elements of the Modelica Mechanics Rotational library The relative angle q rad and the relative angular velocity qd rad s are used as state variables lt p gt lt p gt The following parameters are used to define the joint lt p gt ilModelicaddditions MultiBody Joints Revolute lt pre gt M TreeJoint ModelicaAdditions MultiBo n Axis of rotation resolved in frame a same a
86. Dymola Dynamic Modeling Laboratory User s Manual Dymola Dynamic Modeling Laboratory User s Manual Version 5 3a Copyright 1992 2004 by Dynasim AB All rights reserved Dymola is a trademark of Dynasim AB Dymola is a registered trademark of Dynasim AB in Sweden Modelica is a registered trademark of the Modelica Association Dynasim AB Research Park Ideon SE 223 70 Lund Sweden E mail Support Dynasim com URL http www Dynasim com Phone 46 46 2862500 Fax 46 46 2862501 Contents What is Dymola oso base ias 13 Features or Dala seers sis uto eh al E M Wah at oy nee redes uariis 13 Architecture Dymold ons so LEVEL LITERA HRS MN ERE IL M 14 Basic Operatiafis vo dra ove at el dee a e ts d pi 14 Simulating an existing model cuo sot opi ca om dl Gee DE 15 Buldins model 22550825 09 Jay eG p dana d A a E anni adhe eru salt bte shafts 16 beatutes ob MOodellea s c oly cha etd ad v ate Ra ERA cbe BA S OE AT pad 19 Backeroundu 3 ties cue aei Ma ses beum iles t e Ab er not voi Bon 19 Equations amd Teuseu cos st outer uetus ev eee uer enr i a edu 19 Modelica Hist ry o escondo ibas bass 64 pida eA tet EPIIT 20 Getting started with Dymola 1 1 1LL 1L1 1 uusue 23 Introduce MONS sas Besuche e ens heh SP d eo tee topo NN 23 Simulating a model industrial robot 0 000 o 24 SUA ONG so ter ser SL Der endis een eiut tate detur ast opes doped 32 Other demo examples oce
87. Dymola For detailed information about the program you are referred to the on line documentation and the user s manuals The on line documentation 1s available in the Help menu after se lecting Documentation The tool tips and the What s this feature are fast and convenient ways to access information Start Dymola A Dymola window appears A Dymola window operates in one of the two modes Modeling for finding browsing and composing models and model components Simulation for making experiments on the model plotting results and animating behav lor Dymola starts in Modeling mode The active mode is selected by clicking on the tabs in the bottom right corner of the Dymola window The operations tool buttons available and types of sub windows appearing depends on the mode and additional ones have been added after this guide was written Dymola starts with a useful default configuration but allows customizing GETTING STARTED WITH DYMOLA 23 The Dymola window E Dymola Dynamic Modeling Laboratory Diagram Ela x amp File Edit Simulation Plot Animation Commands Window Help lej xi e PQS MINODOVABY Dri Zi gt BBR EHE Modelica Reference amp 7 Modelica amp E ModelicaAdditions amp 7 MultiBody Unnamed Simulating a model industrial robot This first example will show how to browse an existing model simulate it and look at the results
88. ICA 103 Mosterman P J M Otter and H Elmqvist 1998 Modeling Petri nets as local copn straint equations for hybrid systems using Modelica In Proceedings of the 1998 Summer Simulation Conference pp 314 319 Society for Computer Simulation International Reno Nevada USA Otter M H Elmqvist and S E Mattsson 1999 Hybrid modeling in Modelica based on the synchronous data flow principle In Proceedings of the 1999 IEEE Symposium on Computer Aided Control System Design CACSD 99 IEEE Control Systems Society Ha wall USA Pantelides C 1988 The consistent initialization of differential algebraic systems SIAM Journal of Scientific and Statistical Computing 9 pp 213 231 Pfeiffer F and C Glocker 1996 Multibody Dynamics with Unilateral Contacts John Wi ley Piela P T Epperly K Westerberg and A Westerberg 1991 ASCEND An object ori ented computer environment for modeling and analysis the modeling language Comput ers and Chemical Engineering 15 1 pp 53 72 Sahlin P A Bring and E F Sowell 1996 The Neutral Model Format for building sim ulation Version 3 02 Technical Report Department of Building Sciences The Royal In stitute of Technology Stockholm Sweden Astrom K J H Elmqvist and S E Mattsson 1998 Evolution of continuous time mod eling and simulation In Zobel and Moeller Eds Proceedings of the 12th European Simu lation Multico
89. II io sd a maed intem 121 Creating graphical objects cocos dx eua phe Peed kis e oa ENTER 123 Changing graphical attributes ee eoo x ii xS 124 huh as ee een a 125 TJocunmientattolee woe crc odo gee Er P Add de d Leti eS TE ao helt 126 HTML documentation 25 04225 res tte depor PATE bd dee 129 External references sigino a AR cece vases ogee bh eee seek 129 HEME options a sort eet sae Laat ttes od eek else deed a n ee 130 Editor command reference dra snot ee seva tats ta cnuseesee se bee een EUR us 131 Eilcdnenio eost Sd su ki one ce DARA a ee cu S ALLE eae A M 131 EMMA ead eot E raso dE Gi oe ot os Bute on hd 138 Wmdow men as oos zoe ped vol otc dtes tes e ete DS E vers Se aL rasa OR 141 Help menuten eth A CRUS LEER PED 142 Special keyboard Conia seis cs se LR Ep pc EE bu 143 Model editor initialization le brides e p tes led d an a 143 Simulating a model 147 IE TS IIS cs ed Eo dto e o e e eli da een e Oa a ol bed 147 Simulation e DUC 2 Vos euet at rb o tito d E be dob 149 Si Pee ETT 156 Natale SeleGlgko yesos teslis aea yume re iine elas ee ce 157 Plot window interaction liliis 159 PANG menia scd ete Se So Rh tale eei teat Ue Les Fat doo ois obe 160 Plot meti 2 2a Ves dh hat sui eee er Ned stor MU Del EM LE Aena 160 Animation Ido soe ete ce E croco a phim cedi SO IA SI p IUE da 166 Defining Graphical Objects 2 5 ooo ode LEY p RR EI OX REN EE Nu 166 TESIS dusts osea Bes oL pobre cute Y rcu hada cd ue ctu bea Dekh ed cir 168 A
90. Inertia Modelica Mechanics Rotational Inertia Read Only Modelica Text E E File Edit Simulation Plot Animation Window Help S gj xi lade amp Np met Al i szie memHHLo r model Inertia lD rotational component with inertia extends Interfaces Rigid Ez Rotational parameter SIunits Inertia J 1 Moment of inertia ji SIunits ngularVelocity w Absolute angular velocity of component Examples SIunits ngularAcceleration a Absolute angular acceleration of compor interfaces m E EH elnertia arica el bldealGear w der phi a der w J a flange a tau flange b tau end Inertia V oldealPlanetary QrldealGearR2T Switch to the Modelica Text representation where you find Euler s equation as the last equation After this introduction of how to access model components and documentation of a library we will continue by actually building a model for an electric DC motor This task will give us more experience Creating a library for components It is a good idea to insert developed components into a library It is a good way to keep track of components and it supports also the drag and drop feature when you will use the models as components Let us collect all developed components in a library called DriveLib To create it go to the Dymola window and select File New Package and a dialog 1s opened Ei Create New Package Bond xil Name of new package p riveLib Descri
91. Inertia load J 0 5 m r 2 a Modelica Mechanics Rotational Sensors ingleSensor phiload a Modelica Blocks Math Feedback positionerror a Modelica Blocks Continuous PID controller 8 equation i MotorDriveT est connect gearbox flange b load flange a a connect load flange_b phiload flange a a connect positionerror inPort2 phiload outPort a connect motor flange b gearbox flange a a connect positionerror outPort controller inPort a connect controller outPort motor inPort a fa Esa K end MotorDrive 62 Binding a parameter to an expression It is also possible to expand the annotations such as the graphics for the icon of the model the positions and sizes of the icons of the components the path of the connections etc by clicking the right mouse button and select Expand Show entire text However we refrain from showing it in this document Activate the diagram representation Double click on the load icon to open the parameter window load in DriveLib MotorDrive 2 x General Add modifiers Icon Component Name load Comment m Model Path Modelica Mechanics Rotational Inertia Comment 1D rotational component with inertia Inertia JE r Parameters J 0 5 m r 2 kg m2 Moment of inertia Click in the value field of J and enter the expression for J Click OK The model window now displays the expression for the lo
92. Length C Add class parameter with default Modelica Slunits Length Add base type Modelica Slunits Length ox cea The choice to add a component 1s preselected Click OK A menu to declare a variable pops up 40 Declare variable Ts ease Sogn uH n __ Modelica Slunits Length Complete the description E Dedare variable parameter z Weis Soi Lega n 7 Length ofthe pendulu a parameter Modelica Slunits Length L 1 Length of the pendulum Click OK and the text appearing in the bottom row is inserted into the Modelica text win dow The other quantities are defined in analogue ways You have now Length selected in the package browser to find the quantity Mass in Modelica Slunits enter M and the browser goes to the first component starting with M If it is not the desired one press M once again and so on to find it When completing the form to declare the angle phi the start value of the angle 1s defined by clicking on the small triangle to the left of the value field and selecting Edit A submenu pops up GETTING STARTED WITH DYMOLA 41 Variable dedaration in Pendulum ax General Model Path Modelica Slunits Angle Comment r Parameters displayUnit min max start 01 fixed E nominal stateSelect ki OK Info Cancel Enter 0 1 for start After entering the equ
93. MINA emerit acia e SE ht poet qi Drei asd LE Det E LN dd 169 Scripting language oo on tote Rf DATEN G A E ee wis O es ee ae 173 Basic Operations scout ps ce eer ca Sec ee ar ath e pL mue 173 SOHO A DA Lee Sete nca etait uf veritus TEM eee A 176 Help commalds o 2 Sud evo tore dex trav gatio d vao ast atu da uto haue x 176 Simulator API osebne Cd 0 Seats Deut E Ela oa see Eta 178 SCDDETUTIC HOS So ue so bou an Gy vox E usas seme ido LU el o 181 Debuscine models tasca lence eb he oi bee pee d 182 Over specified initialization problems liii llle eee 182 Basic steps in debugging models er oo oo on Se he ams deu tee dade La tut 182 Finding errors in models es ouo ta Sheet At PRSE EM botado de 183 Improving simulation efficiency 184 Inline integra O votos tra ce eee oe eru bred sS ados Ste 190 DVIS MLS OT AOI sii cete m eese a Peur dk Des tete S Dep ADR S Dd AS 190 Inline integration ur Dymola a t e eme Cae aye eng Bee Be 192 RETIENEN A ne x E n ut pace e 192 M de handlite sioe a TS a poi ao MA ale aa o LOL ei tae TAN 192 Collecune modes ci iori eser Dp nA 34H AGUS SD a Eius heath ard i 192 Using mode information in real time simulation 0 0 193 Known Limitations Na iaa AC 193 ii CES sac cgi tienes RTT 193 Dynamic Model Simulator 1 1 197 OVEIMICW c pos ug oii Krew Peek EAE RES ELNDE ES MeL V Ns 197 Whats DIMAS tae Suite S tees cred 197 Who wrote Dymosim et ds atu
94. MULATING A MODEL 177 function arcsin function arccos function arctan function arctan2 function sinh function cosh function tanh function ceil function floor function integer function sign function simplesign function div function rem function abs function delay function openModel open a Modelica file function instantiateModel instantiate a model function translateModel translate a model function checkModel check a model function closeModel function simulateModel simulate a Modelica model function linearizeModel linearize a Modelica model function plot plot given variables function printPlot plot and print given variables function plotArray plot given data function printPlotArray plot and print given data document document func Write the Modelica declaration of the given builtin function and describe the function document document function document write calling syntax for named function input String function name of builtin function output Boolean result true if successful i e function existed end document true Simulator API These routines all return a Boolean status to indicate the success true or failure false openModel openModel file mo Reads the specified file and displays its window This corresponds to File Open in the menus Note This will automatically cd to the right directory 178 checkModel checkM
95. Means to control the selection of states Dymola supports automatic state selection according to the specification of Modelica Variables being subtypes of Real has an attribute stateSelect to give hints or even impera tively control the selection of variables to use as continuous time state variables Note that the state selection is separated from the specification of initial conditions The fixed attribute should exclusively be used for specifying start conditions and it should not influence the selection of states at all Motivation The general view 1s that selection of states ought to be done automatically This 1s also pos sible and unproblematic in most models and we thus clearly understand that manual state selection can easily be overused However there are several reasons for allowing model li brary developers as well as users to influence or control the state selection Accuracy There are often many sets of state variables that will work from a pure math ematical point of view However they may have drastically different numerical proper ties For mechanical systems it is favourable to use relative positions as state variables If absolute coordinates are used then accuracy 1s lost when taking differences to calculate relative positions The effect is drastic in rotating machinery systems and power systems where angular positions are increasing with time but relative positions are rather con stant at least in normal ope
96. Objects Springer Verlag Barton P I 1992 The Modelling and Simulation of Combined Discrete Continuous Proc esses Ph D Thesis University of London Imperial College Barton P and C C Pantelides 1994 Modeling of combined discrete continuous process es AIChE J 40 pp 966 979 INTRODUCTION TO MODELICA 101 Benner P V Mehrmann V Sima S Van Huffel and A Varga 1998 SLICOT A sub routine library in systems and control theory In Datta Ed Applied and Computational Control Signals and Circuits vol 1 Birkhauser Breunese A P and J F Broenink 1997 Modeling mechatronic systems using the SI DOPS language In Proceedings of ICBGM 97 3rd International Conference on Bond Graph Modeling and Simulation Simulation Series Vol 29 No 1 pp 301 306 The Soci ety for Computer Simulation International Cellier FE 1979 Combined Continuous Discrete System Simulation by Use of Digital Computers Techniques and Tools Diss ETH No 6483 ETH Z rich Switzerland ClauB C J Haase G Jurth and P Schwarz 1995 Extended Amittance Description of Nonlinear n Poles Archiv f r Elektronik und bertragungstechnik International Journal of Electronics and Communications 40 pp 91 97 Dymola Homepage http www dynasim se Eich Soellner E and C F hrer Numerical Methods in Multibody Dynamics Teubner 1998 Elmqvist H 1978 A Structured Model Language for Large Conti
97. Row Delete Column Insert Row Insert Column The matrix editor has an extended dialog for plotting one and two dimensional table func tions which 1s displayed by pressing the Plot gt gt gt button DEVELOPING A MODEL 119 Matrix editor with plot Rows 7 Coli E columns el 3 9 0 0 25 OK Cancel Table Map Rows Mep Columns The contents of the table can be interpreted 1n three different ways when plotted The type of plot is selected by pressing the corresponding button Maps are available if the matrix size 1s greater than 2x2 Table Plots columns 2 n versus first column Vectors are plotted against index number Map Rows Plots rows of a 2D map Plots rows 2 n versus first row except the first ele ment of each row Map Columns Plots columns of a 2D map Plots columns 2 n versus the first column ex cept first element of each column At present it s not possible to directly adjust the size of the plot However it 1s possible to adjust the size of the matrix editor when the plot 1s not shown When the P1ot button 1s pressed the plot size will be squared with the same height as the matrix editor Component attributes Several component attributes can be changed with Attributes from the context menu These attributes reflect component properties specified in the Modelica language The illus tration below shows the default settings 120 The component at tributes d
98. Sample time input Real xref Reference input Real x fixed true start 2 discrete Real xd fixed true start 0 discrete Real u fixed true start 0 equation Plant model der x x u Discrete PI controller when sample 0 Ts then xd pre xd Ts T xref x u k xd xref x end when The model specifies all the initial values for the states explicitly The when clause is not en abled at initialization but it is replaced by xd pre xd u pre u The initialization problem 1s thus x x start 2 pre xd xd start 0 pre u f gestarte 4 0 xd pre xd 0 u pre u 0 der x x u ff 5502 Variant 2 Initial values are given explicitly and the controller equations are used during initialization It is as Variant 1 but the when clause is enabled Same declaration as variant 1 equation der x x u when initial sample 0 Ts then xd pre xd Ts T xref x u k xd xref x end when It means that the when clause appears as xd pre xd Ts T xref x u k xd xref x in the initialization problem which becomes x x start 2 pre xd xd start 0 pre u u start 0 98 xd pre xd Ts T xref x u k xd xref x der x x u Variant 3 As Variant 2 but initial conditions defined by initial equations discrete Real xd discrete Real u Remaining declarations as
99. This on each class to display its documentation in a small popup window inside Dymola DEVELOPING A MODEL 109 Remove Rename Duplicate Class Extend From New Class in Package gt Order gt A library window with icon view only Several editing operations are also available in particular to create remove modify classes of a package Remove Removes the class from its enclosing package Rename Renames a class This can move the class the class to a different package For changing the order of classes within a package use Order Duplicate Class Duplicates a class see File New Duplicate Class on page 133 Extend From Creates a new class which extends from the selected class See also File New Model etc on page 131 New Class in Package Creates a new class of the desired type in the selected package See also File New Model etc on page 131 Order Moves the class up or down in the package browser This requires that the class and the enclosing package are both stored in the same file Use Rename 1f you want to move the class to another package Note that dangling references to the removed or renamed class may not be detected Make Check on the enclosing package to detect some potential problems see Edit Check on page 140 Library window A library window shows the contents of a Modelica package typically models connectors or other packages The user may inse
100. Use of undeclared variable shaftl nDrive indicate that the connectors of typical components have changed name To fix that we 1n clude in Convert mos before openModel myNewModel mo convertElement Clutch Shaft Gear pDrive flange a convertElement Clutch Shaft Gear nDrive flange b Error messages of the type Error Modifier fnMax not found in Clutch indicate that a parameter has changed name In simple cases when a simple renaming works use convertElement Otherwise use convertModifiers Run the updated Convert mos file when asked 1f update myModel in the file myNew Model answer No Keep a copy of the conversion script Convert mos since it can be useful for converting similar models Now save the model In some rare cases 1t might be necessary to edit the model by hand or it is necessary develop model wrappers or a new model component Note that default values for parameters are not translated For example if there 1s a model component m1 that has a parameter p declared as parameter Real p 1 0 and the new model component also has a parameter p declared as parameter Real p 0 276 then the old default value of 1 0 1s lost and the new one being zero 1s used If it 1s important to preserve the old parameter default values this can be done by making a new model com ponent that extends the new m1 and modifies its parameter values according to the old ml
101. _ __ x clutchl mue pos IN clutch peak J1 phi 0 Start values Ji w LERNEN clutchi phi rel nh J2 w PA clutch2 phi rel PA J3 w PA B Close Window It is now possible to change parameters and initial values by entering their values in the new fields Note that for array variables it 1s not possible to change the size of the array The parameter settings are kept even if you press Compile assuming they match To re set parameters and start values to the default in Dymola press Reset Parameters In order to make the Dymola model useful as block in Simulink you need external inputs to the Dymola block and external outputs from the Dymola block You change this in your model in Dymola and it can in either be accomplished by declaring variables as input or output in the top level model or graphically by adding input filled and output non filled connectors e g from Modelica Blocks Interfaces OTHER SIMULATION ENVIRONMENTS 221 Dymola model for use in Simulink with external inputs and outputs e 9 amp torque n J2 J3 J4 p A imm imm 1mm 1mm 3 ao gt au e aum emu a gt amm o tau as j ij ae torque a u peeds Ca E peads Qo ka paads u peeds As an example consider a rewrite of the coupled clutches example where each source in Modelica has been replaced by an input connector and speed sensors have been added and connected to output con
102. a makes automatic default selection of initial conditions The approach is to select continuous time states with inac SIMULATING A MODEL 151 Output tab of Simula tion Setup tive start values and make their start values active by virtually turning their fixed to true to get a structurally well posed initialization problem Output information on the automatic state selection reports on the state selection for index reduction Output information when differentiating for index reduction reports about which equations that are differentiated Output read classes to screen during parsing Warn about parameters with no default lists all free parameters not given an explicit value in the model Output tab includes vipul Debug Compier Realtime General Translation Format Textual data format Double precision Store v State variables M Derivatives I Input variables Iv Output variables Iv Auxiliary variables Protected variables Output selection IV Equdistant time grid M Store variables at events Store in model Cancel Textual data format stores result in textual format instead of binary Double precision stores results in double precision instead of single precision Store defines which categories of variables to store Equidistant grid stores result equidistantly as given by simulation setup Store variables at events stores variables before an
103. a simulation run especially the stop time the initial values for the state variables and the actual values of the model constants 7 Dy mola parameters Use a text editor to overwrite the default values provided in the file The complete structure of the self explanatory input file 1s described on page Dymosim input file dsin txt A simulation run is executed by command dymosim or by dymosim dsin txt dsres mat In both cases the simulation run 1s performed by reading the input file dsin txt and by storing the simulation result on the binary file dsres mat The data on this file can be plotted by Dymoview Alternatively the result file can be imported into Mat lab by executing command s n tload in the Matlab environment The signal cc 22 names are stored in text matrix n whereas the simulation results are stored in the numeric cc 05 cc 05 LEE matrix s The first column of s is the time vector whereas a subsequent column i ec a 22 corresponds to signal i Signal indices and corresponding names are printed by the pro vided Matlab m function tnlist n Signal i can be plotted by Matlab command plot s 1 s i Alternatively the provided Matlab m function tplot s i1 i2 i3 n plots columns i1 12 13 of s with respect to s 1 cc 22 using the corresponding signal names stored in text matrix n as a legend In the subdirectory dymtools
104. able By running e g Kinematic loop of an engine demo which takes about 5 seconds without profiling one gets results such as Profiling information for the blocks Estimated overhead per call 4 us total 0 939 s the estimated overhead has been subtracted below Block Total CPU s Mean us Min us to Max us Called 0 5 002 252 38 to 30434 22058 1 0 047 329 237 to 9271 149 2 0 030 Zt 0 to 8632 22058 3y 0 935 47 11 to M 22057 4 0 000 15 4 3 to 0 4 Dy 0 000 30 8 to 1 4 6 0 000 Lr 3 to Ty 1 7 0 067 3x 3 to 5045 21812 8 0 562 29 lt 21 to 8675 21812 9 0 036 2 1 to LAT 21812 10 0 063 Srl 2 to 8843 21812 11 0 178 9 4 to 25083 21812 125 0 154 8 6 to 9243 21812 13 1 774 90 76 to c 21812 14 0 015 Ll 0 to 46 7346 15 0 069 9 8 to a 7346 The first lines state that we have estimated the overhead of the timers to 4 microseconds and subtracted them from all timing estimates thus making it easier to find the problematic block The total overhead is also included for comparison SIMULATING A MODEL 187 It is then necessary to examine the file dsmodel c in order to determine what block number corresponds to what variable s The start of block 6 1s marked by DymolaStartTimer 6 and the end by DymolaEndTimer 6 The first blocks are special Block Task 0 Is the total time for all model evaluations l Is the total time for model evaluations duri
105. able 1s declared with the type and size of the expression on the right hand side of the assignment Typing the expression consisting of just the variable name outputs the value i zeros 3 Declaring variable Integer i 3 i 0 0 0 eS EA O A Declaring variable Real r 3 E do lr55 21 b false Modelica Math sin 5 lt 0 Declaring variable Boolean b 2 b false true s Modelica script Declaring variable String s 2 s Modelica script Such variables can be used in calculations r r scalar product 0 25 r 2 7 5 174 s 2 script t s 1 s 2 ing r 2 realString r 2 1 1 Declaring variable String t t Modelica scipting r 2 7 5 A list of the interactive variables and their values can be obtained by the command list list Integer i 3 0 0 0 Real r 3 1 7 5 2 Boolean b 2 false true String s 2 Modelica script String t Modelica scipting r 2 7 5 Predefined variables We might want to introduce several variable categories like system variables interactive variables model variables etc System variables might involve pragmas to the translator about preferred handling Evaluate true utilize parameter values in manipulation These settings are also available in the Setup menu where e g Evaluate corresponds to se lecting Evaluate parameters Functions for string ma
106. ach mode and by only performing it for the modes that actually occur it avoids an exponential explosion in code size Collecting modes In order to collect modes one must first decide which variables determine the modes this is done automatically by Dymola and then which modes are interesting automatically col lected from simulations The following describes the preparatory steps during off line simulation and the result of these steps 1s a new model that with mode variables and modes 1 open model to show it 192 2 set Hidden GetModeVariables true 3 translate model this automatically detects mode variables and outputs code for find ing new modes in dsmodel c If the manual selection of mode variables fails it possible to manually set BigModeVari ables in the model 4 simulate to collect mode values in model Modes mat and output new model with mode values in model Mode Values mo 5 repeat the last step under various conditions to get additional modes automatically merged Using mode information in real time simulation The above describes how to obtain the modes during off line simulation and we are now ready to use them during real time simulation 6 not necessary set Hidden GetMode Variables false 7 translate model ModeValues using mode values no new mode variables should be found and simulate it no new mode values should be found One potential problem 1s that intermediate modes
107. ad inertia When entering the expression you are some times not sure about the exact name of the variables names for example 1s the radius called r rO or r1 The problem is even more pronounced when you would like to reference a variable a bit down in the component hierarchy Dymola can assist you First you enter 0 5 and then you click on the small triangle to the left of the value field Select Component Reference and then m GETTING STARTED WITH DYMOLA 63 fi positionerror controller You have now 0 5 m in the value field for J Enter Use the menus to get a reference to r Complete the expression with the square Click OK The model window now displays the expression for the load inertia The component s pa rameter definition is visible in the model controller uum sod positi motor load Switch to Simulation mode Translate MotorDriveTest 64 A bound parameter cannot be changed in teractively E MotorDriveTest MotorDriveTest Plot 1 T a 4B xl Y Eile Edit Simulation Plot Animation Window Help l x CONTE E OA N AA N Variables Values Unit 1 motor 0 94 lload Lini 0 rad W 0 rad s 0 84 der phi 2 tad s 2 flange b J kg m2 0 74 der phi rad s der w rad s s flange a 0 64 d rad s2 controller aad
108. age protected Integer iStatus external C iStatus AI VRead iDevice iChannel iGain dVoltage end AI VRead The Library annotation 1s either a single string or a vector or strings that name several bina ry libraries and the compiler will link with all listed libraries Note that for this example to work the header and library files must be 1n the search path of the compiler This could be accomplished by placing the header in 3DYMOLA3 source and the library in the correct sub directory of 3DYMOLAS bin or by placing both of them in the current directory Other languages Functions written in C or FORTRAN 77 are supported provided the C compiler supports cross linkage with C or FORTRAN When using languages other than C provisions must be made to ensure that the required runtime libraries are linked C Functions written in C must declared as extern c to be linkage compatible with C Wrapper functions are needed for example to use virtual functions or other C features that are not present in C FORTRAN FORTRAN code can be linked in two ways Perhaps the most straight forward approach is to convert the FORTRAN code to C using a tool called 2c This tool translates the code into portable C code and also includes libraries for common FORTRAN runtime routines The alternative 1s to use a link compatible FORTRAN compiler In either case wrapper functions are most likely required to map argument types 256
109. agram H Pendulum Pendulum Plot Mj xl Y File Edit Simulation Plot Animation Window Help lex jw AS MiRe yu e EPA DEI M 0 m 9 uU phi phi co N Advanced 0 2 4 6 8 10 GETTING STARTED WITH DYMOLA 39 Values of parameters are changed in a similar way To change the length of the pendulum just enter a new value for L Improving the model The parameters and variables are more than real numbers They are physical quantities The Modelica standard library provides type declarations for many physical quantities Let us redo the model Start Dymola or 1f it is already started then give the command File Clear All in the Dymola window As previously click on the tab for Modeling at the bottom right Select File New Model Name it pendulum Click OK Press the Modelica Text tool bar button the second rightmost tool button Open Modelica SIunits in the package browser To define the parameter length drag Length to the component browser A menu pops up 3 Pendulum Pendulum Modelica Text ni x Ed File Edit Simulation Plot Animation Commands Window Help lex ld M Qe met AIZ t zim mesBBE ov end Pendulum E Dymola Drop dass lx Action for dropped class Change type of to Modelica Slunits Length Add component of type Modelica Slunits
110. al C cannot be found Dymola cannot find the Microsoft Visual C compiler im C Program Files Microsoft Visual Studio YC98 Please check environment variable MSVCDir and ensure that it points to the Visual C compiler directory See also Installation Troubleshooting in the Dymola manual This most likely reason is that the compiler is installed but not in the location Dymola ex pects this can happen if the compiler is installed after Dymola You then have to manually set the location see Microsoft compilers on page 283 Simulink If the Dymola Simulink interface does not work please check the following some of which may sound elementary You have a Dymola license that supports the Simulink interface Note that Simulink sup port is a separate option but included in the demo version You have included the directories dymola mfiles and dymola mfiles traj in the Matlab path These have to be included every time you want to use the Dymola Simulink interface and it is a good idea to store the included paths in Matlab You can find the interface in Simulink s browser as Dymola Block DymolaBlock if not you have probably not included the directories mentioned above into the Matlab path Make sure you have a working Matlab Mex configuration by trying to compile and link an example Mex file e g mat lab extern examples mex yprime c You have created external inputs to the Dymola Block and outputs from the Dymola Bloc
111. al switching elements have been handled by a using variable structure equations which are controlled by finite automata to describe the switching behaviour see e g Barton 1992 Elmqvist et al 1993 and Mosterman et al 1996 or by b using a complementarity formulation see e g L tstedt 1982 and Pfeiffer and Glocker 1982 The approach a has the disadvantage that the continuous part 1s described in a declarative way but not the part describing the switching behaviour As a result e g algorithms with better convergence properties for the determination of a consistent switching structure cannot be used Furthermore this involves a global iteration over all model equations whereas param eterized curve descriptions lead to local iterations over the equations of the involved ele ments The approach b seems to be difficult to use in an object oriented modeling language and seems to be applicable only in special cases e g it seems not possible to de scribe ideal thyristors INTRODUCTION TO MODELICA 89 Initialization of models A dynamic model describes how the states evolve with time The states are the memory of the model for example in mechanical systems positions and velocities When starting a simulation the states need to be initialized For an ordinary differential equation ODE in state space form dx dt f x t the state variables x are free to be given initial values However more flexibility in specifying
112. already running an application that uses FLEXIm you most likely already have a running license daemon In this case only the vendor daemon dynasim exe is required GL OBEtrotter recommends that you use the latest version of the FLEXlm 1mgrd exe at all times as it includes bug fixes enhancements and assures the greatest level of compati bility with all of your FLEXIm licensed applications GLOBEtrotter guarantees that it will work correctly with all earlier versions of FLEXIm The latest available license daemon can be downloaded from the website of GL OBEtrotter APPENDIX INSTALLATION 287 Old license daemons cannot be used License server setup http www globetrotter com flex1m lmgrd shtml Dymola requires support of FLEXIm version 8 0d or later A recent version of 1mgrd exe is part of the Dymola distribution Note that some older versions distributed with MATLAB are not compatible Installing the license server This section describes the simple case where we assume there are no other FLEXIm license daemons Start the utility program dymola bin lmtools exe In the Service License File tab Select the radiobutton Configuration using Services LMTOOLS by Globetrotter Software http www globetrotter com E oj xj File Edit Mode Help Service License File System Settings Utilities Start Stop Reread Server Status Server Diagnostics Configure Services Services allow FLEXLM Servers to run in
113. alues changed and a simple interactive session can be changed to a parameter sweep by adding an enclosing for loop The scripts can later by run by selecting Run script in the menus and interactively by using the command file specification The rest of the line following is treated as the file specification The syntax of the file specification 1s thus operating system dependent The script feature is recursive 1 e a script file may run other other script files If an error 1s encountered in a command script all script files are closed and interactive command input is resumed Help commands These routines all available for interactive help help help Gives a short overview of these commands listfunctions listfunctions A one line description of all builtin functions listfunctions function ndims number of dimensions of array 176 function size size of array function scalar convert an array to a scalar function vector convert an array to a vector function matrix convert an array to a matrix function transpose transpose a matrix function outerproduct compute the outer product of two vectors function identity identity matrix function diagonal construct a diagonal matrix function zeros construct an array of zeros function ones construct an array of ones function fill fill an array function symmetric make matrix symmetric function cross cross product of 3 vectors
114. ams The file 5DYMOLA bin dymola setup contains C shell commands to set these environ ment variables but will need editing to match the installation directory if other that the us er s login directory Note that dymola setup must be read with the source command in C shell not executed as a shell script to be effective We suggest that you put the command source HOME dymola bin dymola setup in the Login file in your home directory Users of sh bash or ksh should use the following syntax to set environment variables set DYMOLA HOME dymola export DYMOLA Alternatively the setting of DYMOLA can be done when starting the program A small command script with this contents will usually do bin csh setenv DYMOLA HOME dymola SDYMOLA bin dymola5 On some UNIX systems the default font is tiny and hard to read The dymola setup file can be modified to set up a reasonable font for Dymola Additional setup Adding libraries and demos to the File menu You can add your own libraries or demo examples to the File Libraries menu This 1s done by editing the file dymola insert dymodraw ini which contains further instructions 286 Compilation of model code Dymola produces C code which must be compiled in order to generate a simulation model On Windows we supply a free compiler as part of the distribution GCC On UNIX sys tems we rely on an ANSI ISO C compiler already installed on the computer On UNIX
115. ania LEDS ar on 33 Solving a non linear differential equation A Powe E CO ES 33 SPM AMON cea asta ater OA S sta ana ea ethan dT DARIN A AES Ao M ace aba aces 36 Improving themodel ve du vies o arte as ES Sense ese ds 40 Using the Modelica Standard Library 42 The Modelica Standard Library 20 il ces Pits caine wn oe ous Sea GPs 43 Creating a library for com ponents z duc de turc LX ePi Lond et bees 48 Creating a model for an electric DC motor ooo 49 Testing the model ecos sole ld RARIUS ET yt use ER E DES 56 Creating a model for the motor drive suc Luo orbes e Madea eee wile dt 59 Parameter expresstOlls 2 sete vue dos ea Pew Chie d hou perve S Pe Shae 61 Building a mechanical models 42s use fat eeu utes ate deeds 65 Introduction to Modelica os 73 Mode OA UASICS tt vom r ae regios ci abt us 73 Annon cot pest x gel soit tee etek iota aang wre Loader ahh BEEN eee Re ARR dopa hell A kien ac Aaa 74 Connectors and connections eens 75 Partial models and inheritance ool a ESTIS 75 causal modeling te Fae roe es ue eae it eet Se teu ere gd os ag tuoi d 76 B ckeround a oiee o eg el AS oa teat wh BN thea E 76 Differential algebraic equations lt 2 0 6 5 25 0 kde Eri deca sedan ees BLASS 78 Advanced modeling features 10 ii ia SY eee 79 Vectors matrices and arrays puso ptr pie colts a av Ese ts Memes 79 Class parameters uox coe a e tue mq we eee aie Se ots s isis oe 79 Algorithms and functions SE pO oa es POI pie dedecus eet 8
116. animating the results are described See also Getting started with Dymola on page 21 which includes several examples The section Simulation menu on page 149 describes the commands and options for set ting up and running a simulation Plotting of results are described in the section Plot win dow on page 156 and animation in the section Animation window on page 166 The section Scripting language on page 173 describes the scripting feature How to find errors and improve simulation efficiency are discussed in the section Debugging models on page 182 The two sections Inline integration on page 190 and Mode handling on page 192 describes to approaches to increase simulation speed for real time simulation The basic steps when simulating a model will be out lined below The focus will be on the use of Dymola s graphical user interface The script facility is described in section Script ing language on page 173 SIMULATING A MODEL 147 The variable selector for setting parameters and initial values I Selecting model The model to be used in a simulation experiment 1s selected 1n Modeling mode The pack age browser is used to select a model as the active model The title of the Dymola window is set to the name of the active model To enter the Simulation mode click on the Simulation tab in the bottom right corner of the Dymola window Translation To prepare a model for simulation
117. aning and the absolute tolerance tolabs approximately defines an upper abso lute limit on the local error Since user s often have difficulties to see the difference be tween the relative and the absolute tolerance in Dymosim tolabs tolrel This is not a good choice if signals are permanently very small In the Dymosim input file it 1s possible to define a scaling value for every component of the state vector The integrators effectively solve for the scaled state variables x i xs cale i If some state variables are very small or 1f there are big differences in the magni tudes of elements of x the scaling vector should be assigned appropriate elements E g 1f x 1 1s always near 10 and x 2 1s always near 10 the scales xscale 1 10 xscale 2 10 should be used For the scaled equations it makes again sense to use the relative tolerance as an absolute tolerance too Global error The global error 1s the difference between the true solution of the initial value problem and the computed approximation Practically all present day codes including the ones used in 1 More specifically a root mean square norm is used to measure the size of vectors and the error test uses the magnitude of the solution at the beginning of a step DYNAMIC MODEL SIMULATOR 201 Dymosim control the local error at each step and do not even attempt to control the global error directly Usually but not always the accuracy of the c
118. another set of routines can be found that perform a similar task as tload use help dymtools in Matlab for more information The function dymbrowse al lows you to select and plot signals directly 1n Matlab and dymload and dymget allows you to extract signals from a result file They use substantially less memory than tload by not storing the result in a simple matrix Another alternative for using less memory 1s to ensure that only the necessary signals are stored in the result file This can be accomplished by plotting the appropriate signals and then selecting Save As from the context menu of the result file in the plot selector and selecting the file type Matlab file only plotted If the file dsu txt 1s present when Dymosim is started Dymosim reads the trajectories of input signals from this file The file can either be in ASCII format or can be a Matlab mat file in the format of the result file dsres mat 1 e the result file can be at once used as in 1 Matlab is a product of Math Works Inc DYNAMIC MODEL SIMULATOR 199 put file of another model It is convenient to generate an input function within Matlab and save the data on file e g t 0 100 1 20 s t t t sin t B time 1 control dist i tsave dsu txt s n Here control and dist are names of variables which are declared as input at the highest hierarchical level in the Dymola model Dymosim and Matla
119. anslator is then exploited to trans form the equations into a representation that 1s efficient for numeric simulation The method of inline integration was presented in Elmqvist et al 1995 Inline integration Consider an ordinary differential equation on explicit state space form x fx X x where x is the vector of state variables and f denotes time It 1s straightforward to solve this problem by using an explicit integration method In the most simple case using the Euler forward method the derivative of the state vector is approximated by a forward difference formula Xn 1 n X f X 5 190 where X X f j is the unknown value of X at the new time instant t n l and is the chosen step size Inserting the discretization expression into the model equa tions leads to the recursion formula f th x X f is the known value of X at the previous time instant f Xa 1 7 X tA f x f xo is known which is used to solve the ODE Unfortunately explicit integration methods are not well suited if systems are stiff These are systems with dynamically fast and highly damped components If an explicit method 1s used to integrate such systems the step size is limited due to stability problems of the inte gration method If the step size is too large then the computed trajectory starts to oscillate and diverge The standard cure 1s to use implicit methods However this leads to a non lin ear equat
120. ar usually been treated by hand modeling each mode of operation separately In Modelica component models are used for shafts clutches brakes gear wheels etc and Dymola can find the different modes of operation automatically The modeling effort 1s considerably reduced since model com ponents can be reused and tedious and error prone manual manipulations are not needed WHAT IS DYMOLA 19 Modelica history Reuse 1s a key issue for handling complexity There had been several attempts to define ob ject oriented languages for physical modeling However the ability to reuse and exchange models relies on a standardized format It was thus important to bring this expertise together to unify concepts and notations A design group was formed in September 1996 and one year later the first version of the Modelica language was available http Awww Modelica org Modelica is intended to serve as a standard format so that models arising 1n different domains can be exchanged between tools and users It has been designed by a group of more than 25 experts with previous know how of modeling languages and differential algebraic equation models After more than 30 three days meetings during a five year period version 2 0 of the language specifi cation was finished in January 2002 20 GETTING STARTED WITH DYMOLA Getting started with Dymola Introduction This chapter will take you through some examples 1n order to get you started with
121. ard condition As an example consider guarding against taking the square root of a negative number An idealized model of a tank that 1s emptied through a hole in the bottom 1s ch ifh gt 0 0 otherwise 5 The model 1s best written as Real h Height of water in tank equation der h if noEvent h 0 then c sqrt h else 0 As an alternative we could in this particular case rewrite it using the max function resulting in equations that are more compact but less readabe Real h Height of water in tank equation der h c sqrt max 0 h Note that we guard against h being negative even if the exact solution to the differential equation has h t gt 0 The reason 1s that the numerical solution generates an approximate h t which will be slightly negative In general one must not only guard against the possible values for the exact solution but also for all nearby approximate values Another example concern guarding against division by zero Real x Real sinc x 260 equation sinc x if noEvent abs x lt Modelica Constants eps then 1 else sin x x In these two examples the noEvent 1s necessary 1n order to make it possible to evaluate the model for all values Note that in the second example we do not compare abs x with O but with the slightly larger Modelica Constants eps This provides a guard against roundoff er rors The extra error 1s insignificant since the error in the sinc approximation it 1
122. as occurred A significant change of a variable 1s determined from absolute and relative tolerances set table by the DDE client as follows x0 value last sent to client x current value absmax max abs x0 abs x absdiff abs x x0 changed absmax lt 1 absdiff gt abstol_ absdiff absmax gt reltol_ The variable is sent to the client when changed is true The variable is also sent at the first output point following the hot link operation MATLAB example ddeadv channel time t t x x Dymosim counts the number of links to a variable and any corresponding unlink messag es Updates for the variable are sent while the link count 1s greater than zero Extended graphical user interface If the environment variable DYMOSIMGUI is defined Dymosim will start with a slightly extended user interface The Operations menu then also contains commands to manually Run Pause the simulation or toggle realtime mode The Toggle Log command enables log ging of all DDE communication on the file ddelog txt Another difference 1s that simulation does not start automatically when the program 1s exe cuted instead the user must give a Run command 236 APPENDIX MODELICA Appendix Modelica Modelica syntax specification The Modelica syntax specification 1s taken from the Modelica Language Specification Lexical conventions The following syntactic meta symbols are used extended BNF ii opti
123. ass DriveTwoCut TwoFlanges convertElement DriveTwoCut pDrive flange a convertElement DriveTwoCut nDrive flange b Assume that the old library contains the models Shaft and Gear which are to be converted as Inertia respectively IdealGear convertClass Shaft Inertia convertClass Gear IdealGear Assume that Shaft and Gear extend from DriveTwoCut Unfortunately there will be no translation of references in for example connect statements to their connectors pDrive and nDrive since the conversion uses the model structure after conversion To have a proper translation we need also to specify convertElement Shaft Gear pDrive flange a convertElement Shaft Gear nDrive flange b where the vectorization allows a compact definition The convertElement command can also be used when a parameter 1s renamed For more complex reparameterizations the command convertModifiers 1s useful convertModifiers The command convertModifiers oldClass oldParameterBindings newParameterBindings APPENDIX MIGRATION 273 specifies how parameter bindings given in modifiers are to be converted The argument old ParameterBindings is a vector of strings of the form oldParameter default Value and the argument newParameterBindings is a vector of strings of the type newParameter expres sion To use the value of an old parameter in the new expression use oldParameter A
124. ates a new connector at the cursor position and the connection is completed This connector has the same type as the connector at the start of the connection This operation 1s typically used to draw a connection from a component which should end with an 1dentical connector in the enclosing class Create Node Creates a new protected connector internal node at the cursor position and the connection 1s completed This connector has the same type as the connector at the start of the connection The size of the new connector 1s 1 10 of the normal component size Cancel connection Cancels the connection operation no connection is made Nested connectors When a connection between incompatible connectors 1s attempted it 1s checked 1f one of them has nested connectors If so a dialog for selecting a subconnector 1s presented El connect Resistorl n Cable1 L2 x1 Unmatched components in connectors connector Cable Modelica Electrical amp nalog Interfaces Pin Pint Modelica Electrical Analog Interfaces Pin Pin2 end Cable connector NegativePin Slunits Current i Slunits Voltage v end NegativePin Make the connection connect Resistorl n Cablel ah Pin a CA Cancel 122 The drawing toolbar Lines are not connec tions In this case a connection from the Pin Resistorl n to the connector Cablel is made Cable has two nested connectors Pinl and Pin2 The pull down choices shows these alternat
125. ation and then runs the simulation You may explicitly invoke translation yourself by selecting Simulation Translate or click on the Translate toolbar button GETTING STARTED WITH DYMOLA 37 Plotting the angle El Pendulum Pendulum Plot loj x B Y Eile Edit Simulation Plot Animation Window Help la x jw OS NY amp e Co SERA MH i M 4 der phi der w Advanced When the simulation 1s finished the component browser displays variables to plot Click in the square box in front of phi to get the angle plotted as shown above Let us study a swing pendulum with larger amplitude and let it start in almost the top posi tion with phi 3 It 1s easy to change initial conditions Just enter 3 in the value box for phi Click on the Simulate tool button 38 Pendulum angle when starting in almost the top position Pendulum Pendulum Plot Bl x B Y Eile Edit Simulation Plot Animation Window Help la IB amp wiz E EKR DOE 1 N M 44 m EEI U Values Unit phi Pendulum 1 3 3 w 0 y 2 der phi der w m 1 L 1 1 g 9 81 D 1 2 3 gt Advanced 0 2 4 6 8 10 The results of previous simulations are available as the experiment Pendulum 1 and we can open it up and have phi of the two runs plotted in the same di
126. ation fails to initialize properly This 1s most likely caused by incorrect system DLLs Dymola uses two system DLLs for OpenGL support They are called opengl32 dll and glu32 dll If these DLLs are incorrect e g do not recognize the graphics card or fail initialization in some other way you get an er ror message like this Note that with Windows NT 4 0 you get a more specific error message that mentions a problem with DLLs In Windows 2000 it just says that the application failed Windows XP requires Service Pack 1 or later to run Dymola Otherwise XP displays the message Windows encountered a problem with Dymola5 exe and suggests sending a problem report Space characters in filenames In some cases Dymola cannot handle filenames which contain space characters notably the directory Program Files This bug will be fixed in a future release Deep directory hierarchies Compilation and simulation of the model may fail in a very deep directory hierarchy if the length of the directory path exceeds 250 characters This is caused by a bug in Microsoft software and we are investigating ways to work around it Writable root directory Due to a bug in the Microsoft runtime library the root directory C should be writable in order to store temporary files If that is not the case Dymola will create working files in the current directory which are not automatically deleted APPENDIX INSTALLATION 293 Windows environment space
127. ations textually as previously the Modelica Text windows displays model Pendulum Modelica SIunits Mass m 1 Mass of the pendulum Modelica SIunits Length L 1 Length of the pendulum Modelica SIunits Acceleration g 81 Gravity of acceleration Modelica SIunits MomentOfInertia J m L 2 Moment of inertia Modelica SIunits Angle phi start 0 1 Pendulum angle Modelica SIunits AngularVelocity w Angular velocity equation der phi w J der w m g L sin phi end Pendulum The icon on the second line indicates graphical information or annotations It may be dis played Put the cursor on in the window click the right mouse button to get the context menu Select Expand Show entire text which reveals that it is an annotation documenting which version of the Modelica standard library was used Dymola uses this information to check 1f compatible versions of libraries are used and to support automatic upgrading of models to new versions of libraries A model developer can provide conversion scripts that specify how models shall be upgraded automatically to new versions of a library Using the Modelica Standard Library In this example we will show how a model 1s built up using components from the Modelica Standard Library The task is to model a motor drive with an electric DC motor gearbox load and controller 42 Motor drive built with standard compon nents Opening the Modelica Standard Library controller
128. b Dymosim can be directly called as an m function from Matlab The power of Matlab can be used to perform parameter studies or optimization runs such that every function evalua tion requires one simulation experiment When called from Matlab Dymosim runs as a separate process The Dymosim executable has to be built in the same way as in the previ ous section Dymosim 1s executed by the command s n dymosim experiment x0 param where the three input arguments correspond to the three matrices of the Dymosim input file see a more detailed description by command help dymosim within Matlab The results cc 05 ec o of a simulation run are stored in matrix s Every column of s contains the result data ec a 25 for one signal column 1 is the time vector The signal name of column i is stored as string in row i of character matrix n A simulation of the Van der Pol equation togeth er with a plot of the result signals can therefore be performed by the following commands s n dymosim 0 50 0 1 0 1 E 4 1 0 5 0 0 2 o tplot s 2 size s 2 n plot all result signals Often it is convenient to use the default input file dsindef txt of Dymosim to define in put parameters which do not change between simulation runs The format of this file 1s identical to the Dymosim input file dsin txt If dsindef txt is present the data stored in this file are used as default values The default valu
129. be calculated from the initial conditions we define it as parameter Real L fixed false Recall that the attribute fixed 1s by default true for constants and parameters otherwise fixed 1s by default false The semantics of parameters in Modelica 1s a variable that 1s constant during simulation The possibility to let the parameter value to depend on the initial values of time dependent continuous time or discrete variables does not violate this semantics This feature has many useful applications It allows powerful reparametrizations of models As an example consider the model of an 1deal resistor It has one parameter R being the re sistance Assume that we would like to have use it as a resistive load with a given power dissipation at a steady state operating point It 1s just to extend from the resistor model given in the Modelica Standard Library and 1 Add a parameter PO to specify the power dissipation 2 Set fixed false for parameter R 3 Add an initial equation section with v 1 PO In power systems it is common practice to specify initial conditions in steady state and use different kind of load models including resistive load and specify their steady state operat ing conditions in terms of active and reactive power dissipation In some cases parameters may be provided outside of a Modelica model and the actual val ues may be read from file or parameter values may be inquired from a database system dur ing initial
130. be used when the relative scale of vertical and horizontal axes 1s important Fit Plotted Data rescales the diagram to fit plotted variables This 1s same as pressing the Rescale button and then reads the default range rg ae aa in Bode plot Magnitude 1 0 01 0 0001 0 01 0 1 1 10 100 1000 Phase deg SIMULATING A MODEL 165 Animation window Animating models re quires the Animation option The animation window Dymola supports a 3 dimensional model view built up by graphical objects such as boxes spheres and cylinders rendered with shading and hidden surfaces removal Animation BEE Visual modeling Dymola supports visual modeling in addition to dynamic modeling with a library of graphi cal objects When a model class is described in Dymola with equations and submodels it 1s also possible to define its visual appearance This 1s done by including predefined graphical objects of various shapes Any model variable can be used to define the changes of the visu al appearance Graphical objects Examples of supported 3D graphical objects are Box Sphere Cylinder Cone Beam Gear wheel and Vector arrows Parameters such as size can be specified Coordinate systems can be defined by a complete 3 dimensional transformation 3x3 matrix translation The information can either be para metric or depend on the dynamics of the model Defining Graphical Objects Graphical 3D objects can either be created
131. bles To obtain consistent values the initialization uses all equa tions and algorithms that are utilised during the simulation Additional constraints necessary to determine the initial values of all variables can be pro vided in two ways 1 Start values for variables 2 Initial equations and initial algorithms For clarity we will first focus on the initialization of continuous time problems because there are some differences in the interpretation of the start values of continuous time vari ables and discrete variables Also there are special rules for the usage of when clauses dur ing initialization All this makes it simpler to start discussing pure continuous time problems and after that discuss discrete and hybrid problems 90 Continuous time problems Initial equations and algorithms Variables being subtypes of Real have an attribute start allowing specification of a start val ue for the variable Real v start 2 0 parameter Real x0 0 5 Real x start x0 The value for start shall be a parameter expression There is also another Boolean attribute fixed to indicate whether the value of start is a guess value fixed false to be used in possible iterations to solve nonlinear algebraic loops or whether the variable 1s required to have this value at start fixed true For constants and parameters the attribute fixed 1s by default true otherwise fixed 1s by default false For a continuous time variable the c
132. by using one of the models in ModelicaAddi tions MultiBody Parts or by directly declaring a VisualShape object The vector visualizers are created by using one of the models in ModelicaAdditons MultiBody Visualizers note that the force and torque sensors must be inserted between the objects The model Visu alShape has the following interface model VisualShape General Visual Object parameter Real r0 3 0 0 0 Origin of visual object parameter Real Length 1 Length of visual object 166 parameter Real Width 1 Width of visual object parameter Real Height 1 Height of visual object parameter Real LengthDirection 3 1 0 0 Vector in length direction parameter Real WidthDirection 3 0 1 0 Vector in width direction parameter String Shape box Name of shape parameter Real Material 4 1 0 0 0 5 Color and specular coefficient parameter Real Extra 0 0 Additional parameter for cone and pipe input Real S 3 3 3 x 3 transformation matrix input Real r 3 Position of visual object end VisualShape Note that r is given in the global coordinate system whereas the vectors r0 LengthDirec tion and WidthDirection are in the local coordinate system as defined by S cc c Shape specifies the name of the shape Predefined shapes are box sphere cylinder cone pipe beam gearwheel and wirebox External sha
133. chanical system is put together as intended Click on the toolbar button Visualize The animation window shows the initial configuration of the system GETTING STARTED WITH DYMOLA 69 3D View Control Translate the model In the plot dialogue open R2 and enter a value for phi_start say 170 degrees and simulate for 5 seconds View the pendulum in the animation window you may want to adjust the perspective by using Setup 3D View Control E 3D view Control Change parameters and study the different behavior Try to control the pendulum in such a way as to get a stable upright position A trick is to use a mechanical PD controller 1 e a spring and damper attached to the tip of the second bar and to a high position 70 INTRODUCTION TO MODELICA Introduction to Modelica Modelica basics Schematic picture of a motor drive Modelica supports both high level modeling by composition and detailed library component modeling by equations Models of standard components are typically available in model li braries Using a graphical model editor a model can be defined by drawing a composition diagram by positioning icons that represent the models of the components drawing connec tions and giving parameter values in dialogue boxes Constructs for including graphical an notations in Modelica make icons and composition diagrams portable controller p wr motor RET ol P 1 n 100 To
134. clarations in the class and Its base classes and the actual modifier values are defined 1n the component in the edited class DEVELOPING A MODEL Edit Edit Text Copy Default R View Parameter Settings Propagate Class Reference gt Component Reference Select Class The actual value of a variable is changed by clicking in the corresponding field and typing in the new value An existing actual value is erased by clicking in the corresponding field and pressing the Delete key The Tab Shift Tab keys move from one input field to another The Add Modifiers tab 1s used to add new modifiers e g start values or nested modifiers Pressing the OK button will generate a modifier list for the component Only modifiers with non empty value fields are used The modifiers that appear and can be set are Normal parameters 1 e variables declared with the keyword parameter in the model These can be set to a value that 1s either numeric or computed from other parameters Class parameters 1 e replaceable classes in the model that can be redeclared to another class here Suitable choices are presented in form of a drop down list with the icons of the classes It 1s also possible to write the class name directly e g by copying a name from the model browser before opening the dialogue and then pasting it into this field One can also add hierarchical modifiers to class name The choices can be given usin
135. con stant elements it 1s straightforward to make it automatically However for non linear problems such as closed kinematics loops it is difficult to establish that a time varying Ja cobian always 1s non singular For reasons of efficiency 1t would be favourable to avoid the overhead of dynamic state selection and allow a user to inform that a certain selection of states will always work Tools can support such an explicit control Using dynamic state selection and making off line simulations one can find a fixed choice that will work for real time simulation where efficiency 1s really needed The reinit construct The construct reinit x requires that x 1s state Use auxiliary variables as states To avoid unnecessary differentiation it is useful to consider only variables appearing differentiated 1n a model as candidates when selecting states It means that if a user would like to see an auxiliary variable v as a state variable he has today to introduce another variable say derv and an equation derv der v to make the derivative der v appear in the model It would be convenient to have a simpler way to introduce a variable as a state candidate Sensors A sensor for measuring speed v makes a variable differentiated v der r and in most cases it is not desirable to have the variable of the sensor model as a state variable Introduction of variable for just plotting should not influence the state selection The state select att
136. cting dy namic states Selecting a less nonlinear representation Different sets x of states gives an ODE der x f x where the right hand side f have different properties In general the problem is simpler to solve if f is a less nonlinear problem The Park transformation for three phase APPENDIX ADVANCED MODELICA 257 power systems 1s a classical way of transforming a nonlinear time varying ODE into a time invariant linear ODE For control design it 1s very favourable to have linear time invariant models because there are lot of analysis and design methods and tools for such models When using linearized versions of Modelica models it 1s important that the set of state variables 1s insensitive to minor changes in the model Avoiding dynamic state selection When selecting states the problem consists of a set of algebraic state constraints that relate dynamic variables It may be remarked that these constraints are equations that are differentiated by Pantelides s algorithm The task when selecting states 1s actually to use the algebraic constraints to solve for some of the vari ables which thus are deselected as states and the remaining dynamic variables become state variables A subset of dynamic variables can be deselected locally 1f its Jacobian 1s non singular In the general case the state selection must be made dynamic but in many real applications it 1s possible to make a static selection of states If the Jacobian has
137. d after events The information from this tab can also be stored in the model by selecting store in model 152 Debug tab includes General Translation Output l Debug Compiler Realtime General simulation debug information Iv Normal waming messages Settings included in translated model Event logging Events during simulation Events during initialization m Nonlinear solver diagnostics Nonlinear solution Nonlinear iterations Details State variable logging which states that dominate error Dynamic state selection Final selection of states Store in model Cancel This tab makes it possible to track down problems during simulation e g chattering prob lems with non linear systems of equations state selection How to use these are described in more detail in Debugging models on page 182 Normally these settings do not require a new translation but does on the other hand only take effect when running inside Dymola Normal warning messages If you want to disable all non fatal warnings and errors Settings included in translated model Useful if you want to debug the model when not running inside Dymola Events during simulation Log events during the simulation Useful for finding errors in the event logic including chattering Events during initialization Also log events during the initial phase Nonlinear For finding problems w
138. declared in Modelica as type Angle Real quantity Angle unit rad displayUnit deg type Torque Real quantity Torque unit N m where Real is a predefined type which has a set of attributes such as name of quantity unit of measure default display unit for input and output minimum value maximum value and 74 initial value The Modelica Standard Library which 1s an intrinsic part of Modelica in cludes these kinds of type definitions Connectors and connections Connections specify interactions between components A connector should contain all quantities needed to describe the interaction Voltage and current are needed for electrical components Angle and torque are needed for drive train elements connector Pin Voltage v flow Current i end Pin connector Flange Angle r flow Torque t end Flange A connection connect Pinl Pin2 with Pin1 and Pin2 of connector class Pin con nects the two pins such that they form one node This implies two equations namely Pinl v Pin2 v and Pinl i Pin2 1 O The first equation indicates that the voltages on both branches connected together are the same and the second corresponds to Kirchhoff s cur rent law saying that the current sums to zero at a node Similar laws apply to flow rates in a piping network and to forces and torques in a mechanical system The sum to zero equa tions are generated when the prefix flow is used in the connector declarat
139. ded images created with File Export Image This format is the closest to the command log as shown in Dymola Textual log without any images but including command output As script file containing all commands given but without the output from the commands File Clear Log Erases the contents of the command log File Recent Files Shows a list of the most recent files which were opened with File Open see page 133 or Simulation Run Script see page 149 Selecting one of the files opens it again typically to open models after File Clear All or to re run a script File Exit Terminates the program Before terminating Dymola will ask 1f modified model classes should be saved one by one exit The exit command can also be given as a textual command for example in a script Edit menu Toolbar cO oQAIM Z 2S iun The toolbar contains buttons for the drawing operations to toggle gridlines and to toggle connect mode The final button checks the model for errors 138 Undo Redo Cut Copy Paste Delete Duplicate Select All Ctri z Ctrl Ctrl x Ctrl C Ctrl Del Ctrl D Ctrl 4 Order Manhattanize Rotate 90 Rotate 90 Flip Horizontal Flip Vertical Ctrl M Ctrl R S Check Draw Attributes Options Bring to Front Send to Back Bring Forward Send Backward Edit Undo and Edit Redo Undoes or redoes the previous editing operation Edit Cut Copies th
140. delica Text layer This 1s also the editor for entering Modelica code 1 e declarations and equations for low level models amp Dymola Dynamic Modeling Laborato Modelica Text extends Interfaces Rigid parameter SIunits Inertia J 1 Moment of nertia SIunits AngularVelocity w Absolute ang velocity of component SIunits AngularAcceleration a Absolute ahgular acceleration of compor i eain w der phi a der w J a flange a tau flange _b tau end Inertia I IT amp ldealGearl J Inettia2 amp SpringD amperl i Fixed 18 Features of Modelica Equations facilitate true model reuse Modelica 1s an object oriented language for modeling of large complex and heterogeneous physical systems It is suited for multi domain modeling for example for modeling of mechatronic systems within automotive aerospace and robotics applications Such systems are composed of mechanical electrical and hydraulic subsystems as well as control sys tems General equations are used for modeling of the physical phenomena The language has been designed to allow tools to generate efficient code automatically The modeling effort 1s thus reduced considerably since model components can be reused and tedious and error prone manual manipulations are not needed Background Modeling and simulation are becoming more important since engineers need to analyse in creasingly complex systems composed of componen
141. describe how the details of a component are modeled consider a simple motor drive sys tem as defined above The system can be broken up into a set of connected components an electrical motor a gearbox a load and a control system A Modelica model of the motor drive system 1s given below excluding graphical annotations INTRODUCTION TO MODELICA 73 A Modelica model of the motor drive A motor model model MotorDrive PI controller Motor motor Gearbox gearbox n 100 Shaft J1 J 10 Tachometer wl equation connect controller out motor inp connect motor flange gearbox a connect gearbox b Jl a connect Jl b wl a connect wl w controller inp end MotorDrive It is a composite model which specifies the topology of the system to be modeled in terms of components and connections between the components The statement Gearbox gear box n 100 declares a component gearbox of class Gearbox and sets the default value of the gear ratio n to 100 A component model may be a composite model to support hierarchical modeling The ob ject diagram of the model class Motor 1s shown above The meaning of connections will be discussed next as well as the description of behavior on the lowest level using real equa tions Variables Physical modeling deals with the specification of relations between physical quantities For the drive system quantities such as angle and torque are of interest Their types are
142. dialog by selecting the category RTI simulation options and then pressing Task Configuration The appropriate setting can be determined by trial and error Overrun strategy On task overrun C stop simulation set simState to STOP queue task before simulation stop Max queued task instances 5 C ignore overrun xPC and Real Time Workshop Using Real Time Workshop and in particular xPC it 1s possible to use the DymolaBlock for Hardware in the loop simulation HILS The setup is a bit different from dSPACE in or der to work around some problems in the compilation procedures in Simulink The positive side 1s that 1s easy to handle all you have to do 1s to append 228 USER_INCLUDES Ic dymola source to the make line in the real time workshop build setup Note the quotes and adapt the dymo la path as necessary This works well with e g xPC both Watcom and Visual Studio compiler under Matlab 6 However it has not been tested with all Real Time Workshop targets and thus there might be some potential problems for some targets Real time simulation using RT LAB The RT LAB development environment 1s based on Simulink and Real Time Workshop The generated code 1s executed on one or more target systems running the QNX real time operating system Consequently the Modelica model developed in Dymola 1s exported to Simulink using a pre defined DymolaBlock S function block When the model has been translated b
143. e real number has no real result value In such situations the modeler may explicitly require a literal evaluation of a relation by using the operator noEvent y if noEvent u gt 0 then sqrt u else 0 Modelica has a set of additional operators such as initial and terminal to detect the ini tial and final call of the model equations and reinit to reinitialize a continuous state with a new value at an event instant For space reasons these language elements are not dis cussed Instead in the next section some non trivial applications of the discussed language elements are explained Variable structure systems Parametrized curve descriptions If a physical component 1s modelled detailed enough there are usually no discontinuities in the system When neglecting some fast dynamics in order to reduce simulation time and identification effort discontinuities appear in a physical model real diode ideal diode As a typical example a diode 1s shown in the figure above where i 1s the current through the diode and u is the voltage drop between the pins of the diode The diode characteristic 1s shown in the left part of the figure If the detailed switching behaviour 1s negligible with re gards to other modeling effects 1t 1s often sufficient to use the 1deal diode characteristic shown in the right part of the figure which typically give a simulation speedup of 1 to 2 or ders of magnitude It 1s straightforward t
144. e Diagram window now displays the mechanical structure consisting of connected joints and masses The component browser 1s opened up to also show the internals of the mechan ics model component The mechanical struc ture of the robot amp Fie Edit Simulation Plot Animation Commands Window Help EFE ls HaQejvi met A7j ki t Elementary Loops A Systems amp JRobotR3 Double click on for example rl at the bottom of the diagram window This is a revolute joint The Parameter dialogue appears The Parameter dialogue can also be accessed from the right button menu Double clicking the left button selects the first alternative from the right button menu GETTING STARTED WITH DYMOLA 27 Parameter dialogue Choices for n 3 mechanics r1 in MultiBody Examples Systems RobotR3 fullRobot General Animation Advanced Component Icon Name mechanics 11 L le Model Actuated Path MultiBody Joints ActuatedRevolute Comment Actuated revolute joint 1 rotational degree offreedom 2 potential states r Parameters animation y true if animation shall be enabled show axis as cylinder n y Axis of rotation resolved in frame_a same as in frame_b phi_offset deg Relative angle offset angle phi from_deg phi_offset Initialization initType z Type of initialization defines usage of start values below phi_start deg Initia
145. e Edit menu Undo Redo Undoes and redoes the last editing operation in the editor Same as Edit Undo and Edit Redo Cut Copy Paste Copies text between the clipboard and the editor Delete Deletes all text in the editor Select All Selects all text in the documentation layer Find Find and replace text in the text editor Enter the text you search for and press OK Goto Line Sets cursor at specified line and scrolls window 1f necessary Edit Source Switches the documentation layer back to viewing mode HTML documentation Dymola can produce HTML code for Modelica classes Models are described both graphi cally with bitmaps of the icon and diagram layers and textually with descriptions and full model code The HTML code may include all classes used as base classes or as components to ensures a complete description of the model or the package All references to classes are hyperlinks which makes browsing easy and efficient Class libraries are described with a clickable list of its components followed by the description of each component Pressing the Info button will use HTML documentation if it is available both for the Dy mola standard packages and for classes written by users This requires the conventions of the default online documentation External references Four different types of HTML documentation can be generated They differ in terms of what classes are documented and how links to other files are created What kind
146. e Parts library Drag over a compo nent Double click on the icon Name it Bl We would like the bar to be 0 5 long and initially horizontal and pointing in the positive x direction This 1s specified by setting the vector r between the two ends of the body to 0 5 0 0 Click on the Edit icon just to the left of the value field of r and an vector editor pops up Enter 0 5 in the first field Click OK Since you did not set all value explicitly you will get question 1f default values should be used Click Use defaults The width and height will be 0 1 by default To get nicer animation you can set different colors for the bars For example use the list of choices of color to make the bar red From the bar B1 we connect another revolute Joint R2 having a horizontal axis of rotation n 1 0 0 and a Body Box B2 rotated 90 with r 0 0 5 0 To get a double pendulum create another similar joint and another BodyBox and connect them This is accomplished easily by selecting the two already present and choosing Edit Duplicate 68 You should now have arrived at a model that is similar to the following The diagram of the Fu ruta pendulum B Modeing Now it is time to simulate To enter the Simulation mode click on the tab at the bottom right The simulation menu is now activated and new tool bar buttons appear a When building 3D mechanical models it is possible to get visual feedback to check that the me
147. e current selection to an internal clipboard and deletes them Text 1s copied to the operating system clipboard Edit Copy Copies the current selection to an internal clipboard without deleting them Text 1s copied to the operating system clipboard Edit Paste Pastes objects from the internal clipboard to the current window The current selection is not replaced by the pasted objects Edit Delete Deletes the current selection The objects are not placed in the internal clipboard See also Deleting objects on page 115 regarding deletion of connections Edit Duplicate Creates a duplicate set of the selected objects Duplicated components are given new names by appending a digit to the old name in order to avoid name conflicts The new objects are offset one grid point from the originals The new objects become the current selection Connections between duplicated components are also duplicated connections to unselected objects are not Edit Select All Selects all objects in the current window Note that it also selects objects inherited from base classes Edit Order The ordering operations are used to move graphical objects or components forward drawn later or backward drawn earlier The relative order of the selected objects 1s maintained Note that for components Bring to Front or Bring Forward means that the component is moved down in the component browser because components are drawn in order Bring to Front B
148. e defined carefully In order to handle stability problems it is possible to define a smaller fixed step size and in this case the communication step size should be a multiple of this smaller fixed step size On the other hand there are integration methods called dense output methods which treat communication points differently The step size of such integrators 1s not influenced by the communication grid The step size 1s only chosen according to the required tolerances and the estimated local error Such methods integrate past the desired communication points and determine the values of the state variables x at the communication points by interpolation which involves no evaluation of the differential equation This 1s advantageous since the choice of the communication grid even 1f a dense grid is used has nearly no influence on the efficiency of the integration In Dymosim the maximum allowed step size for dense output integrators can be explicitly restricted by parameter method hmax in the input file additionally it 1s possible to turn off dense output Variable order Integration methods approximate the solution x t internally by a polynomial of order korq Some methods use a fixed order other methods vary the order during the simulation The integration step size can be usually chosen larger for the same maximum local error if the order 1s bigger which in turn implies a greater efficiency The step size and error control of the int
149. e for k 1 1s very slow Increase it to find out what happens We leave the problem of tuning the controller to the interested reader Parameter expressions Modelica supports parameter propagation and parameter expressions which means that a parameter can be expressed in terms of others Assume that the load is a homogeneous cyl inder rotating long its axis and we would to have its mass m and radius r as primary pa rameters on the top level The inertia 1s J 20 5 m r 2 We need to declare m and r in MotorDrive Open MotorDrive Activate the Modelica Text representation press the Modelica Text toolbar button the second rightmost tool button The parameters and variables are more than real numbers They are physical quantities The Modelica standard library provides type declarations for many physical quantities Open Modelica STunits in the package browser For the parameter r which is a radius it is natural to declare 1t as being of type Radius To find it enter R and the browser goes to the first component starting with R If it is not the desired one press R once again and so on to find GETTING STARTED WITH DYMOLA 61 it When you have found Radius drag it to the component browser below The choice to add a component 1s preselected Click OK A menu to declare a variable pops up Complete the declaration Dedare variable m Type and name parameter y Modelica Slunits Radius Ir
150. e installation will ask for a directory to install Dymola The default is C NDymola The installation program will then copy files from the server to the client computer and set up the Start Programs menu No CD is required to install Dymola on the clients Troubleshooting Occasionally the installation will not succeed or the program will not operate as intended after installation This section will outline some of the problems that have been detected in the past In most cases these problems are specific to the Windows environment 290 License file License file is not authentic The error message License file not authentic indicates either an error in the license file or a mismatch between your computer system and your license file Ifyour Dymola distribution included a dongle drivers for the dongle must be installed and the dongle must be present See also Dongle installation on page 283 The license file is locked to your computer system which means that you cannot execute Dymola from another computer You cannot copy the Dymola distribution directory from one computer to another instal lation must be performed using the Dymola distribution CD or from the downloaded file To install Dymola on client computers when a license server 1s used see Installing on client computers on page 290 The license file on the Dymola CD for Windows is not complete You cannot copy the license file from the CD
151. e_a same as in frame_b phi offset 1 0 0 x axis deg Relative angle offset angle phi from deg phi offset WANN ILS r Initializatio 0 0 1 z axis initType 1 0 0 negative x axis phi start 0 1 0 negative y axis 0 0 1 negative z axis Type ofinitialization defines usage of start values below Initial value of rotation angle phi fixed or guess value w start deg s Initial value of relative angular velocity w der phi a start deg s2 Initial value of relative angular acceleration a der w OK Info Cancel Change the name to R1 The axis of rotation is set as the parameter n We would like to have a vertical axis of rotation use the list of choices and select y axis When simulating it is natural to try different initial configurations by setting angles and possibly angular veloci ties for the joints Use the list of choices of initType to select the alternative initialize gen eralized position and velocity variables The initial value of the angle is specified by setting the parameter phi_start and the initial velocity is specified by setting w_start These two values are easy to change between simulation runs Click OK Connect the connector of world to the bottom connector of the revolute joint A bar 1s then connected to the revolute joint There 1s one bar which has the visual appear ance of a box during animation called BodyBox in th
152. ectories data names Dymosim tcomp tcut tder tdiff tinteg tplot tplotm trange tsame tzoom Functions on trajectoy name matrix perform time simulation of a Dymola model compress trajectory data extract signals and corresponding names from a trajectory calculate first derivative of trajectory numerically determine absolute difference of two trajectories calculate integral of trajectory numerically plot trajectories and use signal names as legend plot trajectories 1n multiple diagrams and use signal names as legend find trajectory index range of a given time range make same time axis for 2 trajectory matrices cut out a trajectory of a given time range tnhead add the same string to all signal names of a trajectory name matrix tnindex get row index of string 1n trajectory name matrix tnlist list trajectory names with preceding row numbers Other functions tload load trajectory e g dymosim simulation into Matlab work space tsave save trajectory on mat file e g to be used as input signals for dymosim tfigure set meaningful default values for figures e g white background and same colors on screen and printer Dymosim command line arguments Dymosim is a stand alone program which accepts command line arguments with the follow ing syntax Usage Options dymosim options file in file out simulate a DSblock model with dymosim 5 simulate default
153. ed value column 1 weight for optimization column 2 desired value use weight 1 since automatic scaling usually leads to equally weighted terms column 2 fixed free or desired value according to column 1 column 3 Minimum value ignored if Minimum gt Maximum column 4 Maximum value ignored if Minimum gt Maximum Minimum and maximum values are used for scaling purposes both in the simulator and for the initial value calculation Furthermore they restrict the search range in initial value calculation DYNAMIC MODEL SIMULATOR 211 column 5 column 6 Initia If parameters are FREE min sum are zero SE SR SR SE SE SE SE SE SE SE SE SE OSE SE OSE SR SR SR OSE SE OSE SR dk SR SE SE SE SR OSE ek SE values are ca no specia FREE parameters FIXED state derivatives equation is solved In all other cases weight i at the initial time to the automatic scaling scale i DESIRED i minimum and maximum values given in column 3 and 4 Category of variable 1 parameter 2 state 3 state derivative 4 output 5 input 6 auxiliary variable Data type of variable real 1 boolean integer states and inputs are FIXED action takes place If there are only FIXED and FREE variables states and inputs is IDENTICAL outputs and auxi if DESIRED i Otherwise Scale i 1 is used char initialDescrip
154. egrators are based on the assumption that the solution x t can be differentiated at least k 1 times Therefore if it is known for example that the result of a system is not very smooth a low order method should be chosen In Dymosim the maximum order of a variable order method can be explicitly set in the input file via method ordmax If the 202 maximum order 1s set to one the variable order integration methods reduce to the simple explicit or implicit Euler formula Stiff systems Usual integrators get in trouble if fast and slow signals are present in the solution x t For linear differential equations this corresponds to problems where the system matrix has eigenvalues whose real part 1s negative and large in magnitude compared to the recip rocal of the time span of interest Such systems are called stiff There exist different algo rithms for the integration of stiff and non stiff systems However note that problems with undamped highly oscillating signals are not called stiff here At present there exists no production code to cope with this problem satisfactorily the step size 1s limited by the fre quency of the highly oscillating components and therefore the simulation 1s slow The step size of an integration method is always limited by a method specific stability boundary The integration only remains stable and produces reliable results 1f the step size 1s lower than this boundary If a system
155. eh88 Gaus91 Gay 93 Hind80 Hind83 Hair87 Lubi91 Kaps79 Otte91 Petz82 Sham75 Sham80 Brenan K E Campbell S L and Petzold L R Numerical Solution of Initial Value Problems in Differential Algebraic Equations Elsevier Science Publishers 1989 F hrer C Differential algebraische Gleichungssysteme in mechanischen Me hrk rpersystemen Ph D dissertation Mathematisches Institut Technische Univer sit t M nchen 1988 Gaus N and Otter M Dynamic Simulation in Concurrent Control Engineering IFAC Symposium on Computer Aided Design in Control Systems Swansea UK Preprints pp 123 126 July 15 17 1991 Gay D Feldman S Maimone M and Schryer N A Fortran to C Converter Com puting Science Technical Report No 149 AT amp T Bell Laboratories Murray Hill N J 07974 The f2c compiler and the documentation 1s available via anonymous ftp from netlib att com cd netlib f2c Hindmarsh A C LSODE and LSODI Two New Initial Value Ordinary Differential Equation Solvers ACM Signum Newsletter vol 15 no 4 pp 10 11 1980 Hindmarsh A C ODEPACK a systematized collection of ODE solvers Scientific Computing edited by R S Stepleman et al North Holland Amsterdam 1983 Hairer E Norsett S P and Wanner G Solving Ordinary Differential Equations Nonstiff Problems Springer Verlag Berlin 1987 Lubich C Extrapolation integrators for constrained multibody systems IMPACT Comp Sci Eng No
156. elica Standard Library is hierarchically structured into sub libraries GETTING STARTED WITH DYMOLA 43 The sub libraries of the Modelica Standard Li brary E Dymola Dynamic Modeling Laboratory Modelica Text OE x H File Edit Simulation Plot Animation Commands Window Help m ajx 2 gt Hh Zle gt BBA Blo d or oS moy An model Unnamed Packages equation HI Modelica Reference Modelica gj Blocks fm Constants fea Electrical Icons Math Mechanics J Slunits E Thermal end Unnamed 5 MedelicaAdditions As shown by the package browser the Modelica Standard Library includes 1 7 8 Blocks with continuous and discrete input output blocks such as transfer functions filters and sources Constants provides constants from mathematics machine dependent constants and con stants from nature Electrical provides electric and electronic components such as resistor diode MOS and BJT transistor Icons provides common graphical layouts used in the Modelica Standard Library Math gives access to mathematical functions such as sin cos and log Mechanics includes a one dimensional translational and rotational components such as inertia gearbox planetary gear bearing friction and clutch SIunits with about 450 type definitions with units such as Angle Voltage a
157. en subtracted below Block Total CPU s Mean us Min us to Max us Called 0 28 284 1425 465 to 51172 22058 T 0 315 2191 1930 to 10815 149 2 0 020 tot 0 to 5621 22058 3 1 024 52 i 12 to 41656 22057 4 0 000 Tut 4 to 50 4 280 0 022 1 0 to 8116 21812 281 0 611 31 22 to 9959 21812 282 0 014 d 0 to 99 21812 301 0 028 1 0 to 8533 21812 302 0 132 7 4 to 8530 21812 303 0 032 2 0 to 8680 21812 348 0 019 1 0 to 464 21813 349 17835 94 80 to 50319 21813 350 0 024 1 0 to 8747 21813 The two dominating blocks 281 and 349 are the equation blocks found with the more coarse grained profiling However note that block 302 1s a complex equation giving the gas force of the engine Since the equation has event generating gt and one might try to use the noEvent opera tor When using noEvent one must first check that the equation is sufficiently smooth Since part of the equation 1s a piece wise polynomial one evaluates both pieces at the switch and observe that they give the same result There is also an outer if v rel 0 which is not continuous However for this complete model v_rel changes sign when x is a the minimum 0 and thus for this specific model SIMULATING A MODEL 189 Turning events off may increase simulation time that expression 1s in fact continuous Using such global information breaks the idea of ob ject orien
158. er formance reasons We revisit the interpolation example from How to use noEvent to improve performance on page 261 and let a boolean parameter control whether we generate events or not Real x parameter Boolean generateEvents parameter Real cpos cneg equation der x if if generateEvents then x gt 0 else noEvent x gt 0 then cpos x APPENDIX ADVANCED MODELICA 263 else cneg x tif time 1 then y else 0 If generateEvents 1s not a boolean parameter but changes continuously we have to be more careful Real x Real level parameter Real eventLimit parameter Real cpos cneg equation level noEvent abs der x time 2 abs x time der x if if level gt eventLimit then x gt 0 else noEvent x gt 0 then cpos x else cneg x if time gt 1 then y else 0 Here level must be computed using noEvent since we do not want to introduce extra events every time der x or x changes sign but level 1s used without any noEvent in the 1f expres sion since the number of relations generating events would otherwise change between events It is not possible to store the expression in parenthesis in the if expression in a boolean vari able since it can change its value between events To re use it introduce an extra Real vari able as follows Real x Real level parameter Real eventLimit Real xIsPositive parameter Real cpos cneg equation level noEvent abs der x time 2 abs x time
159. erated by Dymola in order to simulate the model and then used to perform simulations and initial value com putations Dymosim contains the code necessary for continuous simulating and event han dling Three types of events are supported time state and step events Model descriptions are compiled to machine code such that maximum execution speed 1s reached during simu lation no interpretation of model equations takes place Dymosim 1s a stand alone program which can be used in several different environments It 1s especially suited to be used in conjunction Dymola Dymola transforms such a definition into a state space description which in tum 1s solved by the Dymosim integrators The re sults of a Dymosim simulation can be plotted or animated by Dymoview Dymosim can be used in other environments too Special support is given for Matlab and for ANDECS However it can also be used as a stand alone program or can be called di rectly from a user program as a C function DYNAMIC MODEL SIMULATOR 197 Who wrote Dymosim The first version of Dymosim was called DSSIM and was written by Norbert Gaus and Martin Otter as part of the ANDECS project in 1991 Gaus91 Otter91 The DSSIM inte grators are mainly based on high quality public domain software which was selected and enhanced by Claus F hrer Tuan van Tran and Martin Otter In 1992 1993 major enhance ments to DSSIM have been realized by Martin Otter user interface improved even
160. es are overwritten by the data given as arguments to the dymosim m file function 200 Selecting the integration method Dymosim provides a number of different integration methods for the simulation of dynamic systems In this section the major characteristics of these methods are discussed and rules of thumb are given which method should be selected for a problem at hand Note however that one should not rely on just one integration method for simulation experiments Instead some selected results should be checked by two or three other different integration meth ods First of all some important issues of integrators are explained in order to classify the avail able integration methods in Dymosim If you are familiar with these issues just skip the next section Integrator properties Relative and absolute error tolerances Relative tolerances have to be assigned to tell the integration methods how accurately the solution x t should be computed The tolerance must be greater than zero and is used in a local error test for each component of the state vector x roughly requiring at each step that local error tolrel xi tolabs The relative tolerance tolrel approximately defines the number of expected true digits in the solution That is if 3 4 true digits are required in the solution the default value of 104 should be used If an element of x 1s exactly zero or near to zero the relative tolerance 1s without me
161. est to build a library with function definitions using software de velopment tools outside of the Dymola environment and then link the library to the model In this way libraries are easily shared between a variety of applications 254 Dynamic libraries are not supported A major benefit compared to including function definitions 1s that the risk of interference between the code generated by Dymola and the code of the external functions 1s greatly re duced The only parts included in the compilation of the model are header files declaring the external functions in C and the implementation is compiled separately It is currently only possible to link static libraries not DLLs Building an external library Using an external library the C code consists of two parts a header file declaring the func tion and an implementation It is common to use a single header file to declare a group of related functions The header file for the example above would be ifndef ADD2 H define ADD2 H extern double add2 double x double y endif The implementation 1s very similar to the code used for inclusion in the model code but the header file should be included to ensure compatibility in the event of changes in the inter face The ifndef and endif wrappers are not needed include lt add2 h gt double add2 double x double y return x y Using the default compiler GCC the function 1s compiled and included in the l
162. factor for forces to le 3 a force of 100N will be represented by an arrow 0 1m le 3 m N 100N long in scale of the the diagram SIMULATING A MODEL 171 Vector scaling setup gt Animation Setup Animation 3D View Control Creates a window with controls for 3D viewing The view controls act on an imaginary camera panning the camera left moves the subject closer to the nght edge of the window 3D view control 3D View Control 172 Scripting language There 1s a script facility that makes it possible to load model libraries set parameters set start values simulate and plot variables by executing scripts This is how the demo exam ples are setup The script facility is useful when running a series of simulations as for exam ple a parameter study Basic operations It 1s possible to set and get model parameters initial values and translator switches Compu tations using all Modelica functions and array operations are allowed It 1s possible to call translated functions thus gaining access to external functions Interactive variables are au tomatically created Set and get of both arrays as a whole and of individual elements Named arguments allowed to functions like simulateModel with default values Modelica expressions can be stored in script files or as Modelica functions Interaction By typing a Modelica expression at the command prompt the result 1s output Modelica Math sin 5 0 958924274663138
163. ferenses Generate online documentation C Generate HTML for referenced classes C Generate links to online documentation C Do not generate external links r Diagram image size C Small image 75 Normal image C Large image 150 C Huge image 200 Editor command reference New E Open Ctrl o Libraries Demos Li ll Save Ctrl s Save As Save All Save Total Clear All Q Search Change Directory amp Print Ctrl P Export b Save Log Save Script Clear Log Recent Files Exit Drag from the pack age browser to extend or insert in a package File menu Toolbar ar bed Q amp v The toolbar contains buttons open and save models and to print The final button enabled interactive help see Help What s This on page 143 File New Model etc Creates a new model connector record block or function Dymola presents a dialog win dow where the user must enter the name of the new model a short description and if this 1s a partial model The name must be a legal Modelica identifier and not clash with existing models The fourth field 1s the name of the base class 1f the class should extend from an existing model It is possible to drag a class name from the package browser into this field The fifth field 1s the optional name of the package the new model should be inserted into The package must already exist Leave this field emp
164. ferent views When specifying a behavior direct ly in terms of equations it is most convenient to work with the model as the Modelica Text Press the Modelica Text toolbar button the second rightmost tool button The right sub window can now be used as a text editor To declare the parameters and the variables enter as shown the declarations for the parame ters m L and g which also are given default values The parameter J is bound in terms of other parameters Finally the time varying variables phi and w are declared A start value 1s given for phi while w 1s implicitly given a start value of zero GETTING STARTED WITH DYMOLA 35 Declaration of parame ters variables and equations Modeling E bt model Pendulum parameter Real m 1 parameter Real L 1 parameter Real g 9 81 parameter Real J m L 2 Real phi start 0 1 Real w equation der phi w J der w m g L sin phi end Pendulum New text will not automatically be color coded To get the color coding of keywords and types press the right mouse button and select Highlight Syntax E Pendulum Pendulum Modelica Text Editing Ei Fle Edit Simulation Plot Animation Commands Window Help al le d QejN met mm nszis mes amp HBE ov model Pendulum parameter Real m 1 Modelica Reference parameter Real L 1 7 Medelica parameter Real g 9 81 L 2 amp 7 ModelicaAdditions A iiie i Real phi
165. for documentation 112 Description and information The first level 1s a short one line description of the class which 1s shown in the documenta tion layer and in the modifier window The second level of extended documentation 1s available in the documentation layer or by using the right mouse button menu Other comments are associated with declarations or equations Units and declaration comments are also shown in the modifier window HTML documentation Dymola can automatically produce HTML code for Modelica models The HTML file may contain all classes used as base classes or as components this ensures a complete descrip tion of the model or the package All references to classes are clickable links which makes browsing easy and efficient Class libraries are described with a clickable list of its compo nents followed by the description of each component The user may include arbitrary HTML code in the documentation This makes it possible to take advantage of images tables and other forms of formatting Coordinate system Every class has a master coordinate system that 1s used for all graphical information in the class The view of a class in a window is normally scaled so the entire master coordinate system 1s visible The surrounding parts of the window are empty if the aspect ratios of master coordinate system and window do not match The user can change the zoom factor to show more or less of the model The master coordi
166. g C Program Files Mi crosoft Visual Studio vc98 Bin vcvars32 bat for Visual Studio 6 and then strip off the trailing bin vcvars32 bat to get the right directory The directory structure differs between compilers Optional libraries Optional libraries e g hydraulics are distributed on separate CDs They should be in stalled after installing Dymola as the files are installed in the Dymola distribution directory Dongle installation If your Dymola distribution contains a dongle a small hardware device that attaches to the parallel or USB port of your computer the appropriate dongle driver software must also be installed 1 The driver installation file 1s stored on the Dymola distribution CD 2 Double click on 1exid exe to start the installation process Please follow the instruc tions on the screen 3 The dongle drivers are ready for use after the installation process reboots your computer APPENDIX INSTALLATION 283 Shortcuts start Dymola in the right directory Only for old models in the Dymola language 4 Attach the dongle either to the parallel printer port or a USB port on your computer de pending on the type of dongle Please note that the dongle must be present every time the Dymola program is executed If the dongle is not present or the drivers have not been installed Dymola will issue a mes sage and terminate Additional setup Creating shortcuts to Dymola Sometimes it 1s convenient
167. g the an notation choices as described in the Modelica specification Note that the declaration in side choices refer to global scope 1 e must use full lexical path Hierarchical and other forms of free form modifiers e g x start 2 unit m This is used as a catch all for more complex cases and can replace values for normal parame ters class parameters e Add modifiers This is a comma separated list of free form modifiers and can be used to add free form modifiers for new variables The next time the modifier dialogue is opened the list elements have been moved to the items The field does not appear if the model 1s read only Grey backgrounds for modifiers indicate default values e g from the class of the compo nent One can see where the default originates from by clicking What s This on the modi fier field or using View Parameter Settings in its context menu The context menu of a modifier can be accessed by pressing the triangle to the right of the input field or by using the right mouse button inside the field The context menu allows you to Edit Allows hiearchical inspection and editing This uses a matrix editor for matrices see page 119 a function call editor for function calls and a parameter dialog for structured modifiers and redeclarations Edit Text Shows a larger input field for modifying long modifiers Copy Default Copies the text of the default value to the input field for further editing
168. gt 0 switches between true and false Expression x 0 2 time 0 became true x 0 2 time 0 0 0016 Iterating to find consistent restart conditions 184 The solution may be to rewrite the model Debug monitor during event at Time 0 252 Expression x 0 2 time gt 0 became false x 0 2 time 0 0 0008 Iterating to find consistent restart conditions during event at Time 0 254 Expression x 0 2 time gt 0 became true x 0 2 time 0 0 0008 Iterating to find consistent restart conditions during event at Time 0 256 Expression x 0 2 time gt 0 became false x 0 2 time 0 0 0016 Iterating to find consistent restart conditions during event at Time 0 258 In this case a fixed step size solver was used an adaptive integrator would normally have had the events at almost identical times The result 1s a clear indication of chattering and the solution is to rewrite the model Exactly how depends on the physical system e g friction models usually have a stuck state in order to avoid similar problems and bouncing balls can be modeled by an elastic impact zone If the events are time events it is not chattering and only indicate fast sampling In order to reduce the simulation time 1f there are many step one can select an explicit solv er see Specify simulation run on page 148 In some cases it 1s possible to replace a detailed model generating many events by an aver aging modes wi
169. he guard for other values In those rare cases one can use the same technique without any extra epsi lon i e noEvent abs x lt 0 APPENDIX ADVANCED MODELICA 267 268 APPENDIX MIGRATION Appendix Migration Migrating to newer libraries Dymola supports migration of models using one set of model libraries to another set of model libraries with model components of similar structure but for example having other class names or different connector names or parameter names Dymola has commands to build up internal translation tables which will take effect when a model library or a model component is loaded These commands can be collected in a script allowing all models that use a specific library to upgrade to the new one How to migrate Assume that we would like to migrate myModel that uses a package OldLibrary to exploit a NewLibray In many cases in particular when release a new version of a library the library developer will provide a convert script which specifies the translation from the old version to the new version of the library Assume that the model is stored in a file named my Model mo It is advisable to also have a backup copy of the file Assume also that a specification of the translation when migrating from using OldLibrary to using NewLibrary is specified in the script file Convert mos To migrate myModel proceed as follows 1 Start with a fresh Dymola APPENDIX MIGRATION 271 2
170. he same situa tions as DOPRIS if a higher precision is required say tolre1 107 GRK4T If the calculation of the right hand side of the differential equation 1s relatively cheap and your problem is stiff and or contains highly oscillating solution components use method GRKAT GRKAT is a A 89 3 stable linearly implicit Rosenbrock type method of order four i e the stabili ty region of the integrator is nearly the whole left half plane GRKAT can be also used for non stiff problems without any problems but with a higher amount of computing time than a non stiff solv er as DOPRIS or DOPRIS DASSL If you have differential algebraic equations DAE you have to use DASSL since this is the only DAE solver available in Dymosim DASSL is designed to integrate stiff systems using a BDF method Method DASSL calls integrator DASSL 1f no indicator functions are defined no step events can appear and calls integrator DASSLRT otherwise DASSLRT is a modified version of DASSL for which a root finder was added Method DASSL may also be used to integrate stiff ordinary differential equations Dymosim makes the necessary conversions of the right hand side ODASSL ODASSL solves higher index differential algebraic equations or overdetermined differential alge braic equations It is a modified version of DASSL Therefore if you integrate an ODE system with ODASSL you will get nearly the same results with respect to the number of functi
171. hen running in Dymola and the same as the real time step size when running on other platforms Simulation Visualize Visualizes initial configuration of 3D models Simulation Show Log Opens the message window and shows a log for the last simulate command SIMULATING A MODEL 155 Plot window Default plot window User defined titles and location of legend Dymola supports plotting of any variable In Simulation mode multiple plot windows may be created Each plot window may contain several diagrams Multiple curves in each dia gram are allowed Multiple diagrams in a plot window allow the user to lay out the curves nicely with aligned time axis and different heights and y scales of the diagrams The default layout of plot window displays the names of plotted signals in a legend above the diagram and the unit of the signals 1f available along the vertical axis L ox Hw J2w J3w J ww The user can set diagram heading and axis titles The legend can be located in several dif ferent places for example inside the diagram See also Plot Setup on page 161 Plot 0 x Coupled Clutches Angular velocity rad s Time s When plotting there must be an active plot window If the active plot window has multiple diagrams one of the diagrams 1s active indicated by an enclosing grey rectangle and the plot commands are directed to this diagram 156 A plo
172. hile the handle is moved Common reshaping operations are also available in the Edit menu for example rotation and flipping horizontally and vertically Deleting objects Pressing the Delete key deletes the current selection Connections attached to any deleted components or connectors are also by default deleted in order to maintain model consisten cy Only objects defined in the class being edited can be deleted Inherited objects while also shown as selected are not deleted Objects in read only models cannot be deleted Components and connectors Inserting a component or a connector Components and connectors are inserted by dragging a class from the package browser or a library window into the editor The dragging procedure 1s Select a class in the package browser or in a library window While pressing the left mouse button move the cursor to an edit window and position the icon at the desired position Release the left mouse button to confirm the insertion The size of the inserted component or connector is according to the specified component size defined in the enclosing class The newly inserted component or connector is automatically given a name composed from the name of its class and a sequence number to avoid name conflicts Name comment and modifiers can be changed in the modifier window see Modifier window on page 116 DEVELOPING A MODEL 115 Parameters Show Component Open Class i
173. his introduction to Dymola It 1s possible to show several curves in the same diagram It 1s just to tick the variables to be plotted A curve 1s erased by ticking once more The toolbar button Erase Curves white rectangle erases all curves in the active diagram It also possible to have several diagrams To get a new diagram select Plot New Diagram or click on the toolbar button The new di agram becomes active Tick Motorl Jm w and the result shown below is obtained Selecting a diagram makes it active Selecting Plot Delete Diagram removes the diagram 58 Angular velocity El TestMotor DriveLib TestMotor Plot 1 E x Y Eile Edit Simulation Plot Animation Window Help l x sde N E amp te ola Ear Oy m m an l Motor1 flange b phi 1 2 0 8 0 4 rad s rad s s 0001 kgm2 rad s2 N m rad Stepl Advanced 0 6 0 8 1 ES Modeling V Simulation Creating a model for the motor drive The task was to build a model for a motor drive and it ought now to be a simple task to com plete the model We will just give a few hints Note that the full name of the components are given in the component browser at the lower left To generate the position error you may use the model component Modeli ca Blocks Math Feedback For the controller there is Modelica Blocks Continuous PID For the meaning of ra
174. ialog Connections are imme diately checked E Change attributes for lx m Variability of component C Constant Parameter C Discrete a f m Properties Final Protected Replaceable r Dynamic typing Normal C Inner C Outer m Causality None C Input C Output ox Cancel Connections A connection 1s a graphical representation of a connect statement between two connec tors Connections can be made when Dymola is in connect mode as indicated by the pressed down tool button If the model 1s read only or connect mode 1s off connections cannot be made Creating a connection Connections are defined interactively in Dymola in a manner similar to drawing lines Click on a connector and draw a line possibly with multiple line segments see Lines and polygons on page 123 Note that the mouse button must be pressed down while drawing the first line segment Click on another connector to finish the connect operation Double clicking outside a con nector presents the context menu The line segments of the connection snap to the grid of the class by default but are then ad justed so the connection end points reach the corresponding connectors This may cause skewed lines if the grid is coarse but it can usually be adjusted with Edit Manhattanize The manhattanize operation inserts points until there are at least four points to work with so the line can be d
175. ibrary with these DOS commands On Windows the directory of the GCC compiler dymola egcs bin must have been added to the PATH environment variable set PATH c dymola egcs bin PATH The compile and link commands are gcc c add2 c ar rv libext a add2 o ranlib libext a The name of the library shall start with lib and the extension for GCC is These con ventions are assumed when the model is linked Library annotation The Modelica interface uses two special annotations Include and Library to specify the header file and the name of the library function add2 Sum of two numbers input Real x y output Real sum external C annotation Include include lt add2 h gt Library ext end add2 APPENDIX ADVANCED MODELICA 255 Prefix and extension are not given Note that the library name is ext the lib prefix is added by the linker and the extension depends on the used compiler a for GCC and 1ib for Microsoft C This ensures porta bility of the Modelica interface to different platforms and compilers As a more complex example consider an interface to National Instruments AI_VRead 1n its Ni Daq library A protected variable is used to pick up the status code returned from the function function AI VRead Analog in annotation Include include lt nidagex h gt Library nidaq32 input Integer iDevice 1 input Integer iChannel 1 input Integer iGain 1 output Real dVolt
176. ical axis title or in the legend The unit is shown in the axis title 1f all signals have the same unit or in the legend 1f there are multiple units on one axis Show variables description adds the description of the variable as specified 1n the mod el to the vertical axis title or the legend The variable description 1s shown along the axis if it 15 the same for all signals Use line styles instead of color solid dashed dotted to distinguish curves This is useful for printing diagrams on monochrome printers If disabled curves are distinguished by color Do not use markers to distinguish curves with identical color or line style By default markers are used when so many curves are plotted that colors or line styles must be re used The layout of the legend is controlled by these settings Show variable legend is the default If unchecked no legend is displayed Arrange legend horizontally lists the signals from left to right in the legend the default If unchecked the signals are listed vertically 1n the legend Draw a frame around the legend when outside of diagram Inside the diagram the frame is always drawn SIMULATING A MODEL 163 Location of the legend is either outside of the diagram above below or to the right of the diagram or close to one of the corners inside the diagram See page 156 for examples of diagrams with different locations of the legend eae aixi window setup Signals Titles Lege
177. ilable on the matching items Double click on a matching class opens that class 1n the associated edit window Double click on a component opens the en closing class and selects the matched item Classes can be dragged into the graphical editor to insert a component File Change Directory Display a dialog which allows the user to change the current directory The current directo ry 1s used as the default location for opening files and for saving simulation results cd Change Directory may also be given as a textual command A cd command without direc tory specification prints the current working directory in the log window Change current directory C Util dymola work El mfiles B a Modelica cys 2 Documentation FE Examples 1 0 Library H readme a m source amp C tmp gt ME E Eudora y coca File Print Prints the contents of the window on the current printer This command is only available in the Windows version of Dymola 136 To Clipboard Image Animation Setup HTML HTML AVI export setup File Export To Clipboard Copies the contents of the active window to the clipboard in Enhanced Metafile Format which can then be pasted in common word processors Such an image can be rescaled and edited in e g Microsoft Word This command is only available in the Windows version of Dymola File Export Image Saves a PNG image of the contents of the active window without
178. ile Libraries Displays a menu with shortcuts to known libraries Selecting one of the libraries 1s equiva lent to opening the filename shown in the statusbar with File Open The library menu is built with library commands in dymola insert dymodraw ini File Demos Displays a menu with shortcuts to predefined demo models Note that in many cases there is a corresponding script file which should be opened after the model See also Simulation Run Script on page 149 File Save Saves the class in the current window Ifthe original model definition was read from a file that file 1s updated Otherwise a the user 1s prompted for a filename The name of the class with file exten sion mo is default If the name of the class is Unnamed for a new class Dymola will ask for a another class name Dymola will ask the user to save a modified class before terminating File Save As Duplicates the current model and saves it to a new file See also File New Duplicate Class on page 133 For a top level class or package it is also possible to save it with the same name but to a different file or directory File Save All Saves all modified model classes with a File Save operation File Save Total Saves the class in the current window and all classes used by it This creates a single file with the complete definition of a class which is independent of other files and libraries File Clear All Perfor
179. imation windows j animation window controls WHAT IS DYMOLA 15 The variable browser allows selecting plot variables changing parameters and initial condi tions S MotorDriveT est MotorDriveTest File Edit View Simulation Plot Animation Window Help jee HMotorDriveT est 1 MotorDriveT est 2 i ad AL i ad s 2 de b kgm2 Me rad s de i rad s s de Change initial rad s2 AE condition Change parameter Plot selection An animation window shows a 3D view of the simulated model The animation can be run at different speeds halted single stepped and run backwards Building a model The graphical model editor is used for creating and editing models in Dymola Structural properties such as components connectors and connections are edited graphically while equations and declarations are edited with a built in text editor Find a component model The package browser allows viewing and selecting component models from a list of models with small icons It 1s also possible to get a large icon view 16 Package browser fJExamples Interfaces 8 Inertia pldealPlanetary QyldealGearR2T J lunits 7 ModelicaAddiions sl Inertia model Library Library large icon siveBpiing Examples Interfaces sce Damper pe SpringDamper the ElastoBacklash EP BearingFric
180. in Follow selected object enables the view to dynamically change to follow the animated object This can be done conditionally in different directions by enabling disabling Follow object in X Y or Z direction or Follow rotations of object The Follow feature is useful for animating mechanisms that move in the global coordinate system such as vehicles Frames tab sets a number of attributes related to history frames History frames gradually fade to the grey color of the background Animation Setup zix Vectors Number of history frames o Interval between frames h Number of history frames introduces motion blurr showing several frames Zero will turn off all history frames A large number of history frames may slow down the anima tion considerably If the number of history frames times the interval between history frames 1s greater than the total number of frames all frames are displayed and there 1s no performance penalty Interval between history frames With the default frame interval 1 frames 1 2 n older than the leading edge frame are shown With a frame interval of m frames m 2m 2mn are shown It is sometimes necessary to increase the frame interval to get a suit able visual separation between the history frames Vector tab is for controlling the scaling of vector visualizers found in ModelicaAddi tions MultiBody Visualiers The units indicate that if you for example set the scale
181. in the last iteration b Try all possible combinations of the values of the relations systematically exhaustive search In the above example both approaches can be simply applied because there are only two possible values s lt 0 1s false or true However if n switches are coupled there are n rela tions and therefore 2 possible combinations which have to be checked in the worst case Below parameterized curve descriptions of the ideal thyristor and the ideal GTO thyristor are shown for further demonstration Especially note that also non unique curve parameters s can be used by introducing additional discrete variables here fire to distinguish the branches with the same parameterization values 88 Ideal Thyristor Ideal GTO thyristor fire 0 i i i i ces 2 u uU Y s lt 0 or pre off and not fire if off then s else 0 if off then 0 else s fire 0 i ti i i 1 2 u v tv vi v off s lt 0 or not fire u if off then s else 0 i if off then 0 else s The technique of parameterized curve descriptions was introduced in Clauf et al 1995 and a series of related papers However no proposal was yet given how to actually imple ment such models in a numerically sound way In Modelica the new solution method fol lows logically because the equation based system naturally leads to a system of mixed continuous discrete equations which have to be solved at event instants In the past ide
182. ing View Plot Win dow Results from other files can be plotted within Dymoview by selecting the appropriate file via menu File Open Result As explained in the next section the results can also be di rectly loaded into Matlab and plotted with the Matlab plot functions The translate commands generates the file dsmodel c compiles and links this to the gen erate the executable dymosim exe and then runs dymosim i to generate default initial values Compiling and linking uses a scrip dsbuild provided by Dymola in directory DY MOLA bin If necessary you can adapt this script to your needs e g to choose different 1 Matlab stands for Mathematical laboratory and is a registered trademark of The Math Works Inc 2 ANDECS stands for Analysis and Design of Controlled Systems and is a registered trademark of DLR 198 compiler options Dymosim as a stand alone program Dymosim is essentially a stand alone program without any graphical user interface which reads the experiment description from an input file performs one simulation run stores the result on an output file and terminates Instead of controlling this action via Dymolas graph ical user interface Dymosim can also be called directly by the user A default input file for a simulation run named dsin txt is generated by command dy mosim i in the shell to get all possible command line arguments use dymosim h The file contains the complete information about
183. ing simulation when the when clause 1s not active Non unique initialization In certain situations an initialization problem may have an infinite number of solutions even if the number of equations and unknown variables are the same during initialization Examples are controlled systems with friction or systems with backlash or dead zones As sume for example backlash 1s present Then all valid positions in this element are solutions of steady state initialization although this position should be computed from initialization It seems best to not rely on some heuristics of the initializer to pick one of the infinite num 96 ber of solutions Instead the continuous time equations may be modified during initializa tion in order to arrive at a unique solution Example y if initial then smooth characteristics else standard characteristics Well posed initialization At translation Dymola analyses the initialization problem to check if it is well posed by splitting the problem into four equation types with respect to the basic scalar types Real In teger Boolean and String and decides whether each of them are well posed As described for the pure continuous time problem Dymola outputs error diagnosis in case of over specified problems In case of under specified problems Dymola makes automatic default selection of initial conditions How many initial conditions Basically this 1s very simple Every discrete variab
184. instant dur ing simulation Due to this assumption the total number of continuous and discrete equa tions shall be identical to the number of unknown variables It 1s possible to rewrite the model above by placing the when clauses in an algorithm section and changing the equa tions into assignment statements algorithm when h1 lt 3 then close true end when when h2 1 then close false end when In this case the two when clauses are evaluated in the order of appearance and the second one gets higher priority All assignment statements within the same algorithm section are treated as a set of n equations where n is the number of different left hand side variables e g the model fragment above corresponds to one equation An algorithm section 1s sort ed as a whole together with the rest of the system Note that another assignment to close somewhere else in the model would still y1eld an error Handling hybrid systems in this way has the advantage that the synchronization between the continuous time and discrete event parts 1s automatic and leads to a deterministic behav iour without conflicts Furthermore some difficult to detect errors of other approaches such as deadlock can often be determined during translation already Note that some dis crete event formalisms such as finite automata or prioritized Petri nets can be formulated in Modelica in a component oriented way see Elmqvist ef al 2000 84 A d
185. ion system that has to be solved at each step The simplest example of an implicit method 1s Euler backward The derivative of the state vector 1s approximated by a backward difference formula n Xn 1 h leading to the discretized problem X 2 x MH cub n l which at each time step this has to be solved for x 1 The idea of inline integration is to let the Dymola translator manipulate the discretized problem to reduce and simplify the problem that has to be solved numerically at each step A set of differential algebraic equations can be written as 0 g t x X v where x is the vector of variables appearing differentiated and v is the vector of unknown algebraic variables Normally Dymola manipulates this problem to solve for V and X and a numerical integration algorithm is used to integrate for x When inline integration is used the Dymola translator first reduces the DAE index to one and then adds the discretization equations Assume that the original problem 1s index one then using Euler backward turns the problem into 0 fU ox xv x X p x n n with x x and V being the unknowns to be solved for The Dymola translator manipu lates the problem to facilitate the numerical solution work SIMULATING A MODEL 191 Inline integration in Dymola Inline integration is turned on by issuing the command Advanced InlineIntegration true on the command line before translating the model Euler forward 1
186. ions The Modeli ca Standard Library includes also connector definitions Partial models and inheritance A very important feature in order to build reusable descriptions 1s to define and reuse par tial models A common property of many electrical components is that they have two pins This means that it 1s useful to define an interface model class TwoPin that has two pins p and n and a quantity v that defines the voltage drop across the component partial model TwoPin Pin p n Voltage v equation v 7 p v n v p i n i 0 end TwoPin The equations define common relations between quantities of a simple electrical compo nent The keyword partial indicates that the model class is incomplete To be useful a con stitutive equation must be added To define a model for a resistor start from TwoPin and add a parameter for the resistance and Ohm s law to define the behavior INTRODUCTION TO MODELICA 75 model Resistor Ideal resistor extends TwoPin parameter Resistance R equation R p i v end Resistor A string between the name of a class and its body is treated as a comment attribute and 1s in tended to describe the class Tools may display this documentation 1n special ways The keyword parameter specifies that the quantity is constant during a simulation experiment but can change values between experiments For the mechanical parts it is also useful to define a shell model with two flange connectors partial
187. iscontinuous com ponent The disadvantage is that the types of systems which can be modeled 1s restricted For exam ple general Petri nets cannot be described because such systems have non deterministic be haviour For some applications another type of view such as a process oriented type of view or CSP may be more appropriate or more convenient Relation triggered events During continuous integration it 1s required that the model equations remain continuous and differentiable since the numerical integration methods are based on this assumption This requirement is often violated by if clauses continuation of branch for switching point detection For example the simple block above with input u and output y may be described by the fol lowing model model TwoPoint parameter Real y0 1 input Real u output Real y equation y if u gt 0 then y0 else y0 end TwoPoint At point u 0 this equation is discontinuous if the 1f expression would be taken literally A discontinuity or a non differentiable point can occur if a relation such as x gt x changes its value because the branch of an if statement may be changed Such a situation can be han dled in a numerical sound way by detecting the switching point within a prescribed bound halting the integration selecting the corresponding new branch and restarting the integra tion 1 e by triggering a state event This technique was developed by Cellier 1979
188. ith non linear system of equations e g ill posed problems or missing noEvent see Using noEvent on page 259 Which states that dominate error If the simulation 1s slow due to tolerance requirements for some state variable this can help in which variables are the critical ones SIMULATING A MODEL 153 Compiler tab of Simu lation Setup Compiler tab General Model Translation Output Bealime r Compiler Gee compiler Microsoft Visual C C Microsoft Visual C with DDE C Watcom C C 11 x Note Microsoft Visual C and Watcom are optional compilers which may not be installed on your system Verify compiler setup Allows the user to change the compiler used by Dymola to compile simulation code into an executable program that performs the simulation Dymola uses a C compiler to compile the generated C code into a simulation program The default compiler shipped with Dymola on PC 1s a distribution of the GNU C Compiler gcc Users of Microsoft Visual C or WATCOM C C may use these compilers 1n stead If support for a compiler has not been selected when installing Dymola the corre sponding choice 1s disabled see also Multiple compiler support on page 282 On UNIX system the default compiler is used The compilation 1s controlled by the shell Script dymola insert dsbuild sh Several different kinds of problems may occasionally arise when compiling the generated C code produced b
189. itmap Draws a bitmap which 1s read from an external file Click on the bitmap button in the tool bar and draw the outline 1n an edit window then specify the bitmap filename Supported file formats are BMP GIF JPEG and PNG The bitmap 1s scaled preserving aspect ratio centered in the bounding box Default graphics Classes without graphical information are automatically given a simple default layout when displayed by Dymola The purpose of the default graphics 1s to provide some meaningful graphics while the model 1s initially edited Components and connectors without graphics are represented by a rectangle and a text with the name of the component at the center The default layout can easily be changed by the user Changing graphical attributes The user must first select one or more primitive graphical objects and then pick one of the style buttons on the toolbar to change the corresponding visual attributes of the selection Note that line color and fill area color are different attributes a rectangle has both for ex ample and have different buttons in the toolbar Text color is set as line color Selecting an attribute from the menu sets that attribute for the selected objects when appli cable and also marks it as the default Clicking on the button sets all line or fill style at tributes for the selected objects 124 Line style 2 The line style attributes are No Color Colors Color or no color fo
190. ives Creating graphical objects Graphical objects are drawn by clicking on buttons in the draw toolbar The corresponding toolbar button 1s shown in a depressed state while the drawing operation 1s in progress The toolbar also contain two buttons for setting line and fill style attributes with associated pull down menus INOOVABY 2 The graphical tools described in this section work in essentially the same way Select a tool by clicking on the appropriate button in the toolbar Move the cursor to the start position 1n the edit window Interact with the tool for example spanning a rectangle After the interaction has been completed Dymola returns to the default select move con nect mode A common operation 1s to define two points for example the end points of a line segment or two opposite corners of a rectangle This can be made in two different ways Click the left mouse button at the start position move the mouse to the end position end click the left mouse button a second time Press the left mouse button at the start position move the cursor while pressing the left mouse button and release the button at the end position The drawing operations snap the definition points to the grid of the model class The details of the drawing operations are described below Lines and polygons Click on the polyline or polygon button in the toolbar and draw line segments Interaction ends when the left mouse butto
191. ixed Processes Hybrid Dynamic Systems ADPM2000 pp 7 16 DASA Dortmund Ger many Engelson V H Larsson and P Fritzon 1999 Design simulation and visualization envi ronment for object oriented mechanical and mult domain models in Modelica In Pro 102 ceedings of the IEEE International Conference on Information Visualisation IEEE Computer Society London UK Ernst T M Klose and H Tummescheit 1997 Modelica and Smile A case study ap plying object oriented concepts to multi facet modeling In Proceedings of the 1997 Euro pean Simulation Symposium ESS 97 The Society for Computer Simulation Passau Germany Fritzson P L Viklund D Fritzson and J Herber 1995 High level mathematical mod eling and programming IEEE Software 12 3 Gautier T P Le Guernic and O Maffeis 1994 For a New Real Time Methodology Publication Interne No 870 Institut de Recherche en Informatique et Systemes Aleatoires Campus de Beaulieu 35042 Rennes Cedex France Halbwachs N P Caspi P Raymond and D Pilaud 1991 The synchronous data flow programming language LUSTRE Proc of the IEEE 79 9 pp 1305 1321 Halbwachs N 1993 Synchronous Programming of Reactive Systems Kluwer IEEE 1997 Standard VHDL Analog and Mixed Signal Extensions Technical Report IEEE 1076 1 IEEE Jeandel A F Boudaud P Ravier and A Buhsing 1996 U L M Un Langage de Mod lisation a modelling
192. ization INTRODUCTION TO MODELICA 95 parameter Real A fixed false parameter Real w fixed false Real x initial equation A w readSineData init txt equation der x A sin w x Discrete and hybrid problems The language constructs for specifying initial conditions for discrete variables are as for the continuous time variables start values and initial equations and algorithms Variables being subtypes of Real Integer Boolean and String have an attribute start allow ing specification of a start value for the variable For discrete variables declarations Boolean b start false fixed true true Integer start 1 fixed imply the additional initialization equations pre b false pre i 1 This means that a discrete variable v itself does not get an initial value v tyte but the pre value of v v tg does When clauses at initialization For the initialization problem there are special semantic rules for when clauses appearing in the model During simulation a when clause 1s only active when its condition becomes true During initialization the equations of a when clause are only active during initializa tion if the initial operator explicitly enables it when initial conditionl then VS ull end when Otherwise a when clause is in the initialization problem replaced by v pre v for all its left hand side variables because this 1s also the used equation dur
193. k in a correct way See also Graphical interface between Simulink and Dymola on page 219 You have compiled all Dymola models used in the model otherwise you will get an error message If Allow multiple copies of block 1s unchecked you should not copy the block Un checking it should only be done if you have a dSPACE system Also note that the parameterizations differ between blocks in the Modelica Standard Li brary and in Simulink For example the frequency of Simulink s Sine block 1s measured in rad s which 1s commonly known as angular frequency and should thus be 2x times the fre quency in the corresponding source in Modelica 292 The default compiler used by Matlab Mex called lcc is very slow for large files Models generated by Dymola may compile slowly using lcc and we suggest using Microsoft Visual C C instead if available dSPACE systems Older dSPACE systems dSPACE release 2 0 3 3 may not support MAP files for Dymola models The error message displayed by ControlDesk is Encountered an error in the MAP file This problem 1s fixed by upgrading to dSPACE release 3 4 or by requesting an updated DLL from dSPACE Other Windows related problems Starting the installation The installation normally starts automatically when you insert the distribution CD If au tostart has been disabled please start D Nsetup exe assuming your CD drive is labeled D from Windows Explorer or Start Run Applic
194. k on a variable while pressing the SHIFT key Plots multiple variables All vari ables from the previous non shifted click to the last click are plotted Note that multiple variables are only plotted if the range 1s limited to a single submodel instance The Erase Curves button erases all variables see Plot Erase Curves on page 161 Selecting independent variable The default behavior for plotting 1s trend curves It means that time 1s the independent vari able x axis variable To select another independent variable go to the variable selector put the cursor on the variable and press right mouse button A menu pops up where the first alternative 1s the current independent variable and then follows the selected variable Time 1s always an alternative to allow going back to plotting trend curves Advanced mode Pressing the Advanced button in the plot selector displays buttons for selecting which categories of variables are displayed in the plot selector It also allows plotting of the differ ence between signals and to compare the results of multiple simulations Advanced p E vot Constants Time varying Online Y Original Difference Compare Results Search Filter Time l p Set parameters of translated model You must first translate the model Xg Set initial conditions of translated model You must first translate the model Vo Set initial guess values of translated model You must first translate the mode
195. k s library browser as Dy mola Block DymolaBlock if it does not appear you have probably not included dymo la mfiles and dymola mfiles traj in your Matlab path or is using a version prior to Matlab 5 3 Simulink 3 You click once to open the library and you then drag the DymolaBlock to other models OTHER SIMULATION ENVIRONMENTS Dymola block before compiling 73 untitled iol xl File Edi View Simulation Format Tools jO cS 5B ne gt he DymolaBlock 100 ode45 The DymolaBlock block with the Dymola logo represents the Modelica model It can be connected to other Simulink blocks and also to other DymolaBlocks The lines at the right and left of the block will be replaced by ports after compiling the model The DymolaBlock is a shield around a S function MEX block 1 e the interface to the C code generated by Dymola for the Modelica model Double clicking on the DymolaBlock open a form where you can set the name of the model and optionally the file name A simple way of setting the model name is to start Dymola and double click on the correct model and then press Select from Dymola gt This automatically gives the model name Note that the model name may contain a dotted name e g Modelica Blocks Sourc es ExpSine and the file name 1s optional but 1s used both to find the model and to ensure that the Simulink model 1s up to date When associating a Modelica model the first time or when
196. l These values are intended to help the initialization of non linear system Constants Show constants in plot selector This includes all variables that do not vary dur ing the simulation including parameters constants and other variables that are bound to parameter or constant expresssions Time varying Show all variables that vary during the simulation excluding parameters constants and other variables that are bound to parameter or constant expresssions Online Load preliminary result during simulation This enables plotting and animation while a simulation 1s running Disabling this gives slightly better performance Original Plot the selected signals Difference Plot the difference between selected signals 158 Tooltip for a single signal Tooltip for multiple signals and a common independent variable Compare Results Use last results as master result file When selecting a plot variable it also plots the corresponding variables from the other results Search Filter Entering a regular expression limits which variables are shown in the plot selector Special symbols in the regular expression are n Match everything Match any single character ab Match characters a or b a z Match characters a through z ab Match any characters except a and b E Match one or more occurences of E ab cd Match ab or cd d Match any digit w Match any digit or letter i Match from s
197. l value of rotation angle phi fixed or guess value w_start deg s Initial value of relative angular velocity w der phi a_start deg s2 Initial value of relative angular acceleration a der w Info Close The parameter dialogue allows the user to inspect actual parameter values In this case the parameter values are write protected to avoid unintentional changes of the demo example Thus the dialogue just has a Close button and an Info button When the parameter values can be changed there is one OK button and one Cancel button to choose between The val ues are dimmed to indicate they are not given at the top level model but somewhere down in the component hierarchy A parameter dialogue may have several tabs This dialogue has the tabs General Anima tion and Advanced In a tab the parameters can be further structured into groups as shown It 1s easy for a model developer to customize the parameter dialogues Graphical illustra tions can be included to show meaning of parameters Next to each parameter field 1s a triangle this gives you a set of choices for editing the pa rameters Edit gives a matrix editor function call editor Edit Text gives a larger input field etc Some parameters have a list of choices where you can select values instead of writing them One example 1s the parameter n which defines the axis of rotation The value for this revolute joint is 0 1 0 1 e the axis of rotation i
198. language In Proceedings of the CESA 96 IMACS Multiconfer ence IMACS Lille France Joos H D 1999 A methodology for multi objective design assessment and flight con trol synthesis tuning Aerospace Science and Technology 3 Kloas M V Friesen and M Simons 1995 Smile A simulation environment for en ergy systems In Sydow Ed Proceedings of the 5th International IMACS Symposium on Systems Analysis and Simulation SAS 95 vol 18 19 of Systems Analysis Modelling Sim ulation pp 503 506 Gordon and Breach Publishers L tstedt P 1982 Mechanical systems of rigid bodies subject to unilateral constraints SIAM J Appl Math Vol 42 No 2 pp 281 296 Mattsson S E M Andersson and K J str m 1993 Object oriented modelling and simulation In Linkens Ed CAD for Control Systems chapter 2 pp 31 69 Marcel Dek ker Inc New York Mattsson S E H Elmqvist and M Otter 1998 Physical system modeling with Model 1ca Control Engineering Practice 6 pp 501 510 Mattsson S E and G S derlind 1993 Index reduction in differential algebraic equa tions using dummy derivatives SIAM Journal of Scientific and Statistical Computing 14 3 pp 677 692 Mosterman P J and G Biswas 1996 A Formal Hybrid Modeling Scheme for Handling Discontinuities in Physical System Models Proceedings of AAAI 96 pp 905 990 Port land OR INTRODUCTION TO MODEL
199. lated to model properties specified in the Modelica lan guage Restriction of the general class e g model or connector Aspects related to protection and redeclaration Dynamic typing inner and outer 140 General model at E Change attributes for IdealPlanetary 2 x tributes Store as one file The Graphics tab contains options that affect the graphics of the class Change the coordinate system of the current class Change the grid and the default component size of the current class See also Coordinate system on page 113 Graphical model at ICE xj tributes DEVELOPING A MODEL 141 Editor options Mode View New Library Window New Dymola Window ae e gt lg spy ldealaearR2T IdealGear Modeling Ctrl F1 Y Simulation Ctrl F2 Edit Options The Appearance tab contains two options that affect the operation of the graphical editor Restrict minimum font size to make small texts more easily readable As a consequence these texts may overflow their bounding boxes Automatic Manhattanize of connections If enabled connections are manhattanized 1m mediately when created moved or reshaped nclude protected classes in package browser If true protected classes are shown in the package browser If false protected classes are not shown ce Graphical editor l Restrict minimum font size Automatic Manhattanize of connections Package browse
200. ld only be done if you have dSPACE multi processor hardware since its build command internally makes copies of the model that should share the original dll name Normally copying of DymolaBlock takes special care to create unique identifications for the block such that the copies use different dll s even 1f they are multiple copies of the same Dymola model This is necessary in order to allow you to connect two copies of the same model to each other but does not work together with dSPA CE s build command DymolaBlock 1s found in DymolaBlockMaster mdl and you can also get DymolaBlock by running DymolaBlockMaster In this case you must copy DymolaBlock to another model Simulation in Matlab There 1s also a low level M file Dymsim m allows you to use Modelica models from Dy mola as building blocks in Simulink and simulate them from within Matlab and Simulink To use dymsim m Select File Translate Model in the Modelica model s window e Start Matlab and change to the same directory 224 e Make sure that Dymola s mfiles are in the Matlab path Run the command dymsim in Matlab this compiles the model and simulates it To simulate it again without recompiling use simulate on the Matlab command line In Matlab you can change parameters p and initial values x0 as well as StartTime and StopTime Real time simulation The model configured to simulate with RTI Dymola provides support for real time simulation of DymolaBlock
201. le for noEvent A more subtle example 1s 1f the noEvent is necessary 1n order to guarantee that we can solve for all algebraic variables This is more complex than merely being able to evaluate the model A simple example occurs for the turbulent flow equation AP oss em m Real mdot Ploss APPENDIX ADVANCED MODELICA 261 parameter Real c equation Ploss c mdot noEvent abs mdot Remember that abs mdot 1s expanded into an 1f expression in this case leading to Ploss c mdot noEvent if mdot gt 0 then mdot else mdot The noEvent allows us to use this equation to implicitly solve mdot from Ploss Without the noEvent it would not be possible to solve the equation past the point where mdot changes sign since it would be tantamount to taking the square root of a negative number We can also manually solve this equation for Ploss resulting in Real mdot Ploss parameter Real c equation mdot noEvent if Ploss c 0 then sqrt Ploss c else sqrt Ploss c Or mdot noEvent sign Ploss c sqrt abs Ploss c We have here not considered the possibility that c might be zero The right hand side 1s here continuous when Ploss passes through zero and thus noEvent can be seen as a performance improvement Additionally we guard against taking the square of a negative number by using noEvent An additional note on style In this example we note an additional reason for using noEvent around the e
202. le the results of a simulation are stored as well as the correspond ing signal names The amount of output on the result file 1s defined by matrix settings in the input file An example of the result file in ASCII format is given in the following table The file format is also self describining explaining how aliases and constant variables are stored compactly char Aclass 3 11 Atrajectory Wal char name 16 8 H lt AAWADWDAWDBaAaQaawnaaa char description 16 53 Time i Potent Curren Potent Potent Voltag Curren Potent Curren Voltag Curren Curren Potenti Current Current n ia ia ia O mh Q Fh Fh O Fh s Voltage drop between at the pin owing into at the pin owing into at the pin rop between owing from at the pin owing into rop between owing from owing into at the pin owing into in ne V two pins pin A pin A two pins p to pin pin A two pins p to pin pin A pin A p v n v V e paw nv Vs n A p v n v V n A Matrix with 4 columns defining the data of the signals it DYNAMIC MODEL SIMULATOR 213 dataInfo i 1 Jes name i data is stored in matrix data j 1 1 0 for ALL data matrices means that name 1 is used as abscissa dataInfo i 2 k name i data is stored in column abs k of matrix data j with sign k used as sig
203. le v needs an initial condition because V to e 1s otherwise not defined Example parameter Real tl 1 discrete Real u start 0 fixed true Real x start 0 fixed true equation when time gt tl then u end when der x x u During initialization and before the when clause becomes active the first time u has not yet been assigned a value by the when clause although it is used in the continuous part of the model Therefore it would be an error if pre u would not have been defined via the start value in the u declaration On the other hand 1f u is used solely inside this when clause and pre u is not utilized in the model an initial value for u may be provided but does not influence the simulation be cause the first access of u computes u in the when clause and afterwards u is utilized in oth er equations inside the when clause 1 e the initial value is never used Since it may be tedious for a modeller to provide initial values for all discrete variables Modelica only requires to specify initial values of discrete variables which influence the simulation result Otherwise a default value may be used Example Initialization of discrete controllers Below four variants to inialize a simple plant controlled by a discrete PI controller are dis cussed INTRODUCTION TO MODELICA 97 Variant 1 Initial values are given explicitly parameter Real k 10 T 1 PI controller parameters parameter Real Ts 0 01
204. ll not be able to find the right viewer program if so the user can de fine environment variable DYMOLAHTMLVIEWER which should contain the path of the viewer program Dymola must be restarted The In fo button or menu choice will also use HTML documentation if available otherwise plain text Installing updates Updated versions of Dymola are either distributed on CD or can be downloaded from http www dynasim se update The old version of Dymola should be removed before installing an update you cannot 1n stall into an existing Dymola directory The downloaded update does not contain any license file During installation of the update you are required to insert your original Dymola CD for authentication You are also prompt ed for the license file which typically is the license file on the CD if you have obtained a newer license file by e mail you should specify this one instead Removing Dymola Under Windows you can remove Dymola by clicking on the Start button in the Taskbar se lect Settings Control Panel and start Add Remove Programs Select Dymola and click on the Add Remove button Note that files that you have created in the Dymola distribution directory for example by running the demo examples are not deleted If so the remaining files and directories may be deleted through the Explorer Installation on UNIX This section refers only to the UNIX version of Dymola Important information
205. ller This 1s a strong modification of the motor drive model and there is the issue of possible in validation of the model The keyword redeclare clearly marks such modifications Further more the new component must be a subtype of PI 1 e have compatible connectors and parameters The type system of Modelica 1s greatly influenced by type theory Abadi and Cardelli 1996 1n particular the notion of subtyping the structural relationship that deter mines type compatibility which 1s different from subclassing the mechanism for inherit ance The main benefit 1s added flexibility in the composition of types while still maintaining a rigorous type system Inheritance is not used for classification and type checking in Modelica The public components of a class are typically its connectors and parameters A model of a PI controller has connectors for the reference signal measured value and control output and parameters such as gain and integral time So it 1s natural to require that also an autotuning controller has those components In many real applications there are many PI controllers This makes it clumsy to use the ap proach described above to change controllers because we need to know the names of all controllers To avoid this problem and prepare for replacement of a set of models one can define a replaceable class Cont rollerModel in the drive model partial block SISOController input Real ref input Real inp output Real out
206. me derivative of w 1 e the angular acceleration For the angular position we have der phi w Start Dymola or if it is already started then give the command File Clear All in the Dymola window Click on the tab for Modeling at the bottom right Select File New Model E Dymola Dynamic Modeling Laboratory Diagram 1 n x el Fie Edit Simulation Plot Animation Commands Window Help lex IC nr gt elem geo Gy Open Ctrl o Connector Libraries Record Demos Block fd Save Ctr s Function Save As Parkane A dialog window opens Enter Pendulum as the name of the model 34 The dialogue to name a new model component E Create New Model 320 xl Name of new model Pendulum Description Partial Extends optional Insert in package optional zl Click OK You will have then have to Accept that you want to add this at the top level You should in general store your models into packages as will be described later E Pendulum Pendulum Modelica Text i BEE Ed Fle Edit Simulation Plot Animation Commands Window Help lex ls dO e moy 5 9 H gt SB Zi model Pendulum Modelica Reference 7 Modelica 3 7 ModelicaAdditions amp 7 MultiBody i Unnamed Pendulum equation end Pendulum amp 2 e gt 6 A model can be inspected and edited in dif
207. meter Real ebounce 0 5 parameter SIunits Velocity vsmall 1e 4 Real fext if time lt 10 then 0 else 350 sin time 1 time Boolean locked start false equation der x v m der v if locked then 0 else f f m Modelica Constants g nt fext when x lt 0 locked then reinit x 0 reinit v if locked then 0 else ebounce v end when locked if pre locked then f lt 0 else x 0 and abs v lt vsmall and f lt 0 end BouncingBall Note that the logic here 1s more complex due to the fact that we have an external force in addition to the inherent bouncing of the ball When writing such state machine logic it is vi tal that the expression used to enter the locked state 1s still true 1n the state 1n order to avoid chattering and to be safer one can rewrite it as locked f lt 0 and if pre locked then true else x lt 0 and abs v vsmall A more advanced model would have these as relative quantities and allow both the ball and the surface to move Guarding against division by zero The sole exception where comparison of two real expressions would make sense 1s when it is used to guard against a single exceptional value e g division by zero By careful analysis 1t is general possible to show that the guard can and should be applied to slightly larger val ues and use the technique in Guarding expressions against evaluation on page 260 In some cases only one exact value 1s exceptional and it 1s not possible to apply t
208. mples Systems RobotR3 fullRobot Read Only File Edit Simulation Plot Animation Commands Window Help te Q amp WPI Spoo o gi E E P3 Bole gt 1 4 4441 i gt gt In addition the simulation menu includes commands to setup and run simulations The Set up menu item opens a dialogue allowing the setting of start and stop times The icon indi cates which toolbar button to use for quick access to the set up dialogue The Simulate menu item starts a simulation In this case however a command script has been prepared To run the script select Com mands select Simulate Dymola then translates the model and simulates automatically The animation window is opened automatically because the simulation result contains ani mation information fullRobot MultiBody Examples Systems RobotR3 fullRobot Read Only Animation Ella Y Fle Edit Simulation Plot Animation Commands Window Help 18 xi e ua ejviempo Bevotz ola EKn EH N a m Start the animation by selecting Animation Run or clicking the run button on the tool bar jb M KM 4D 32 Plotting the speed which contains the usual buttons of pausing rewinding stepping forward and backward re spectively It 1s possible to change the viewing position by opening a view controller Animation 3D View Control The command Plot makes a plot of the speed reference and actual speed of the third joint fullRobot
209. mponent clausel type prefix type specifier component declaration Equations equation clause equation equation annotation algorithm clause algorithm algorithm annotation equation simple expression expression conditional equation e for clause e when clause e connect clause assert clause comment algorithm component reference expression function call expression list function call conditional equation a for clause a while clause when clause a assert clause conditional equation e if expression then equation 242 elseif expression then equation else equation end if conditional equation a if expression then algorithm elseif expression then algorithm eise algorithm end if for clause e for IDENT in expression loop equation end for for clause a for IDENT in expression loop algorithm end for while clause while expression loop met algorithm end while when clause e when expression then equation end when when clause a when expression then algorithm end when connect clause APPENDIX MODELICA 243 connect connector ref connector ref connector ref IDENT array subscripts IDENT array subscripts assert clause assert e
210. ms a Save All operation and then removes all model definitions in Dymola except the Modelica standard libraries File Search Shows all classes or components matching a search pattern File Search will search all classes read by Dymola Selecting Search in the package browser will only search the se lected package 134 The search dialog Find what fiction 0o Find Hits B of 3388 Stop Search topics Details Modelica text v Class name Ful documentation Description Component name Use of class component type and extends Search options Complete match Match case Name fm Description Gr BearingFriction Modelica Mechanics Rotational Coulomb friction in bearings CoefficientOfFriction Modelica Slunits O Friction Modelica Mechanics Rotational Examples Drive train with clutch and brake O Friction Modelica Mechanics Translational Examples Use of model Stop FrictionBase Modelica Mechanics Rotational Interfaces Base class of Coulomb friction elements FrictionBase Modelica Mechanics Translational Interfaces Base class of Coulomb friction elements The search pattern can be matched against two general topics of the classes Modelica text Match search pattern anywhere in Modelica text except for documentation and other annotations The full Modelica text of a package is not searched only the classes inside the package Examples model M pattern
211. n dataInfo i 3 O Linear interpolation of the column data 1 4 Piecewise convex hermite spline interpolation of the column data Curve is differentiable upto order 1 4 The spline is defined by a polygon It touches the polygon in the middle of every segment and at the beginning and final point Between such points the spline is convex The polygon is also the convex envelope of the spline dataInfo i 4 1 name i is not defined outside of the defined time range Keep first last value outside of time range Linear interpolation through first last two points outside of time range t dataInfo 16 4 Or X 20 1 Time Bag Ces C v 1 2 00 G p v 2 d es G p i de 040 C n v zo 4 d Coni 1 4 0 0 R p v 2 5 i C der v Zo Da foc ww Qm C p v nd Ox FF Cspei 2 52 n0 x R v 2 00 ox Hg zc Dea R p i 2 X 0 R n v 2 as R n i oat data 1 2 4 0 0 0 0 1 0 0 0 loat data 2 6 5 0 0000000E 000 2 0000000E 001 4 0000001E 001 6 0000002E 001 8 0000001E 001 0000000E 000 1 0000000E 000 8 1863302E 001 6 7018896E 001 5 4872990E 001 4 4920427E 001 3 6774468E 001 0 0000000E 000 0 0000000E 000 0 0000000E 000 0 0000000E 000 0 0000000E 000 0 0000000E 000 1 0000000E 000 8 1863302E 001 6 7018896E 001 5 4872990E 001 4 4920427E 001 3 6774468E 001 1 0000000E 000 8 1882674E 001 6 6999793E 001 5 4875731E 001 4 4958425E 001 3 6768275E 001 214 Bibliography Bren89 Fu
212. n Blot Arination Window Hep 18 x ee amp M Gi OC A Z SH RII gt BSB Bho l Packages E i Sensors 2 GG Translational istis la J Modelicaddions teol oi r t 1 AA E staitTine ER MotorDrive Drivelib MotorDrive motor ffi gearbox load ffi phiload El posiionesrar controler Step Modeling Mode Simulation Mode Browsing Tree Browser for model packages and models Component hierarchy Viewer diagram documentation The Simulation Mode 1s used for experimentation It has simulation setup to define duration of simulation etc plot windows animation windows and variable browser Dymola Dynamic Modeling Laboratory Mm Ei Ele Edt View Simulation Plot Anjratign Window Help jg amp NUBE gt Y gt W M n n Variable browser Simulate Mode Experiment name HE Experiment Setup General Model Translation f Compir Experiment 7A Experiment A TED Simulation Interval O o Start time 0 Stop time 1 Dutput Interval C Intervallength o Number of intervals 500 Integration Algorithm Coo MO Fixed Integrator Step IO Co coses Simulate controls Setup Simulate Plot windows EBD M 411 plot window controls An
213. n New Window Attributes Info Parameters can be or ganized in Tabs and Groups Size can be adjusted by moving the handles Orientation 1s changed with commands in the Edit menu It is also possible to insert a name into the Modelica text editor by dragging from the pack age browser or a library window This can for example be used to declare variables of types from Modelica SIunits or functions from Modelica Math Context menu for components Pressing the right mouse button when a component 1s selected presents a menu with the fol lowing choices A similar menu is presented when pressing the right mouse button in the component browser Parameters Opens the modifier window see below Show Component Shows the class of the component or connector in this window Press the Previous button to go back Open Class in New Window Opens a new main window with the class of the component or connector Attributes Opens a Component Attribute dialog see Component attributes on page 120 Info Displays extended documentation for the class of the component or connector HTML documentation will be used if it 1s available both for the standard packages and for classes written by users Modifier window Double clicking on a component or connector in the graphical editor displays a dialog win dow with additional information The modifier window can also be started from Parame ters in the context menu of com
214. n has been clicked twice at the same position Polygons are automatically closed by Dymola Skewed lines can be cleaned up with Edit Manhattanize which applies a manhattan mode algorithm to the intermediate points of the line Note that drawing a line between two connectors does not create a connection although the difference may be impossible to see in the editor Rectangles and ellipses Click on the rectangle or ellipse button in the toolbar and draw the shape in an edit window Ellipses are drawn to touch the bounding box at four points DEVELOPING A MODEL 123 Text Click on the text button in the toolbar and draw the text object in an edit window Dymola prompts for a new text string in a separate dialog window The text 1s centered 1n the bounding box the size of the text 1s chosen as big as possible without overflowing the bounding box If the minimum font size option 1s set the text may be truncated indicated with ellipses and a small bounding box may overflow vertically If space 1s extremely limited the text 1s not drawn at all These tokens are expanded in a text string class Name of the enclosing class name Name of the component this text 1s enclosed in path The full path name of the component Spar The value of parameter named par in the model par The value of parameter named par in the model printed as par value Double clicking on a text displays a dialog window for changing its contents B
215. n models It requires that no models outside of this list depend on them This 1s not primarily an interactive function but designed to be called by other programs con structing and changing models Corresponds to Delete in package windows Note translateModel and simulateModel have named arguments as 1s indicated above and the default for problem 1s corresponding to the most recently used model Thus simulate Model stopTime 10 method Euler corresponds to simulateModel 0 10 0 0 Eul er 1e 4 Note If you give the name of the model you can skip translateModel and go directly to sim ulateModel Note The current version does not allow you to first compile the model and then change translator switches or parameters 1f you have Evaluate true and then simulate the model 180 You must call closeModel and translateModel if you have compiled the model and wants to change them Script functions The Modelica based scripting language 1s extensible since functions written in Modelica can be called in the same way as the predefined functions Thus the functions 1n the Model 1ca standard library can be used directly from the scripting language allowing e g table 1n terpolation As an example consider a function for reading the A matrix of a linearization using read Matrix The function can be written as follows function ReadA input String linfile dslin mat input String abcdname ABCD input String nx
216. name nx protected Integer ABCDsizes 2 readMatrixSize linfile abcdname Real ABCD ABCDsizes 1 ABCDsizes 2 Integer nxi integer scalar readMatrix linfile nxname 1 1 public output Real A nx nx algorithm ABCD readMatrix linfile abcdname size ABCD 1 size ABCD 2 A ABCD 1 nx 1 nx end ReadA Because of the default values the function can be called as ReadA without giving any ar guments This can easily lead to a large number of top level functions and in order to avoid this it is advisable to create a Modelica package e g myFunctions and place ReadA inside this package The myFunctions package must be stored in the MODELICAPATH Provided this 1s done it then possible to call myFunctions ReadA from the command line or inside models without having to load any files first It 1s also possible construct pre compiled functions by selecting Translate in the menu of the function This constructs an executable and it 1s possible to call exactly as the non com piled function When calling functions from the command pre compilation automatically occurs for external functions Note The executable must be in the path for the command to be interactively callable It 1s not checked that the executable 1s up to date SIMULATING A MODEL 181 Debugging models Over specified initialization problems At translation Dymola analyses the initialization problem to check if it is well posed by s
217. nate system is defined with real num bers and does not depend on screen or window size A class may also have a grid specification which is used to make drawing operations easier Points defined by the user will jump to the nearest grid point Points read from a file are not snapped to the current grid Associated with every model class 1s also a default component size Components and con nectors dragged into the model class will initially have the default size but can be reshaped after insertion Specification The coordinate system can be defined by the user in the Graphics tab of Edit Attributes The default coordinate system grid and component size are either Inherited from a base class or Copied from the program defaults 100 100 to 100 100 with grid 2 2 The default component size is 20 20 Alignment of components in a diagram 1s facilitated by gridlines Gridlines are drawn for every 10th of the class grid points DEVELOPING A MODEL 113 Model editing Left mouse button se lects moves and re shapes Right mouse button presents a context menu Basic operations The default interaction mode known as select mode or pick mode is used both to select and move objects and also to connect connectors Other modes are temporary for example after inserting a component the program goes back to select mode Selecting objects Visible objects 1 e components connectors and g
218. nction that returns the sum of two real numbers Its implementation in ANSI ISO C is called ada2 c ifndef ADD2 C define ADD2 C double add2 double x double y return x y endif This function requires a declaration that provides a mapping between Modelica and C and also specifies the name of the file containing the implementation function add2 Sum of two numbers input Real x y output Real sum external C annotation Include include add2 c end add2 The first two declarations define the input and output arguments and their types 1n the Mod elica context The external declaration identifies this as an external function The types of the parameters in the external function must be compatible with the Modelica specification The Include annotation is a string which in this case includes the implementation of the function The contents of the Include string 1s inserted into the generated C code hence it should contain valid C code It can even contain eader line breaks in order to include sever al files or even preprocessor macros There is no guarantee that the header will only be in cluded once and thus necessary to guard against multiple inclusion with ifndef and endif wrapping The code add2 c should be located either in the current directory in a relative location include lt source add2 c gt or in directory dymola source Linking to external library For most application it is b
219. nd mYariable selection JV Automatically rescale plot to fit data Range v Erase plot when loading new file after simulation JV Automatically replot after simulation r Data set Number of results to keep 2 Time window from end s if gt 0 o Options tab Sets up options controlling plotted variables Automatically rescale plot to fit data when zoomed out When diagram is zoomed in automatic rescaling is disabled Erase plot when loading new file after simulation to have automatic erase of the dia gram when new results are load and thus when a simulation 1s run Automatically replot after simulation if not selected signals must be manually plotted after a simulation Number of results to keep when simulating Manually loaded results are not included Time window from end defines the size of the time window during online plotting 164 Range tab of the plot I Plot Setup window setup Signals Titles Legend Options Vertical range Min 2 Max fi 2 Logarithmic scale Horizontal range Min o Max fi 2 Logarithmic scale r Scaling Same horizontal and vertical axis increment Fit Plotted Data EUER Range tab Allows the user to define the minimum and maximum ranges of the axes and to select logarithmic scale instead of linear scale Other setings are Same horizontal and vertical axis increment may
220. nd Inertia Thermal provides models for heat transfer To get documentation for the entire Modelica Standard Library place the cursor on Modeli ca press the right mouse button and select Info Your web browser 1s directed to an html file containing documentation for Modelica This documentation has been generated automati cally from the Modelica description of the library There 1s basic information such as the content of the library conventions and conditions for use Dymola comes also with other free model libraries To have a list select File Libraries The package menu gives direct access to the sub libraries We will need components from various sub libraries We will need rotational mechanical components as well as electrical components for the motor To open the Modelica Mechanics click on Mechanics double click shows its text 44 Opening Modelica Me chanics A library window dis playing the Modelica Standard Library Dymola Dynamic Modeling Laboratory Modelica Text H File Edit Simulation Plot Animation Window Help la W SMX mova s gt th gt sa model Unnamed equation E Modelica Blocks EJ Constants e Electrical Icons Math Mechanics E Rotational Es Translational E Slunits y To get documentation on Modelica Mechanics as previously demonstrated place the cur sor on Mechanics press the right mouse button and select Info end U
221. nector You can then close this parameter screen and observe that input and output ports been added to the DymolaBlock corresponding to the inputs and outputs connectors in Dymola The name of the ports are the names of the Modelica input output variables The order of the graphical inputs and outputs correspond to the order in which they were added to the model Simulation 1s made in the usual way after connecting the input and output ports to other Simulink blocks and setting suitable tolerances and integration algorithm in Simulink If you want to recreate the example above you should also be aware that the parametriza tions differ between Modelica standard library models and Simulink blocks e g the fre quency of Simulink s Sine block 1s measured in rad s which 1s commonly known as angular frequency and should thus be 2 p1 times the frequency in the corresponding source in Modelica If you have not compiled all Dymola models used in the model you will get an error mes sage In that case double click on those blocks to bring up the forms and click on Compile Model 222 Dymola block after untitled Pala ES in d With named AA ports Bajacio e 0s us s1_signal p 1_signal s2_signal p 2_signal s3_signal p s4_signal DymolaBlock 1 1002 ode45 E Hierarchical Connectors as Buses Sometimes it 1s desirable to use buses for signals in Simulink
222. nference ESM 98 pp 9 18 Society for Computer Simulation International Manchester UK Tummescheit H and J Eborn 1998 Design of a thermo hydraulic model library in Modelica In Zobel and Moeller Eds Proceedings of the 12th European Simulation Mul ticonference ESM 98 pp 132 136 Society for Computer Simulation International Manchester UK 104 DEVELOPING A MODEL Developing a model This chapter describes the Dymola environment for developing models The general aspects of the Dymola main window are described first followed by a more detailed command ref erence Simulation of the developed model is described in Simulating a model on page 147 General concepts Window types Dymola uses two types of windows the main Dymola window and the library window that support different kinds of operations and also have different visual appearance Window modes The main Dymola window can operate in two modes Modeling and Simulation The mode of the window controls which operations are available and the default appearance of the window Going back to a previous mode restores its layout This chapter discusses the graphical editor 1 e the modeling mode The simulation mode is described in Simulating a model on page 147 DEVELOPING A MODEL 107 Window mode tabs Editor showing the icon layer The mode of the window is set by clicking on the tabs at the lower right corner of the Dy mola
223. ng event handling 2 Is an empty block included just for compari son 3 Is the total time spent between model evalua tions For these blocks we have only subtracted the overhead for their own timers and not for ad ditional timer calls that occur during their call Thus the total time all model evaluations should more accurately be around 5s 0 9s total overhead 4 1s We can also estimate this by first measuring the total CPU time before including profiling in this case 5s and sub tracting the time outside of the model evaluation block 3 we get 5s 0 933s 4 1s In this example the event iterations are insignificant compared to the rest even though there are 72 event iterations The remaining blocks are code blocks either system of equations including a trailing part of torn equations or blocks of non equations Among these blocks the major costs are block 8 which is a non linear equation for solving the angle of the cylinder and block 13 which is the linear system for the loop three un knowns Together they account for about 2 3s out of the models total of about 4 1s Thus these two blocks explain more than half of the time spent evaluating the model Since the model contains a kinematic loop this was as expected Note that block 5 has the largest average time of the normal blocks but no influence on the total CPU time This block consists of variables that are parameter dependent and thus are constant
224. ng comment STRING STRING APPENDIX MODELICA 245 annotation annotation class modification 246 APPENDIX ADVANCED MODELICA Appendix Advanced Modelica Declaring functions In Modelica it is possible to define and use functions and the functions be used in equations of a model in defining parameters and called interactively from the command line Functions inherently reduce the possibility for symbolic manipulations and should thus not be used unless necessary In particular index reduction requires that all functions are differ entiated which cannot be done in a straightforward way without help This help is pro vided in form of an annotation giving the derivative of the function The functions themselves can either be written 1n Modelica or as external functions in C or FORTRAN 77 In most cases the external function 1s provided in a binary library with a corresponding header defining the function User defined derivatives In order to reduce the index 1t 1s necessary to differentiate arbitrary expressions with respect to time This derivative must be very accurate 1n order to not introduce unnecessary numer ical errors The functions are seldom simple scalar functions from one scalar input but in APPENDIX ADVANCED MODELICA 249 stead have vectors and or records as input and several inputs and or outputs Often second order differentials are also needed For solving non linea
225. ng workstation which does not run in real time is represented by the console block shown below In this case several scopes are used to watch the output signals Input blocks could also have been used A special OpComm block must be inserted as well which represents data communication from the real time computers Even after these manipulations the Simulink model can be simulated in offline mode This helps verify that the model is correct before going to real time simulation 230 An RT LAB console block The RT LAB Main Con trol window Etrepor sccowo A File Edit View Simulation Format Tools Help Die S tele m Normal g Nb Overruns Eff step size Side acceleration Signals Y aw velocity Longitudinal speed Lateral speed Ready 10095 ode1 7 RT LAB setup The model is now ready for processing by RT LAB Most of the work is done through the RT LAB Main Control window The figure below shows the main control window after the Simulink model has been opened z RT LAB Main Control clutchtest mdl lol xi AAA Mu ID 5 C Util dymola work itlab clutchtest mdl m Model Selection Model Preparation r Model Execution Open Model Disconnect Target platform Execute m Utilities Tuis Probe Control Parameters Edit Configuration Store Embedded Compile Single step Assign Nodes Snapshot Fixed step size p 092 load _ Software synchro
226. nipulation The string manipulation routines are constructed for formatting numerical results as strings The routines are realString and integerString for converting numbers to strings and the Modelica built in operator that concatenate strings They behave as Modelica functions declared as function realString input Real number input Integer minimumWidth 1 input Integer precision 6 output String result end realString function integerString input Integer number input Integer minimumWidth 1 input Integer precision 1 output String result end integerString These functions are can be used for presenting results and for accessing a sequence of files SIMULATING A MODEL 175 r 12 3 Modelica scipting r realString number r Modelica scipting r 12 3 sumA 0 for i in 1 10 loop A readMatrix a integerString precision 2 number i txt A 2 2 sumA sumA sum A end for Script files Script files can be automatically constructed First select File Clear Log Then perform in teractively the operations by using menu commands or by entering written commands When done select File Save Log For Save as type select As script file mos see File Save Log on page 137 Dymola will record all written commands and also all menu commands that have an equivalent Modelica script function Since the script files are readable text files they can easily be cleaned up parameter v
227. nized y Time Factor fi Reset Close Apply Cancel jv Use model r Step size information The most important operations are located at the center of the RT LAB Main Control The Edit button opens the model in Simulink should any changes be required The Compile button processes the Simulink model and builds the target code with the help of Real Time Workshop The Load button initializes the QNX target s with the executable code and es tablishes communication channels The Execute button is used to run the model in real time As a side effect the Execute button starts Simulink with the console block active and receiving data from the real time nodes OTHER SIMULATION ENVIRONMENTS 231 RT LAB file transfer settings During model separation RT LAB creates new MDL files with new names and in a new di rectory These new files cannot be used to edit or compile the DymolaBlock press the Edit button in RT LAB Main Control to edit the original model File transfer settings Configuration settings are needed to set up processing and compilation of the model One important step is to setup the transfer of files from the console to the target compiling the model This 1s done by pressing the Configuration button and then selecting Advanced Files amp Commands Advanced Settings NEUTRINO xj Advanced seltings Real time communication Files amp Commands Compilation options Drive
228. nnamed Besides using the package browser of the Dymola window it 1s also possible to open a li brary browser It 1s done by either selecting Window New Library Browser or using the right mouse button and selecting Show Library Window Library Window E ModelicaAdditions i Unnamed mE m Blocks Constants Electrical Icons Librar 2 wj m x Math Mechanics A Library window includes a package browser where the components of the selected sub library are displayed in a special window Itis possible to close the package browser by toggling the button to the bottom left GETTING STARTED WITH DYMOLA 45 A library window dis playing the compo nents of the Modelica Standard Library Modelica Mechanics E Modelica package Modelica Mf x Constants Electrical Icons ex Mechanics Slunits By using the right button at the bottom 1t 1s possible to go up 1n the package hierarchy and by double clicking on the 1cons in the window it 1s possible to go down in the hierarchy The left and right arrow buttons allow going back and forth as in an ordinary web browser Open Modelica Mechanics Rotational in the library window by first double clicking on the icon for Mechanics S Mechanics package Modelica Mechanics 5 xi and then on the icon for Rotational It contains components for
229. no 5 no no 6 dopri8 ode no 8 no no 7 grk4t ode yes 4 no no 8 dassl dae yes 1 5 yes yes 9 odassl hdae yes 1 5 yes yes 10 mexx hdae no 2 24 no no 11 euler ode no 1 no yes 12 rkfix2 ode no 2 no yes 13 rkfix3 ode no 3 no yes 14 rkfix4 ode no 4 no yes 4 pues qmm te OSS Ph Oo See SSS Seed F euler and rkfix have fixed stepsize Method tuning parameters double method 27 1 T grid type of communication time grid defined by DYNAMIC MODEL SIMULATOR 209 Ru ca in 0 oror rre n 1 3 0 1 0 0 0 0 0 0 0 0 100 0 0 0 0 re 0 1 0e 014 1 00e 10 20 1 000000000000000E 006 1i T I 2473 Output parameters t settings 13 1 Tic cH dk dk Sk dk Sk Sk Se Se Sk ek Sk Sk SH Se e SE OSE dk SHE Sk Sk Sk SH e e Se SE SE dk dk Sk Sk Sk dk Sk Sk Sk Sk Sk Se e Se SE SR Se Se SHE nt dense evgrid evu evuord error jac xdOc F3 f4 f5 debug pdebug fmax ordmax hmax hmin ho teps eveps eviter delaym fexcep tscale shared lprec lx lxd lu ly lz equidistant points Increment nInterval 2 vector of grid points tgrid 3 variable step integrator automatically 4 model call of increment in Dymola e g incr Time gt 2 then 0 else 0 1 dummy increment incr 5 hardware clock functions udstimerXXX grid 1 3 is stopped by StopTime grid 2 is stopped by tgrid last grid 4 runs foreve
230. ns and equations of the class Window New Library Window Crates a new library window see Library window on page 110 Window New Dymola Window Creates a new modeling and simulation window Zooming By selecting a zoom factor more or less of the model is shown in the icon or diagram lay ers Selecting 100 will scale the model so the coordinate system fits in the window By se lecting a larger zoom factor parts of the model can be viewed in greater detail Scrollbars makes it possible to move around in the model Help menu Help What s This Displays interactive help for the graphical user interface After selecting help What s This the cursor changes Then click on the item in the user interface you want help on Help Contents Opens the online manual for Dymola Help Documentation Opens a web browser window with the root of the online documentation which contains the Dymola manual articles and links to other resources DEVELOPING A MODEL 143 Help Dymola support Opens a mail window for sending a message to the support staff at Dynasim Help Dynasim website Opens a web browser window with the Dynasim webpage Help About Displays copyright and license information about Dymola Special keyboard commands Delete Deletes the current selection Shift Enables multiple selection of objects Pressing Shift at the end of the connection operation negates the meaning of the automatic manhattanize o
231. ntire expres sion if one of the branches of the if expression contain any relations these relations should also be inside noEvent As an example consider the out commented part of the previous example where we use abs and sign for Ploss c When using that form 1t 1s easy to forget that not only abs but also sign generates events and only have noEvent surrounding sqrt Although it does generate errors we unnecessarily lose performance due to the sign events By having noEvent around the entire expression this 1s automatically handled Mixing noEvent and events in one equation There are no restrictions on using variables computed using noEvent to trigger events in other equations or to applying noEvent to expressions involving variables computed using events This allows a modeler to combine models independently of whether they internally use events or have turned them off using noEvent Sometimes it makes sense to mix noEvent and events in one equation This 1s however only allowed under certain restrictions since the number of active relations generating events can only change at events We would otherwise not be able to determine if the ex pression had changed value or not and thus would be unable to correctly determine when to trigger the event 262 Thus if the condition of an 1f expression 1f clause while clause or the indices of a for loop 1s a relation where events have been turned off by using noEvent the bodies should not c
232. ntrolDesk Developer Version layout lo x Xx Ele Edit View Tools Experiment Platform Instrumentation Parameter Editor Window Help x Mig L8 msc e Da ds Ue lm e o jo m n r amp Simulink B B Local System sl ds1005 olx 0 0020 5 0 0015 w 0 0010 IS 0 0005 Timer Task 1 turnaroundTime Timer Task 1 overrunCount 0 0000 Ma o 0 12 2 vehicle E E Model Root B sideAcceleration Floatleees4Ptr E yawvelocity Floatleees4Ptr Br longitudinalspeed gt Floatleees4Ptr E lateralSpeed Floatleees4ptr For Help press F1 RUN Num 2003 10 24 15 08 E Overrun An overrun situation may arise for several reasons as documented in the dSPACE manual Two additional cases are worth pointing out Event iteration in a model generated by Dymola may require additional CPU resources Whenthe model is downloaded to the dSPACE hardware the first time step must also per form the initialization of global data and the C runtime library In these cases it 1s usually helpful to plot the turnaround time a signal provided by the dSPACE system The turnaround time will show when additional resource are needed In many cases occasional overrun situations are harmless The RTI setup enables you to specify a number of instances of a task that may be queued before the realtime kernel 1ssues an overrun error This 1s done in the Real Time Workshop options
233. nuous Systems PhD thesis TFRT 1015 Department of Automatic Control Lund Institute of Technology Lund Sweden Elmqvist H 1992 An Object and Data Flow based Visual Language for Process Con trol ISA 92 Canada Conference amp Exhibit Instrument Society of America Toronto Elmqvist H F E Cellier and M Otter 1993 Object Oriented Modeling of Hybrid Sys tems Proceedings ESS 93 European Simulation Symposium pp xxxi xli Delft The Netherlands Elmqvist H D Br ck and M Otter 1996 Dymola User s Manual Dynasim AB Re search Park Ideon Lund Sweden Elmqvist H B Bachmann F Boudaud J Broenink D Br ck T Ernst R Franke P Fritz son A Jeandel P Grozman K Juslin D Kagedahl M Klose N Loubere S E Mattsson P Mosterman H Nilsson M Otter P Sahlin A Schneider H Tummescheit and H Vang heluwe 1998 Modelica TM A Unified Object Oriented Language for Physical Systems Modeling Version 1 1 1998 Modelica homepage http www modelica org Elmqvist H S E Mattsson and M Otter 1999 Modelica A language for Physical Sys tem Modeling Visualization and Interaction Proceedings of 1999 IEEE Symposium on Computer Aided Control System Design CACSD 99 Plenary talk Hawaii USA Elmqvist H S E Mattsson and M Otter 2000 Object Oriented Modeling and Hybrid Modeling in Modelica Proceedings of the 4th International Conference on Automation of M
234. o Run C Dymola bin dymola exe 1 mos Dymosim Windows application Dymosim can be compiled as a Windows application using an additional library with Win dows interface routines The advantage of running Dymosim as Windows application 1n stead of a console application is that Dymosim can act as a realtime DDE server Without any action from the user Dymosim will be built and executed in the usual way 1 e without realtime synchronization The noticeable differences are that the current simulation time 1s shown in the minimized Dymosim window and that the dymosim application has a Stop command Realtime simulation If the environment variable DYMOSIMREALTIME is defined Dymosim will start in real time mode where the simulation time 1s synchronized with real or wall clock time The time display will also include the time the simulation 1s delayed at each accepted output point in order to keep synchronized with real time A negative value indicates that the sim ulation 1s faster than real time 1 e that there 1s spare time for additional computations Dymosim DDE server Dymosim compiled as a Windows application will act as a DDE server allowing some oth er application to retrieve data values or set parameters Dymosim must be started before it can accept DDE operations MATLAB s ddeinit will not start Dymosim automatically for example A DDE connection is established by sending WM DDE INITIATE messages with the ap
235. o expanded b vector Real x n State vector equation Controllable canonical form der x 2 n x 1 n 1 a na der x 1 a 1 n x u y bO 1 n b0 na a na a 1 n x bO na a na u end TransferFunction It 1s also possible to have arrays of components and to define regular connection patterns A typical usage 1s the modeling of a distillation column which consists of a set of trays con nected in series The use of component arrays for spatial discretization when modeling heat exchangers is illustrated in Mattsson et al 1998 Class parameters Component parameters such as resistance values have been discussed Reuse of model li brary components 1s further supported by allowing model class parameters INTRODUCTION TO MODELICA 79 As an example assume that we would like to replace the PI controller in the motor drive model on page 73 by an auto tuning controller It is of course possible to just replace the controller in a graphical user environment 1 e to create a new model The problem with this solution 1s that two models must be maintained Modelica has the capability to instead substitute the model class of certain components using a language construct at the highest hierarchical level so only one version of the rest of the model 1s needed Based on the mod el MotorDrive on page 74 a model MotorDrive2 with redeclared controller 1s described as model MotorDrive2 MotorDrive redeclare AutoTuningPI contro
236. o model the real diode characteristic 1n the left part of the figure be cause the current i has just to be given as a function analytic or tabulated of the voltage drop z It is more difficult to model the ideal diode characteristic in the right part of the fig ure because the current at u 0 is no longer a function of u 1 e a mathematical description 86 Ideal diode model Simple rectifier circuit in the form i i u 1s no longer possible This problem can be solved by recognizing that a curve can also be described in a parameterized form i i s u u s by introducing a curve parameter s This description form is more general and allows us to describe an ideal diode uniquely in a declarative way as shown in the figure below i i 0 i ti MS Pac o gt u v tyv v v IT off s 0 u if off then s else 0 i if off then O else s In order to understand the consequences of parameterized curve descriptions the 1deal di ode 1s used in the simple rectifier circuit below ideal diode v 0 Collecting the equations of all components and connections as well as sorting and simplify ing the set of equations under the assumption that the input voltage v f of the voltage source is a known time function and that the states here v7 are assumed to be known leads to INTRODUCTION TO MODELICA 87 off s lt 0 u v v u if off then s else 0 ig if off then 0 else s R io
237. o perform some special action triggered when two real expressions have the same value This 1s not possible but it 1s for continuous varying variables equiva lent to triggering the condition as follows which 1s a part of car model where we want to terminate the simulation when the velocity 1s equal to 100km h Modelica SIunits Velocity velocity constant Modelica SIunits Velocity stopAt 100 3 6 equation when velocity gt stopAt velocity lt stopAt then if not initial then terminate Velocity is 100km h end if end when Assuming this is a normal test of accelerating to 100km h it 1s possible to remove the sec ond triggering condition velocity stopAt because we know that the original velocity is less than 100km h This also allows us to remove if statement Similar reasoning apply to many similar cases 266 Locking when equal In some models e g bouncing balls it is natural to enter another state when the relative ve locity is zero in order to avoid chattering By necessity this should not occur when the rela tive velocity is exactly zero but when it 1s small enough The first challenge 1s thus to guarantee that the ball stops bouncing in this case the second is that if we apply a relative force it should start bouncing anew A model demonstrating this 1s given below model BouncingBall import Modelica SIunits SIunits Height x start 1 SIunits Velocity v SIunits Force f parameter SIunits Mass m 2 para
238. odel problem model Check the model validity This corresponds to Check Model in the menus translateModel translateModel problem model Compile the model with current settings This corresponds to Translate Model in the menus simulateModel simulateModel problem model startTime 0 stopTime 1 numberOfIntervals 0 outputInterval 0 method dassl tolerance 1e 4 resultFile model Simulate the model for the given time Method is a string with the name of the integration method the names correspond to the ones found in the popup menu and the string is case insensitive Note that file extension 1s automatically added to resultFile normally mat For backwards compatibility the default for resultFile is dsres The entire command corresponds to Simulate 1n the menus closeModel closeModel Erases all model variables from the work space You have to call closeModel and reset all parameters and starting values to simulate the same model with different parameters and or start values importlnitial importInitial dsName dsfinal txt Sets up integration or linearization to start from the initial conditions given in the file in cluding start and stop time and choice of integration method The default is dsfinal txt which 1n combination with simulate corresponds to continue After calling importInitial it is possible to override specific parameters or start values be fore simulating Note Ba
239. odels improves simulation speed Use new state selection can give dynamic choices Generate listing of flat Modelica code in mof file Include a variable for elapsed CPU time during simulation Iv Warn about parameters with no default m Logging List continuous time states selected Log default connections Log selected default initial conditions Output information when differentiating for index reduction Output read classes to screen during parsing Store in model Cancel Evaluate parameters to have all parameters except top level parameters evaluated at translation 1n order to generate more efficient simulation code These parameters cannot be set interactively before a simulation run Generate listing of flat Modelica code in mof file to output a listing of all variable dec larations and equations Include a variable for elapsed CPU time during simulation introduces a new extra variable CPUtime with the accumulated CPU time during simulation The slope of this signal 1s an indirect measure of the computational complexity of the simulation Log default connections outputs diagnostics when unconnected connectors receive a de fault value according to the Modelica semantics This may help in finding an incorrectly composed model Log selected default initial conditions reports the result of the automatic selection of de fault initial conditions If initial conditions are missing Dymol
240. of informa tion is emitted for each class 1s controlled by another set of options DEVELOPING A MODEL 129 This is the suggested default mode Generate online documentation HTML documentation and associated bitmaps are created in the help subdirectory of the top level model or package A separate HTML file is also created for each subpackage Dy mola assumes this structure for references to other classes creating links to the he1p subdi rectories of each package This setting generates complete HTML with a full set of links without the need to create duplicate files Model changes require only local regeneration of HTML but all related models should be consistently documented in this way Generate HTML for referenced classes Complete HTML 1s generated for the model and all referenced classes The user will be asked for the filename of the top level HTML file all other generated files will be saved in the same directory This setting creates a directory with a complete set of files and no links to other directories thus ensuring maximum portability of the produced HTML Such a directory can easily be moved to a web server for example The main drawbacks are the storage overhead and the need to regenerate when any referenced model has been changed Generate links to online documentation Generates HTML in the file specified by the user and links to other libraries 1f the HTML files exist This mode is similar to Generate
241. omputed state variables x 1s comparable to the relative error tolerances The methods will usually but not always deliv er a more accurate solution 1f the tolerances are reduced By comparing two solutions with different tolerances one can get a fairly good idea of the true error at the bigger tolerances Variable step size dense output Most integration methods available in Dymosim have a variable step size algorithm At ev ery step a method estimates the local error The integration step size 1s chosen in such a way that the local error is smaller than the desired maximum local error defined via the rel ative and absolute tolerances This implies that usually smaller step sizes are used 1f small er tolerances are defined There 1s one important difference between integrators with respect to the step size algo rithm The step sizes of some integrators are not only influenced by the required tolerances but also by the communication time grid The communication time grid 1s defined by the StartTime the StopTime and a communication grid size and determines the points at which results must be stored The mentioned integrators just proceed from one grid point to the next one 1 e the maximum possible step size of these integrators is limited by the dis tance of two successive communication points The step size 1s always chosen in such a way that the integrator meets the grid points exactly For such methods the communication grid must b
242. on tain relations generating events They can of course depend on variables that are computed using events As a concrete example consider the following l ifx2 1 X 4 x ifx gt 0ax lt 1 2x ifx lt 0 Assuming that we do not want events when x passes through 1 an illegal example would be model ILLEGAL Real x start 2 equation der x if noEvent x 1 then if x gt 0 then x else 2 x else 1 end ILLEGAL In order to explain why this 1s illegal consider what happens after one second when x be comes less than one and x gt 0 is evaluated for the first time without triggering an event be cause of the noEvent The next 1f expression should trigger an event 1f x gt 0 does not have the value from the last event However we did not evaluate it at the previous event and thus we do not know rf it has changed value or not and thus we do not know when to trigger an event We are not allowed to evaluate the relations inside the wrong branch of the if expression since that might involve unsafe operations such as square roots of negative number index ing outside of bounds etc To solve this problem we can either surround the entire right hand side by noEvent or intro duce an auxiliary variable for if x gt 0 then x else 2 x Conditional use of events An extreme example of mixing noEvent and events is to have one variable control whether events should be generated or not This 1s only applicable if noEvent 1s introduced for p
243. on page 160 and then plot and or animate variables This makes it possible to determine if the result 1s correct or not We will assume that you have followed the steps above in particular that you have not 1g nored any warnings and errors detected by the translator and have tested each submodel in 1solation Event logging In order to determine if there 1s a problem with the discrete events one can turn on logging of events during a simulation By activating Event Logging one will see a log where each expression causing an event 1s logged see Debug tab on page 153 This makes it possible to track down errors in the discrete part of a hybrid system Model instability Instabilities often cause the simulation to stop with unphysical values after some simulated time In this case it is advisable to load the simulation result even if the simulation failed and also to store all simulated points by de activating Equidistant time grid see Output tab on page 152 since the integrator will store its steps and it generally uses more steps in problematic regions The first task 1s to determine which variable subsystem becomes unstable first since an 1n stability in one part can then spread to the entire system In almost all cases instabilities are found among the states of the system and can be more easily found by only storing the states of the system and plotting them It is also possible to linearize around various operating
244. on evaluations and computing time as with method DASSL MEXX MEXX is a variant of the MEXX family of codes to solve special index 2 differential algebraic equations with an optional integral invariant It uses a half explicit extrapolation algorithm of or ders 2 through 24 and 1s designed to integrate non stiff systems Presently it is not possible to use MEXX for the integration of ordinary differential equations Dymosim reference Model functions for Dymosim When user defined C functions are called from model equations a reference to the source code file for these functions needs to be put in a file userfunc c in the working directory include myfunc c In addition to the Modelica functions the functions min max are supported Pack Shape and PackMaterial are two functions provided to support visual objects The follow ing functions are also provided for inclusion in Dymola models when Dymosim 1s used as simulator status LogVariable x LogVariable is a function for helping tracking run time problems in models An equation like status LogVariable x It will give a message in the event log of the form DYNAMIC MODEL SIMULATOR 205 status ReadMatrix name M Read matrix with name name from data file dsdata mat into parameter matrix M status WriteMatrix name M Write matrix M into matrix with name name in a new data file with name name mat The following
245. on of class 76 113 diagram layer 111 142 differential algebraic equation 78 discrete equations 83 document 178 documentation HTML 113 of class 112 126 documentation layer 111 142 dongle 283 double clicking 114 116 121 124 dragging 115 dsin txt 207 dsmodel c 198 dSPACE 225 ControlDesk 227 overrun situation 228 turnaround time 228 duplicate class 110 duplicate objects 138 DXF files 167 dymodraw ini 143 296 DymolaBlock 220 DYMOLAGIFCON 137 DYMOLAPATH 143 Dymosim file 197 dsin txt 199 200 209 dsindef txt 200 dslog txt 198 dsres mat 198 199 213 dsu txt 199 200 dymtools 199 E edit menu change attributes 139 check 139 copy 138 cut 138 delete 138 draw shapes 139 duplicate 138 flip horizontal 139 flip vertical 139 manhattanize 139 options 141 order 139 paste 138 redo 138 rotate 139 select all 138 undo 138 edit window 108 114 ellipses 123 124 embedded HTML 128 encapsulated 127 Enhanced Metafile Format 136 environment space Windows 294 environment variables 137 286 equality comparison 266 equation 34 equations 125 eraseClasses 180 errors 182 event 85 logging 183 examples ideal diode 87 motor drive 73 77 motor model 74 polynomial multiplication 81 rectifier circuit 87 sampled data system 82 exit 138 experiment setup 37 export animation 137
246. onal repeat zero or more times The following lexical units are defined IDENT NONDIGIT DIGIT NONDIGIT NONDIGIT _ letters a to z letters A to Z STRING S CHAR S ESCAPE S CHAR any member of the source character set except double quote backslash X S ESCAPE OE Ne Ne NW A foit jp ye an me NER DIGIT 0 11 2 3 4 5 6 7 81e9 UNSIGNED INTEGER DIGIT DIGIT apr and APPENDIX MODELICA 239 UNSIGNED NUMBER UNSIGNED INTEGER UNSIGNED INTEGER e E UNSIGNED INTEGER Note string constant concatenation a Db becoming ab as in C is replaced by the operator in Modelica Modelica uses the same comment syntax as C and Java Inside a comment the sequence lt HTML gt lt HTML gt indicates HTML code which may be used by tools to facilitate model documentation Keywords and built in operators of the Modelica language are written in bold face Key words are reserved words and may not be used as identifiers Grammar Model definition model definition final class definition Class definition class definition partial class model record block connector type package function IDENT class specifier class specifier string comment composition end IDENT au name array subscripts class modification comment composition
247. ondition in Cartesian coordinates defined as x L sin phi y L cos phi If we define Real y start 0 fixed true the pendulum will start 1n a horizontal position However there are two horizontal posi tions namely x L and x L To indicate preference for a positive value for x we can define Real x start L 94 It means that we provide a guess value for numerical solvers to start from They will hope fully find the positive solution for x because it is closer to L than the negative solution For the angle phi there are many values giving the desired position because adding or sub tracting 2x gives the same Cartesian position Also here the start value can be used to indi cate the desired solution How critical it 1s to get a special solution depends of course on what phi will be used for in the model and the aim of the simulation If no start value is giv en zero is used Parameter values Parameters are typically given values in a model through definition equation or set interac tively before a simulation Modelica also allows parameter values to be given implicitly in terms of the initial values of all variables Recall the planar pendulum and assume that we would like to specify the initial position as Real x start 0 3 fixed true Real y start 0 4 fixed true This means that we in fact also specify the length of the pendulum to be 0 5 To specify that the parameter L shall
248. online documentation except that the HTML file 1s not automatically stored in the help directory It can for example be used to docu ment a model in a library during development before creating the final library documenta tion Do not generate external links HTML without any links to other files is generated This setting provides pretty printed documentation for a single model or package only HTML options The generated HTML code 1s controlled with regards to documentation contents references to other files and the size of graphics Class contents Controls what kind of information 1s included in the HTML file for each class This makes it possible to reduce the size of the documentation and hide certain parts such as the equations The parameter section is a tabular description of all parameters in cluding parameters inherited from base classes External references Controls what kind of HTML documentation is generated see above Diagram image size Bitmap images are not scalable and the best size depends on several factors e g the number of components complexity of graphics and the intended use of the documentation Dymola uses a combination of heuristic sizing and user control 130 The HTML options dia log default settings shown m Class contents Information Parameters Equations and components Diagram images Icon images Filename Syntax highlighting Xl 1 XI XI XI I I External re
249. onstruct Real x start x0 fixed true implies the additional initialization equation x x0 Thus the problem parameter Real a 1 b 1 parameter Real x0 0 5 Real x start x0 fixed true equation der x a x b has the following solution at initialization a 1 b ils x0 T 0 5 x x0 0 5 der x a x b 0 5 Initial equations and algorithms A model may have the new sections initial equation and initial algorithm with additional equations and assignments that are used solely in the initialization phase The equations and assignments in these initial sections are viewed as pure algebraic constraints between the initial values of variables and possibly their derivatives It 1s not allowed to use when claus es in the initial sections Steady state To specify that a variable x shall start 1n steady state we can write initial equation der x 0 INTRODUCTION TO MODELICA 91 A more advanced example is parameter Real x0 parameter Boolean steadyState parameter Boolean fixed Real x initial equation if steadyState then der x 0 else if fixed then x x0 end if If the parameter steady State is true then x will be initialized at steady state because the model specifies the initialization equation initial equation der x 0 If the parameter steady State 1s false but fixed 1s true then there is an initialization equation initial equation x x0 If both
250. or example robot axisl Another convenient way 1s to use the component browser and use the right button menu and select Show Component Since this 1s the first menu option double clicking will open up the component in the Diagram window Please recall that double clicking on a component in the diagram window pops up the parameter dialogue bus contro motor gear The drive train includes a controller A data bus 1s used to send measurements and reference signals to the controller and control signals from the controller to the actuator The bus for one axis has the following signals angle ref reference angle of axis flange angle angle of axis flange Speed ref reference speed of axis flange Speed speed of axis flange acceleration ref reference acceleration of axis flange acceleration acceleration of axis flange current ref reference current of motor current current of motor motorAngle angle of motor flange motorSpeed Speed of motor flange There are send elements to output information to the bus as illustrated in the model diagram above Similarly there are a read elements to access information from the bus GETTING STARTED WITH DYMOLA 29 The robot controller The bus from the path planning module is built as an array having 6 elements of the bus for an axis gain2 k ratio gain1 P add3 Pl feedba k ratio e speed ref angle motorAngle motorSpeed jar jueuno bus
251. or model Select in the Dymola window File New Model Enter Motor as name of the new model To have the Motor model being a part of DriveLib we need to enter DriveLib for Insert in package This can be done in several ways Dymola pro vides alternatives to be selected from and DriveLib is an available alternative The are no other alternative because all other open packages are such as Modelica are write protected It 1s also possible to use the drag and drop feature and drag DriveLib into the slot In the package browser put the cursor on DriveLib and press the left mouse button While keep ing it pressed drag the cursor to the slot for Insert in package release the button and the text DriveLib will appear 1n the slot EXT SS ixl Name of new model M otor Description e Partial Extends optional m Insert in package optional zi DriveLib Cancel Click on OK Opening DriveLib in the package browser shows that it has a component Motor as desired 50 An empty Motor model The finished motor model with all compo nents El Motor DriveLib Motor Diagram amp File Edit Simulation Plot Animation Window Help l x ls B amp WINDOVA 4 Sa Hh Ze gt BHn z Constants e Electrical Icons Math Mechanics E Slunits EJ Modelica amp dditions nnamed JDriveLib DriveLib Motor
252. ore x state variables 0 1 do not store xd derivative of states 0 1 do not store u input signals 0 1 do not store y output signals 0 1 do not store z indicator signals 210 lw 0 1 do not s la 0 1 do not s 0 lperf 0 1 do not s 0 levent 0 1 do not s lres 0 1 do not s 0 lshare 0 1 do not s shared memory on dsshare txt lform 0 1 ASCII Mat results it Names of initial variables char initialName 9 8 CS R R EV C der v G p v G p i C n v C n d R p v double initialValue 9 6 mae UE x0 95 20 0 F 626 EL aks Oy 0 tl c0 R R 1 d Q O 2 0 C v 9 Or Ol 40 33 50 C der v 0 Or 20 07 76 UO G p v 00 Oe 000 6 50 G p i Qr OF 0 107 r6 0 C n v 0 0 OQ 0 6 0 F C n i 0 0 0 0 6 0 R p v for simulation linearization core tore a core core Lore Lore Ww auxiliary signals alias signals performance indicators event point results on result file info data for lab binary storage format of not for trimming value initial value Matrix with 6 columns defining the initial value calculation columns 5 and 6 are not utilized for the calculation but are reported by dymosim via dymosim i for user convenience it column 1 Type of initial value 2 special case for continuing simulation column 2 1 fixed value column 2 fixed value 0 free value i e no restriction column 2 gt 0 desir
253. pes are specified as DXF files AutoCAD R12 LT2 format only 3DFace 1s supported External shape must be named like 1 2 etc The corresponding definitions should be in files 1 dxf 2 dxf etc Since the DXF files contain color and dimensions for the individual faces the correspond ing information in the model is currently ignored but the specular coefficient 1s utilized The DXF files are found relative to the directory of the current model Material 4 r g b specularj specifies the color of the object r g b affects the color of diffuse and ambient reflected light Specular is a coefficient defining white specular reflec tion Note r g b and specular are given in the range 0 1 Specular 1 gives a metallic ap pearance The position r and orientation S are inputs to control the movements of the object An ex ample showing some of the available shapes 1s given below model shapes parameter Real r 3 0 0 0 parameter Real Length 0 2 Width 0 2 Height 0 2 parameter Real LengthDirection 3 1 0 0 parameter Real WidthDirection 3 0 1 0 VisualShape vl r0 r 0 0 5 0 Shape box Length Length Width Width Height Height LengthDirection LengthDirection WidthDirection WidthDirection VisualShape v2 r0 r 0 4 0 5 0 1 Shape cylinder Material 0 1 0 0 75 VisualShape v3 r0 r 0 8 0 5 0 2 Shape cone Material 0 0 1 1 VisualShape v4 r0 r
254. plication name dymosim any topic can be used MATLAB example channel ddeinit dymosim xxx After a Stop command or at the end of simulation Dymosim will send a WM DDE TERMINATE message MATLAB example ddeterm channel Note that all transactions between the Dymosim DDE server and the DDE client are logged in the Dymosim window They can also be logged on file 234 Simulator commands The following commands can be sent to Dymosim using WM DDE EXECUTE messages run Start simulation 1f simulation 1s not started automatically or resume simula tion after a pause command stop Stop simulation pause Pause simulation The simulation 1s temporarily halted until a run com mand 1s given Note that DDE requests are handled while pausing logon Enables logging to file 1f logging 1s off logoff Disables logging to file 1f logging is on MATLAB example ddeexec channel run If the environment variable DYMOSIMLOGDDE 1s defined a file logging all DDE com munication to from the simulator 1s created when the program starts Setting parameters Parameters may be set by sending a WM DDE POKE message with the name of the pa rameter and its new value the string representation of a number There are four special variables realtime_ Set to 1 to enable realtime mode or to 0 to disable realtime mode tscale The scale factor between simulated time and real
255. plitting the problem into four equation types with respect to the basic scalar types Real In teger Boolean and String and decides whether each of them are well posed If such a prob lem 1s over specified Dymola outputs an error message indicating a set of initial equations or fixed start values from which initial equations must be removed or start values inactivat ed by setting fixed false Dymola stops translation when an overspecified problem is found It may be the case that this subproblem also has under specified parts 1 e variables that cannot be uniquely deter mined Moreover the subproblems for the other data types may also be ill posed To find this out try to correct the reported problems by removing initial conditions and retranslate to check for additional diagnostics Basic steps in debugging models When constructing models they sometimes generate incorrect results fail to simulate fail to start fail to translate or simply take too long to simulate The ideal situation would be to avoid this problem altogether The 1deal 1s not achievable but some simple rules that reduce the possibility of errors are Use tested libraries Modelica Standard Library and available libraries for Hydraulics PowerTrain Sampled systems MultiBody etc Construct test examples for each model in 1solation Design models for testing e g introduce variables for quantities that are easy to interpret use 3D animation for 3D mechanic
256. points in order to determine the stability of the linearized system By examining the eigenvalues it is in general possible to track down the instability to some state Thus the problem 1s localized to one part of the model and the next step is to correct that submodel In many cases the cause of the problem is a simple sign error in one equation ei ther in a user written equation or in a connection equation due to not using the flow at tribute correctly in the connectors of that model SIMULATING A MODEL 183 Storing the result takes time Improving simulation efficiency We will in this section assume that the model runs generates the correct results but runs too slowly Before the simulation 1s complete one can examine the result by explicitly loading the result file dsres mat and then plot and or animate variables This makes it possible to determine 1f the result 1s correct or not A slow simulation can be caused by either to too much work spent on each time step each step 1s too short and thus too many steps are taken or because of the overhead with storing the result to a file A first step 1s plotting the CPU time to determine 1f the problem occurs at some particular time due to the model behavior at that point Time of storing result One important aspect of a simulation in Dymola 1s to generate results in a file In some cas es the storing of the result and not the integration 1s the cause of the slow simula
257. ponents and extends clauses in the component browser This makes it possible to directly change inherited parameters In the General tab the first section shows the name of the component or connector and the component specific comment The second section shows the full path of the corre sponding class and the class specific comment The icon is shown on the right The rest of the modifier window contains the modifiers of the component or connector For a component or connector that 1s not read only name comment and modifiers can be changed provided the component or connector 1s found at the top level in the component browser Note that it is possible to set parameters even 1f the component or connector is not at the top level these are stored as hierarchical modifiers The parameters of the modifier window can be structured at two levels The first level con sists of Tabs which are displyed on different pages of the window The second level is a framed group on the page Different variables with the same Tab and Group attributes are placed together 116 A modifier window A modifier window for multiple selection E clutch1 in CoupledClutches 2 x Add modifiers ponent Icon Name ciutcht x Comment mua nm aa m Model Clutch Path Modelica Mechanics Rotational Clutch Comment Clutch based on Coulomb friction r Parameters mue pos w mue positive sliding friction coefficient w_rel gt
258. ption Ctrl F1 and Ctrl F2 Changes window mode see Window Mode Modeling Ctrl F 1 on page 142 Arrow keys In the diagram and icon layers selected graphical objects can be moved by pressing the ar row keys See also Moving objects on page 114 Model editor initialization The initialization script file called dymodraw ini contains commands that are executed at program startup to configure the model editor for a particular user A default file is pro vided with Dymola and the user may create a customized file based on the default file for example to add more library windows Dymola uses the environment variable DYMOLAPATH to locate dymodraw ini The con tents 1s a list of directories separated by space or Dymola will search for these files in the current directory then in each of the directories specified in DYMOLAPATH and finally in the default Dymola directory Filenames may begin with a reference to an environment variable in the following form SDYMOLA insert dymodraw ini The current value of environment variable DYMOLA is substituted for DYMOLA In addition to the commands described below comments can be inserted Any text from the character until the end of the line is regarded as a comment 144 SIMULATING A MODEL Simulating a model Basic steps This chapter describes how to simulate a Modelica model in Dymola First the basic steps in setting up a simulation running 1t and plotting and
259. ption pp O 7 A Partial Extends optional m Insert in package optional zi V Save contents of package in one file Cancel Enter DriveLib as the new name of the package and click OK and Accept in the informa tion window 48 An electrical DC motor E DriveLib DriveLib Modelica Text File Edit Simulation Plot Animation Window Help l x li Si m e A package DriveLib Blocks end DriveLib z Constants e Electrical Icons Math Mechanics E Slunits ModelicaAdditions nnamed A package DriveLib 1s created and made visible in the package browser Select Modelica text to get the Modelica representation which at this stage just specifies a package with no contents Creating a model for an electric DC motor GETTING STARTED WITH DYMOLA 49 Inserting Motor in Driv eLib A model of the complexity indicated above will be developed for the electric DC motor For simplicity the voltage supply is included in the motor model The model includes an ideal controlled voltage source The electric part of the motor model includes armature resistance and armature inductance The electromotive force emf transforms electrical energy into ro tational mechanical energy The mechanical part includes the mechanical inertia of the mo tor Let us start building the mot
260. r IV Include protected classes in package browser Window menu Toolbar gt 05858 a The toolbar contains buttons showing the previous and next model viewed in the window and for viewing different layers of the model see also Class layers on page 111 The last control sets the zoom factor Recent Models Clicking on the button displays the previous top level model shown in this window Repeat ed clicks on this button toggles between the two most recently shown models Clicking on the down arrow displays a menu with recent model to allow arbitrary selection Window Mode Modeling Ctrl F1 Changes window to modeling mode This mode 1s used to compose new models or to change existing models Window Mode Simulation Ctrl F2 Changes window to simulation mode This mode is used to set up an experiment and simu late a model The results can be plotted and visualized with 3D animation 142 Previous Next Icon H Diagram i Documentation B Modelica Text 100 y Window View Previous Shows the previous model viewed in the editor Window View Next Shows the next model selected if Window View Previous has been used before Window View Icon Displays the icon layer of the class Window View Diagram Displays the diagram layer of the class Window View Documentation Displays the description and documentation of the class Window View Modelica Text Displays the declaratio
261. r stopped by model grid 5 runs forever stopped by udstimer Use every NT time instant if grid 3 1 2 3 restart step interpolate GRID points 0 1 do not save event points in comm time grid 0 1 U discontinuity does not trigger events Oy T Sese 0 1 2 One message warning error messages U discontinuity order to consider 0 1 Compute jacobian numerically by BLOCKJ 0 1 Compute set XDO 0 1 Ignore use F3 of HDAE index 1 0 1 Ignore use F4 of HDAE index 2 0 1 Ignore use F5 of HDAE invar 0 1 do not print debug information T5190 if gt 0 priority of debug information aximum number of evaluations of BLOCKF aximum allowed integration order if gt 0 if gt 0 if gt 0 aximum absolute stepsize inimum absolute stepsize use with Stepsize to be attempted on first step if gt 0 Bound to check if 2 equal time instants Hysteresis epsilon at event points aximum number of event iterations inimum time increment in delay buffers 0 1 floating exception crashes stops dymosim clock time tscale simulation time if grid 5 gt 1 simulation too slow 1 simulation time real time lt 1 simulation too fast type of process communication if grid 5 no communication single process without clock no communication single process with clock multiple processes with clock if shared 2 shared memory key to be used for shared memory 0 1 do not store result data in double 0 1 do not st
262. r algebra can be utilized to achieve as efficient simulation code as if the model would be converted to ODE form manually For example define a gearbox model as model Gearbox Ideal gearbox without inertia extends TwoFlange parameter Real n equation a r n b r n a t b t end Gearbox without bothering about what are inputs from a computational point of view and use it as a component model when modeling the drive system on page 73 This use actually leads to a non trivial simulation problem The ideal gearbox is rigidly con nected to a rotating inertia on each side It means the model includes two rigidly connected inertias since there is no flexibility in the ideal gearbox The angular position as well as the velocity of the two inertias should be equal All of these four differentiated variables cannot be state variables with their own independent initial values A DAE problem which includes constraints between variables appearing differentiated is sometimes called a high index DAE When converting it to ODE form it is necessary to differentiate some equations and the set of state variables can be selected smaller than the set of differentiated variables There is an efficient algorithm by Pantelides 1988 for the determination of what equations to differentiate and an algorithm for selection of state vari ables by Mattsson and S derlind 1993 In the drive example the position constraint needs to be differentiated t
263. r and one grid squares high In the window prompt for GETTING STARTED WITH DYMOLA 55 Model attributes Documentation View the string enter Yoname The sign has the magic function that when the model is used the actual component name will be displayed We have now edited the icon and the diagram It 1s also important to document the model When creating the model the dialog has a slot Description It is possible to edit this after wards Select Edit Attributes to open the dialogue El Change attributes for Motor 2 x General Graphics r Description la basic model of an electrical de motor m Restricted class C Class C Block Model C Function Connector C Package Record m Properties Encapsulated Partial Protected Replaceable m Dynamic typing Normal C Inner C Outer Cancel Enter a description and click OK A longer documentation can be provided in the following way Click on the toolbar button for Documentation the button between the Diagram button and the Modelica Text button EI Motor DriveLib Motor Documentation EN File Edit Simulation Plot Animation Window Help la del metA ih z gt 8 BE J Name Motor Path DriveLib Motor E EJ Modelica Description A basic model of an electrical de motor To enter a description put the cursor in the window Click right mouse button and selec
264. r example to draw a filled area without border Line Style gt Thickness F Line style solid dashed dotted dash dot or dash dot dot Arrow Thickness single double or quad Arrow style none start end both or harpoon Fill style d The fill style attributes are No Color Colors Color or no color for example to draw a rectangle Fill Pattern gt Gradient gt Fill pattern solid left diagonal right diagonal or cross pattern Gradient flat horizontal vertical or spherical Modelica text Modelica text such as declarations equations and algorithms are edited in the Modelica text layer By default it contains the Modelica text for declarations of non graphical components of the class e g constants parameters and variables and equations of the model Modelica text layer E Revolute ModelicaAdditions MultiBody Joints Revolute Read Only Modelica Text El X H Eie Edit Simulation Plot Animation Window Help 81 x lc eM met A idx szle m2BHDnv 3 1 SIunits Angle q final fixed startValueFixed SIunits AngularVelocity qd final fixed startValueFixed Interfaces SIunits ngularAcceleration qdd Joints A Revolute SIunits ngle qq aijt Prismatic Real nn 3 Real sing Real cosq equation axis phi q bearing phi 0 define states qd der q add der qd f rotation ma
265. r inPort must be compatible with the connector of Vs inPort There 1s a simple au tomatic to get a connector inPort that is a clone of Vs inPort Start drawing a connection from Vs inPort and go to the left until you reach the border of the grid Then you double click and select Create Connector from the menu popped up The connector flange b is cre ated in a similar way If you would like to adjust the position of a connector it 1s easy to get into connect mode This can be avoided by toggling the toolbar button Connect Mode to the right of the Toggle Grid button Click on the toolbar button to left of the button for activating the Diagram view to find that you also there can see 1cons for the connectors Let us draw an 1con for the motor mod el One design is shown below name To draw it we will use the toolbar for editing graphics INDOGA SB Br Start by drawing the big red cylinder shaded rectangle Click the Draw rectangle button yellow rectangle and lay out a rectangle Let it be selected Click on the arrow to the right of the Fill Color button Select Colors and then select a red color Click OK To select the gradient click once again on the arrow to the right of the Fill Color button Select Gradient Horizontal Draw the rest of the parts using draw rectangle or draw closed polygon in an analogous way To enter the text click the Text button the button labeled A and lay out a rectangle that 1s as long as the cylinde
266. r system of equations derivatives can also increase performance by allowing us to compute an analytical Jacobian To allow this we have an annotation that defines the derivative of a one function and Dy mola can use this both to reduce the index and to compute Jacobians for non linear system of equations This 1s defined as an annotation declaring the derivative function for the given function and it can be given both for functions written in Modelica as well as for external functions How to declare a derivative The following define how to declaring the derivative to a function and finally how to verify that the derivative 1s consistent with the function It 1s strongly influenced by forward mode automatic differentation and well suited for differentation with respect to one variable as in index reduction It can furthermore be used to efficiently compute all interesting derivatives in a straightfor ward way as will be explained later A function declaration can have an annotation derivative specifying the derivative function with an optional order attribute indicating the order of the derivative default 1 e g function f0 annotation derivative f1 end 0 function f1 annotation derivative order 2 f2 end f1 function f2 end f2 It 1s also necessary how to write the derivative function for a given function this 1s de scribed in a procedural form below and with examples that make it more clear The lookup for the deri
267. raphical primitives are selected with the left mouse button Many commands operate on the current selection one or more objects marked with small red squares at the corners called handles The component browser also indicates selected components The procedure for selecting objects in the diagram or icon layers 1s as follows Clicking on an unselected object makes this object selected and the previous selection 1s unselected Clicking on an unselected object while holding down the Shift key toggles the select sta tus of this object without unselecting the previous selection Multiple objects can be selected by pressing the left mouse button with the cursor between objects and then moving the mouse while holding the left button down to span a selec tion rectangle All objects inside the selection rectangle are selected and the Shift key has the same effect as described above e Clicking on a selected object does not change the current selection if Shift is not pressed Components can also be selected by clicking in the component browser In an edit window double clicking on an object opens a dialog with additional information For components and connectors several attributes may be changed see Modifier window on page 116 See also Edit Select All on page 139 Context menus Pressing the right mouse button usually presents a menu with operations suitable for the se lected object Context menus are presen
268. ration Say that two rotating bodies are connected by a spring such that the relative distance between them are 1 and that their angular speed is 1000 If the positions are calculated with a relative accuracy of 0 001 after one second there 1s hardly any accuracy 1n calculating the distance by taking the difference The difference behaves irregularly and gives an irregular torque The simulation stops It 1s very difficult for a tool to find this out without actually doing simulation runs Model developers for mechanical systems and power systems know it very well It would be easy for them to indicate that absolute positions are bad choices when selecting states Efficiency by avoiding inverting functions The relations between possible sets of state variables may be non linear For some choices it may be necessary to invert non linear functions while for another set it 1s straightforward to calculate others A typical example 1s thermodynamic problems where you have property functions They often assume two variables to be inputs for example pressure and enthalpy and calculate other properties such as temperature density etc Thus 1f such variables are selected as state variables it is simply calling property functions to calculate other need variables If not it is neces sary to solve equation systems to calculate the input variables A model library developer knows this and it 1s straightforward to him to indicate good choices when sele
269. rawn at right angles If automatic manhattanize 1s enabled connections are manhattanized immediately when created moved or reshaped If automatic manhattanize 1s on moving a component automat ically manhattanizes all connections to the component When a connection has been defined some checks are performed automatically Aconnection that begins and ends at the same connector 1s not allowed DEVELOPING A MODEL 121 Create Connector Create Node Cancel connection Nested connector dia log Two connections between the same connectors are not allowed The connectors at each end of the connection are checked for compatibility The case of nested connectors 1s described below If any other incompatibility 1s detected the error message displays the declarations of the two connectors The connection can then be can celled When drawing a connection the default color 1s taken from the starting connector The con nection gets the color of the outline of the first rectangle polygon or ellipse in the icon layer of the starting connector This change facilitates color coding of connections depending on the type of connector Note that drawing a line between two connectors see line drawing below does not create a connection Context menu while connecting Pressing the right mouse button or double clicking the left mouse button while the connec tion 1s being draw presents a menu with these choices Create Connector Cre
270. rder to compile the model for dSPACE you also have to modify the makefiles The rec ommended practice for dSPACE is to change the model usr mk The easiest way to cre ate a model usrmk is to build the application according to the instructions in the dSPACE documentation which will fail because additional files from the Dymola distribu tion are unavailable i RTI Build Check vehicle 0 x View Font Size Message Source Summary e MHE Error executing build command Error using gt make_rtw Q vehicle Error executing build command Error using gt make_rtw Error using gt rtw c Make process failed while compiling linking or loading Detailed error messages are printed in the MATLAB Command Window Aborted RTI build procedure for model vehicle Open Help Close After modifying the generated lt model gt _usr mk the build process should succeed The vi tal settings are additional source files and directories For a DS1005 system the changes are Additional C source files to be compiled USER_SRCS dymc c dymf c amat c usertab c Directories for C source files USER_SRCS_DIR dymola source Path names for user include files USER_INCLUDES_PATH dymola source 226 Compiler options for dSPACE RTI For dSPACE release 3 4 one more option must be set in the user makefile For your conve nience DYMOL A mfiles tmf appl usr mk contains an example for dSP
271. re a Modelica interface This declaration provides the required information needed to call the function from a Mod elica model and in some simple cases provide argument conversion External functions are declared as Modelica functions but with a body that defined the in terface The Modelica specification defines the details of how function arguments in Mod elica are mapped to similar data types in C and how values returned from the functions are mapped back to Modelica types When the interface of the external function does not match the Modelica specification a wrapper function must be written in C to perform the required conversions APPENDIX ADVANCED MODELICA 253 This section refers only to the Windows version of Dymola In most cases the external function 1s provided in a binary library with a corresponding header file declaring the function In order to support this one can specify a header overrid ing the usual definition of the function and a library that will automatically be linked with Including external functions In simple cases 1t is possible to translate the C code of the function with the model itself The main advantage of this approach is that it does not require any additional effort to build a library The disadvantage 1s that definitions 1n the implementation of the C function may interfere with the generated model code and cause the compilation to fail As an example we will use the following trivial fu
272. reas INTRODUCTION TO MODELICA 81 Sampled data system In Modelica the central property is the usage of synchronous differential algebraic and dis crete equations The idea of using the well known synchronous data flow principle in the context of hybrid systems was introduced in Elmqvist 1993 For pure discrete event sys tems the same principle 1s utilized in synchronous languages Halbwachs 1993 such as SattLine Elmqvist 1992 Lustre Halbwachs 1991 and Signal Gautier et al 1994 in order to arrive at save implementations of realtime systems and for verification purposes Synchronous equations A hybrid Modelica model basically consists of differential algebraic and discrete equa tions r T u y controller lt plant T A typical example is given in the figure above where a continuous plant dx aes f x p y gxy 1s controlled by a digital linear controller xt Ax T B r t y 1 ut Cxjt T Dart yo using a zero order hold to hold the control variable u between sample instants 1 e u t u rj for t t t T where T is the sample interval x is the state vector of the continuous time plant y t is the vector of measurement signals x 1s the state vector of the digital controller and r 1s the reference input In Modelica the complete system can be easily described by connecting appropriate blocks However for simplicity of the fol
273. result on file dsres txt 208 Dymosim input file dsin txt A default version of the Dymosim input file is generated by command dymosim i in ASCII format The Dymosim input file currently have the following structure input file of a simple circuit model The dymosim program is also able to read old versions of this for mat and the file format 1s continuously extended with additional settings Since the files are self documenting the best documentation can be found by generating it by dymosim i and reading the comments 1 char Aclass 3 24 Adymosim 1 4 Modelica experiment file Experiment parameters double experiment 7 1 0 StartTime Time at which integration starts and linearization and trimming time 1 StopTime Time at which integration stops 0 Increment Communication step size if gt 0 500 nInterval Number of communication intervals if gt 0 1 000000000000000E 004 Tolerance Relative precision of signals for simulation linearization and trimming 0 MaxFixedStep Maximum step size of fixed step size integrators if gt 0 0 8 Algorithm Integration algorithm as integer 1 14 it it model dense state Algorithm typ stiff order output event 4 4 4 4 4 deabm ode no 1 12 yes no iy uu lsodel ode no 1 12 yes no 3 lsode2 ode yes 1 5 yes no 4 lsodar ode both 1 t52 1 5 yes yes 5 dopri5 ode
274. ribute A variable being subtype of Real variable has an attribute stateSelect to indicate its possible use as state variable Its value can be never Do not use as a state at all e avoid Avoid it as state in favour of those having the default value default If the variable does not appear differentiated in the model this means no prefer Prefer it as state over those having the default value always Do use it as a state 258 The values of the stateSelect attribute are to given as Real y stateSelect StateSelect never Real y stateSelect StateSelect avoid Real y stateSelect StateSelect default Real y stateSelect StateSelect prefer Real y stateSelect StateSelect always The two extreme values never and always have clear and context independent meanings If stateSelect 1s always the variable will be a state If such a variable does not appear differen tiated in the model the index reduction procedure will differentiate equations in order to be able to calculate the derivative A model with two variables x and y with attribute stateSe lect being always and being algebraically constrained is thus erroneous It 1s compulsory for variables appearing as arguments in reinit expressions It supports explicit control of the selection of states and gives the user full control It eliminates use of dynamic state selec tion A dynamic state selection problem should only include variables having stateSelect
275. rings the selected objects to the front so they are not obstructed by any other objects Send to Back Sends the selected objects to the back behind all unselected objects Bring Forward Brings the selected objects one step forward Send Backward Send the selected objects one step backward DEVELOPING A MODEL 139 DX i a ctangle m pi 0 ipse ID I olygon IE ac x E itmap Toggle Grid SHEO Connect Mode Edit Manhattanize Applies a Manhattan algorithm to make selected lines and connections more pleasing Non endpoints are moved to make all line segments horizontal or vertical Edit Rotate 90 and Edit Rotate 90 Rotates the selected components 90 degrees clock wise counter clock wise Edit Flip Horizontal and Edit Flip Vertical Flips the selected components left right up down Edit Check Checks the class in the current window for errors The class is checked for syntactic errors references to undefined classes and the consistency of equations No simulation code is generated Edit Draw These are the commands to interactively draw new shapes and related setup See also Cre ating graphical objects on page 123 Drawing graphical shapes line rectangle ellipse polygon text and bitmap Show gridlines to make alignment of objects easier Toggle connect mode see Connections on page 121 Edit Attributes The General tab contains options re
276. rismatic The following parameters are used to define the joint ate Screw zi E reed i fa E K n Axis of rotation resolved in frame a same as in frame b n must not necessarily be a unit vector E g Components n 0 0 1 or n 1 0 1 E Modelica amp dditions MultiBody Joints Revolute q0 Rotation angle offset in deg If q q0 frame a and frame b are identical Wi TreeJoint Modelica amp dditions MultiBo startValueFixed true if start values of q qd are fixed Wi axis Lm bearing ModelicaAdditions MultiBody Joints Revolute Modeling y Simulation Z A Context menu when viewing Pressing the right mouse button presents a context menu with common text operations Most of these operations are also available in the Edit menu Copy Copies text from the documentation layer to the clipboard Select All Selects all text in the documentation layer Find Find and replace text in the text editor Enter the text you search for and press OK Goto Line Sets cursor at specified line and scrolls window 1f necessary Edit Source Switches the documentation layer from viewing mode to editing mode see below Editing description The description string is edited by selecting Edit Attributes from the menubar It also possi ble to modify other attributes of the class and to select 1f the class 1s stored in one file or hiearchically see Edit Attributes on page 140
277. rt components into a model by dragging components from library windows to an edit window Double clicking on a model or a nested package opens it The library window can show a tree view of the package an icon view of the package or both Library windows do not allow editing and there 1s no toolbar El Joints package ModelicaAdditions MultiBody J E ni x Pus ph idw XI Revolute Prismatic Screw Cylindrical D 6 Lo Universal Planar Spherical FreeMotion Modifier window Modifiers of a component and possibly its sub components are viewed and modified us ing a modifier window It also shows the name icon comments and full path of the corre sponding model See also Modifier window on page 116 110 A modifier window Add modifiers Component Icon Name feluteht Y Comment mua oum aa r Madel Clutch Path Modelica Mechanics Rotational Clutch Comment Clutch based on Coulomb friction r Parameters mue pos HE w mue positive sliding friction coefficient w_rel gt 0 peak NENNEN peak mue pos 1 2 maximum value of mue for w_rel 0 cgeo 0 Geometry constant containing friction distribution assumption n max 20 gt N Maximum normal force w small J rad s Relative angular velocity near to zero see model info text DK Info Cancel Class layers Edit windows use four layers to represent different aspects of a class The first
278. rting similar models Use that as starting point and at the end add the following lines and remove similar ones openModel myNewModel mo checkModel myMode1 If you are starting from scratch use the following as a template clear Start End openModel myNewModel mo checkModel myModel Converting class names Inthe Dymola main window select File Clear Log and select File Run File Script to run Convert mos There will be error messages such as Error Component type specifier Shaft not found Go through all these message and list all model types that are missing For each missing type find the new one in Modelica Mechanics Rotational You can do that by opening both libraries and comparing 1cons and reading documentation For com ponent Shaft we select Modelica Mechanics Rotational Inertia APPENDIX MIGRATION 275 d 9 Use a text editor to edit Convert mos with a contents as clear Conversion of not found Component type specifiers convertClass Shaft Modelica Mechanics Rotational Inertia convertClass Clutch Modelica Mechanics Rotational Clutch convertClass Gear Modelica Mechanics Rotational IdealGear openModel myNewModel mo checkModel myModel Inthe Dymola main window select File Clear Log and select File Run File Script to run Convert mos Error messages saying Use of undeclared variable shaftl pDrive
279. s and add assert statements for model assumptions Usetypes and descriptions to document all variables Use standard notation and types Regularly check models and components to detect errors see File Exit on page 138 Have connectors of different types e g Rotational Translational Electrical since it al lows early detection of mismatched connectors Design packages along the lines of the Modelica Standard Library Never ignore warnings and errors detected by the translator Do not overuse advanced features of Modelica such as replaceable classes inner outer Use SaveAs or Duplicate to move a class or package in package hierarchies 182 The result file can be loaded even if the sim ulation fails e Examine the start values xp and parameters to see that the start values are correct see Basic steps on page 147 Avoid algorithms in non functions Beware of graphical lines that look like connections Connections are created directly by drawing from a connector see Creating a connection on page 121 Several of these steps are common with normal object oriented development Finding errors in models We will 1n this section assume that the model runs at least for a short while but that the re sults are incorrect Before the simulation 1s complete or after a failed simulation one can ex amine the result by explicitly loading the result file dsres mat see Plot Open Result
280. s an example assume that in the old model Clutch that the viscous friction coefficient mue is given as mue mueVO mueVl abs wrel where mue VO and mueV1 are parameters declared in Clutch as ll o 6 0 parameter Real mueV0 parameter Real mueV1 The model Clutch of the new model library uses linear interpolation with respect to the rel ative velocity wrel with a parameter mue_pos to define the interpolation table parameter Real mue pos 0 0 5 The original mue equation 1s linear and one way of specifying a linear interpolation table 1s to compute its value for two arbitrary velocities The model requires that the first velocity 1s zero with mue mueV and for the other value velocity we use velocity one with mue mueVO mueV1 Thus at translation we would like to obtain a new modifier mue pos 0 value of mueV0 1 value of mueV0 value of mueV1 This is obtained by convertModifiers Clutch mueV0O 0 6 mueV1 0 mue_pos 0 smueV0 1 smueV0 smueV1 Example the declarations in the old model Clutch cl mueV0 0 4 mueV1 0 1 Clutch c2 mueV0 2 p are converted to Modelica Mechanics Rotational Clutch cl mue pos 0 0 4 1 0 4 0 1 Modelica Mechanics Rotational Clutch c2 mue pos 0 2 p 1 2 p 0 1 Note that since c2 did not specify a value for mueV1 the conversion used the default value The substitution automatically adds parenthesis for the substituted arg
281. s grid lines in the diagram if they are not visible otherwise disables grid lines Plot Setup signals Titles Legend Options Bange r Signal name Absolute angular velocity of component rad s r Legend n w rad s Reset File C dymola work dsres mat Number of data points 521 Properties Minimum Maximum Vertical 2 62528 10 Horizontal 0 1 2 Apply Cancel Signals tab Selecting a signal displays the corresponding information in the rest of the window It 1s also possible to navigate by pressing the Up and Down arrow keys to select a signal If a comment for the signal exists it 15 shown below the listbox The Legend field contains the current description of the selected signal Edit the text and press Apply to change the legend If the text 1s empty no legend 1s shown for this signal Pressing the Reset button fills the edit field with the default legend User defined legends are shown on page 156 The Properties group shows the name of the result file the number of data points as well as minimum and maximum values of the signal Plotted values can interrogated in the dia gram see Dynamic tooltips on page 159 SIMULATING A MODEL 161 Titles tab of the plot window setup Signals Titles Legend Options Bange Heading a Vertical axis title C None Description C Custom Horizontal axis title C None
282. s in H azis frame b H beari n must not necessarily be a unit vector E g eanng n 0 0 1 or n 1 0 1 q0 Rotation angle offset in degl If q q0 frame a and frame b are identical startValueFixed true if start values of q qd are fixed zi ModelicaAdditions MultiBody Joints Revolute Modeling y Simulation A A Arbitrary HTML can be The user may include arbitrary HTML code in the documentation by enclosing it in an used for documenta lt HTML gt lt HTML gt escape sequence in the textual documentation This makes it possible tion 128 Undo Redo Cut Copy Paste Clear Select All Find Goto line v Edit Source CZ Ctr Ctrl X Ctrl C Ctrl Ctrl 4 Ctrl F Ctrl G to take advantage of images tables and other forms of formatting For example a plot im age can be referenced with lt HTML gt The result is shown here lt IMG SRC images plot gif gt lt HTML gt In addition the browser also supports universal resource identifiers for anchor tags using the syntax href Step using normal lexical lookup in Modelica or href Modelica Modeli ca Blocks Sources Step using full lexical names These are transformed into references that the browser can understand when exporting HTML code Context menu when editing Pressing the right mouse button presents a context menu with common text operations Most of these operations are also available in th
283. s other variables There are several details worth explaining in this example First and foremost neither abs nor sign are used the reason 1s that by having only one test for the sign of x we guarantee that Dymola can correctly differentiate the expression pro vided g 0 p 0 and use it to reduce the index and to compute Jacobians for non linear sys tem of equations involving this equation If we had used sign as defined 1n Modelica 1 4 the Dymola program would be unable to correctly differentiate the expression Second noEvent 1s used The reason 1s that we assumed that g x p was not valid for nega tive x either because 1t cannot be evaluated or because it generated incorrect results Thus using noEvent guarantees that g x p 1s only evaluated for positive values of x Thirdly the formula is only valid if g 0 p 0 There are anti symmetric expressions that do not obey this such as friction force depending on relative velocity In those cases one should introduce an extra locked state as described in the friction logic models and under no circumstances use noEvent Using the above formula without thinking would for friction lead to a sliding mode and many unnecessary events Although one has to be careful one can construct a variant of this model where we intro duce an auxiliary variable for the sign In this form it is also possible to have expressions generating events in the expanded form of g x p provided they do not depend on x
284. s propor tional to the square of x and thus lost in round off How to use noEvent to improve performance In some cases the derivatives are sufficiently smooth that events need not be generated as an example we have piece wise interpolation polynomials parameter Real cpos cneg Real x y equation der x noEvent if x gt 0 then cpos x else cneg x if time gt 1 then y else 0 For this to be useful the nght hand side must be a sufficiently smooth function of x In this case we note that the switch between the branches occurs for x 0 in which case both branches are zero Note that as for all performance optimizations one should measure the performance to verify that the optimization 1s beneficial Additionally noEvent only surrounds the expression involving x and not the second term which will generate a time event exactly at the time 1 A note on style When using the noEvent operator to improve performance we are implicitly stating that the expression is sufficiently smooth Dynasim has initiated work in the Modelica design pro cess to introduce an operator smooth for this purpose and this thinking explains why no Event is used surrounding the entire expression in the examples above and not only the actual relational operator When viewing it as smooth it only makes sense to view a real valued expression as smooth This also guards against accidentally introducing events in one of the sub expressions Combined examp
285. s the default method To select Euler backward 1ssue the command Advanced InlineIntegrationExplicit false Translate the model Click the Specify simulation run button and select Euler as the integra tion method You will get an error message if improper algorithm is selected Step size can be implicitly defined as output interval or explicitly set by specifying Fixed integrator Step References Elmqvist H M Otter and F E Cellier 1995 Inline Integration A New Mixed Symbol ic Numeric Approach for Solving Differential Algebraic Equation Systems In Proceed ings of ESM 95 SCS European Simulation MultiConference Prague Czech Republic pp XXIII XXXIV Mode handling Mode handling re quires the Realtime op tion In many systems the structure of the system depends on discrete states such that there 1s a linear system with a Jacobian that can only have a number of discrete values during a simu lation Normally we factorize the Jacobian at every step but during continuous integration the matrix 1s not re factorized and thus the solution of the linear system contributes little to the overall time However for real time simulation we have a dead line for each step and do thus want to de crease the maximum time for each step Mode handling does this by pre compiling all modes i e all possible Jacobians used in the simulation This avoids the costly re factor izations allows further symbolic manipulation for e
286. s vertical Press Close n y Axis of rotation resolved in frame_a same as in frame_b phi offset E deg Relative angle offset angle phi from_deg phi_offset 1 0 0 x axis p Initializatiorgrg yo initType 0 0 1 z axis Type of initialization defines usage of start values below phi start 1 0 0 negative xaxis deg Initial value of rotation angle phi fixed or guess value w stam 10 1 0 negative y axis aegis Initial value of relative angular velocity w der phi 0 0 1 negative z axis a cotar janie Initial walia af ralative annidar arcalaratinn a darha 28 The robot drive train To learn more about this component select Info An HTML browser 1s opened to show the documentation of the Revolute Joint If you do only want to see the documentation select the component in the diagram press the right mouse button and select Info An HTML browser 1s opened to show the documenta tion of the Revolute joint By double clicking on the other components you can for exam ple see what parameters a mass has Let us now inspect the drive train model There are several possible ways to get it dis played Press the Previous button the toolbar button with the bold left arrow once to go to the robot model and then use the right button menu on one of the axis 1cons Please note that robot mechanics also has components axisl axis6 but those are just connectors You shall inspect f
287. se seres a dd dais 288 Installing on client computers lt 2 cuota a ER ERI ERE a 290 TroubleshOoune on Lh s Nee Loeb env eo Sens d yu exe bate Aat ede RS 290 Incense Hle od S pee CER EPIS E T UC ERI eB SPEC d vx 291 Compiler problems no Aes peter os acute Fe a LA calls dat 291 Simulink 2220 ble oe A eae ee ah AS SE ha 292 OSPACE SYSIGINS voy s nior tier Lie aos aah ieee ee Say aed Red ir ees Ae does 293 Other Windows related problems 0 0 00 00 0c eee 293 O Cites Aaa anne eno an Cut Ce it e e na 295 10 WHAT IS DYMOLA What is Dymola Features of Dymola Dymola Dynamic Modeling Laboratory 1s suitable for modeling of various kinds of physical systems It supports hierarchical model composition libraries of truly reusable components connectors and composite acasual connections Model libraries are available in many engineering domains Dymola uses a new modeling methodology based on object orientation and equations The usual need for manual conversion of equations to a block diagram is removed by the use of automatic formula manipulation Other highlights of Dymola are Handling of large complex multi engineering models Faster modeling by graphical model composition Faster simulation symbolic pre processing Open for user defined model components Open interface to other programs 3D Animation Real time simulation WHAT IS DYMOLA 13 Architecture of Dymola The archi
288. sically importInitial corresponds to copying dsfinal txt to dsin txt exportlnitial exportInitial dsName txt scriptName mos Generates a Modelica script such that running the script re creates the simulation setup Af ter running the generated script it is possible to override specific parameters or start values before simulating SIMULATING A MODEL 179 By genererating a script from a steady state dsfinal txt it is possible to perform parameter studies from that point Note This cannot be combined with non standard setting of fixed for variables if dsName dsin txt All other cases work fine plot plot ploti plot2 plot3 Plot the given variables in the plot window It is currently not possible to set ranges or inde pendent variable Note the argument 1s a vector of strings the names correspond to the names when selecting variables in the plot window Subcomponents are accessed by dot notation plotArray plotArray x 1 10 y sin 1 10 X y plot for given values printPlot printPlot plot1 plot2 plot3 Plot the variables and furthermore prints the resulting plot on the default printer list list Lists the variables in the variable workspace with their type and value Predefined variables are also described by a comment The command Clear All also clears the variable workspace eraseClasses eraseClasses modell PackageA model2 Erases the give
289. spective view Anti alias Trace selected object Trace all m kam Y 4 4 Y U lt 4 Y Y ET ollow Follow selected object Follow object in x direction Follow object in Y direction Follow object in Z direction Follow rotations of object TUNES Visualtab contains Run animation continuously which toggles continues mode on or off If continuous mode is on running animations automatically restart at the beginning instead of stopping at the end The default mode is off Unit cube reference to display a unit cube with corners at 0 0 0 and 1 1 1 for refer ence Axis reference to display axes where the x axis 1s red the y axis 1s green and the z axis is blue Remember xyz rgb View visual reference for cylinders to make cylinders to be drawn with a black reference line on the side in order to make it easier to see if the cylinders are rotating Highlight selected object colors the selected object red Grid reference to display reference grids in X Y X Z or Y Z plane Perspective view to toggle between perspective view and orthographic projection The default 1s orthographic projection 170 Animation frames tab History frames for the Furuta pendulum Anti alias to obtain smoother edges However it may make the animation much slower Trace selected object to trace the selected object 1 e to show the path of its origin Trace all to trace all objects 1 e to show the path of their orig
290. sses 10 39 35 lmgrd FLEX1lm v7 2c started on x x x x 3 27 2001 10 39 35 lmgrd FLEXl1m Copyright 1988 2000 Globetrotter Software 10 39 35 lmgrd US Patents 5 390 297 and 5 671 412 10 39 35 lmgrd World Wide Web http www globetrotter com 10 39 35 lmgrd License file s C DAG dymola lic 10 39 35 lmgrd lmgrd tcp port 27000 10 39 35 lmgrd Starting vendor daemons 10 39 35 lmgrd Started dynasim pid 124 10 39 36 dynasim Server started on x x x x for DymolaStandard 10 39 36 dynasim DymolaSampledLib DymolaLiveObjects DymolaRealtime 10 39 36 dynasim DymolaSimulinkDymolaAnimation DymolaSupport 10 39 36 lmgrd dynasim using TCP port 1042 The license server should now be correctly configured Please start Dymola to verify cor rect operation The FLEXIm logfile see above should contain additional lines showing what features were checked out You can also do Perform Status Enquiry to check how many license are currently checked out Installing on client computers After Dymola and all optional libraries have been installed on one computer a simplified process can be used to install Dymola on all client computers using the license server The following procedure should be performed on each client 1 Open the Dymola distribution directory on a computer where Dymola has already been installed over the network 2 Execute the installation program dymolaNoinNDymola5client exe and follow the in structions Th
291. systems The package ModelicaAdditions 1s a collection of libraries which is supplied by DLR Ger man Aerospace Research Establishment to provide often needed components which are missing in Modelica Standard Library It 1s planned to provide the components of Modeli caAdditions in an improved form in a future version of Modelica Standard Library Modeli caAdditions includes currently of the following sublibraries Blocks Additional input output control blocks HeatFlow1D Made obsolete by Modelica Thermal HeatTransfer MultiBody 3D mechanical systems Petri Nets Components to model state machines and Petri nets Tables Linear interpolation in one and two dimensions Model classes and their instantiation form the basis of hierarchical modeling Connectors and connections correspond to physical connections of components Inheritance supports easy adaptation of components These concepts can be successfully employed to support hi erarchical structuring reuse and evolution of large and complex models independent from the application domain and specialized graphical formalisms The benefits of acausal modeling with DAE s has been clearly demonstrated and compared to traditional block diagram modeling It has also been pointed out that tools can incorpo rate computer algebra methods to translate the high level Modelica descriptions to efficient simulation code Abadi M and L Cardelli 1996 A Theory of
292. systems the compilation 1s performed by a shell script dymola insert ds build sh Ifnecessary this script can be modified to provide special options to the compil er add application specific libraries etc For example to compile with Sun s ucbec you would have to add the xa flag to the compile command to specify the ANSI compatibility option Removing Dymola Remove the Dymola distribution directory and remove any settings in login that you have made Dymola License Server Background These are instructions for manually installing a FLEXIm license server for Dymola They only apply to users with a floating license For non floating licenses the common case in stallation of the license file is automatic Dymola is installed on all machines which will run the software On the designated ma chine the license server 1s then installed as described below The license server consists of two daemon processes The vendor daemon called dynasim exe dispenses licenses for the requested features of Dymola the ability to run Dymola and various options This program 1s specific for all software from Dynasim e The license daemon called 1mgrd exe sends requests from application programs to the right vendor daemon on the right machine The same license daemon can be used by all applications from all vendors as this daemon processes no requests on its own but for wards these requests to the right vendor daemon If you are
293. t Edit Source The description is given as html code When done click right mouse button and deactivate Edit Source We have now created the model Save 1t Testing the model It 1s possible to check the model for syntactic and semantic errors Select Edit Check Hope fully your model will pass the check and you will get the following message 56 Checking the model Signal sources E Messages Dymola Jof x Syntax Error Translation Check started DAE with 39 unknown scalars and 39 scalar equations Check of DriveLib Motor successful The connector inPort defines the voltage reference and should be defined for the complete model but is viewed as a known input to the model It is important to test all models carefully because that eliminates tedious debugging later on Let us connect the motor to a voltage source Create a model called TestMotor select File New Model or the Edit New Model in the context menu for DriveLib and insert it into DriveLib It is good practice to keep test models Use the package browser to drag over a Motor component from DriveLib to TestMotor We need a source for the signal input to the motor Signal sources are to be found in Modelica Blocks Sources E Sources package Modelica Blocks Sources 1 E 10 x SEAME A nb Lu pw Pur E Exponentials Pulse SawTooth Trapezoid KinematicPTP TimeT able E ES inr Ml BooleanConstant BooleanS
294. t experiment in a tree structured view To inspect the robot model select the icon in the Diagram window red handles appear see below and press the right button on the mouse From the menu choose Show Component h User s Guide Word 0 Examples Elementary Loops Systems E RobotR3 i oneAxis TE 1 9 1 mechanics axis6 axis5 axis4 ElMultiBody Examples Systems Rob mechanics path axis amp axis2 6 axis3 axis4 axis5 axis6 ip bus axis3 Sors vss A It is not necessary to select the robot component explicitly by pressing the left button on the mouse to access its menu It is sufficient to just have the cursor on its icon in the diagram window and press the right button on the mouse The component browser also gives easy access to the robot component Just position the cursor over mechanics The component browser provides a tree representation of the component structure The diagram window and the component browser are synchronized to give a consistent view When you select a component in the diagram window it is also highlighted in the component browser and vice versa The diagram window gives the component structure of one component while the component browser gives a more global view useful to avoid getting lost in the hierarchical component structure 26 Th
295. t han dling Reinhard Finsterwalder off line and on line plotting features and Alexander Lewald parameterized input signals especially suited for trajectory optimization In 1994 Dymosim version 4 0 was realized by Martin Otter Dymosim 1s essentially the kernel of DSSIM version 3 3 which was separated from ANDECS and transformed from Fortran to C using the public domain f2c compiler of the Bell Laboratories The file inter face was newly written in C replacing the previous interface of DSSIM to the RSYST data base system Dynasim has then interfaced Dymola to this kernel and enhanched both the integrators and the interfaces between integrators and models Running Dymosim When translating a model in Dymola an executable Dymosim 1s generated and later when selecting Perform simulation or similar commands this program computes the solution A statistics of the simulation run is always stored in file dslog txt which can be displayed by the menu command Simulation Show Log By setting Experiment Preferences Output Debug information additional Debug information will be written to the log file By default Dymosim stores the results of a simulation run in Matlab binary format on file dsres mat The data can be plotted by clicking on the Plot Window icon of the work space and selecting the variables to be plotted by Variables Additional plot windows can be opened by clicking on the Dymoview icon in the workspace and by select
296. t one input containing reals since we must have something to take the derivative with respect to 252 The output list of the derivative function may not be empty since we otherwise have no de rivative This can occur if the function e g returns a boolean value Verifying Derivatives In order to verty that a derivative 1s consistent with the function it is recommended to fol low the following test procedure The basic idea is to compare the integral of the derivative with the original function Assume one has a model using foo0 model B Real x equation x foo0 time false 0 1 time end B and we want to verify that the derivative of foo0 is correct We do that by extending B as follows model VerifyFirstDerivative extends B Real y equation der y der x initial equation y x end VerifyFirstDerivative That the derivative is correct can be verified by comparing x which is computed directly and y which is computed as an integral of the derivate By setting second derivatives equal one can verify the second derivative as well Note that this procedure does not modify the original model and can therefore be used even when the input arguments to the function are given internally External functions Existing libraries may require wrapper func tions In addition to functions written in Modelica Dymola also allows external functions written in ANSI ISO C For each external function it is necessary to decla
297. t window where 11 the upper diagram is active Variable selector The variable selector displays a tree view of all variables Each submodel represents one level of the hierarchy and all variables of a submodel instance are grouped together Com ponents are by default sorted according to order of declaration in the enclosing class Click ing on the header line toggles alphabetical order If more than one variable is selected they will be plotted in a single diagram with a com mon scale Variables that contain data for 3 D animation are not shown The variable selector window phi der phi der phi 2 Jtorque E clutch1 E sinl stepl Ez phi der phi der phi 2 D rad rad s rad s 2 PA kgm 16 rad s rad s s rad s2 rad rad s rad s 2 1 kg m2 0 rad s X Selecting plot variables Operations when selecting plot variables are SIMULATING A MODEL 157 JT aw Time Advanced plot selector mode Click on the symbol in front of a submodel name or double click on the submodel name If not already open opens the submodel and displays variables and nested submod els Otherwise the submodel is closed Click on a variable Plots the variable 1f it was previously unselected diagram is normal ly rescaled If the variable was already selected it is removed from the diagram Clic
298. tart Match at end Time The value column of the plot selector will show the values of variables for this time Enter time and press return Relative tic mark labels When the range 1s too small to display abosulte tic mark labels diagrams use relative axes instead of absolute axes This mode 1s highlighted by bold underlined text for the base number and signs in front of the relative offsets Plot window interaction Dynamic tooltips Resting the cursor over a plotted signal displays a tooltip with information about the closest data point The data point is also highlighted If several signals are close to the cursor data for all of them are shown if possible a common value for the independent variable is used a AA 2 gH w 4 52547 time 0 6936 2 J w 3 54839 J2 w 3 46643 2 J3 w 3 46643 time 0 8688 SIMULATING A MODEL 159 Open Result New Plot Window New Diagram Delete Diagram UJ Rescale Ll Erase Curves Ha Toggle Grid Setup la pd IH En Zooming the plot window The user can interactively zoom in on interesting parts of a diagram and easily zoom back to a previous zoom level Certain operations reset the zooming Clicking on the left mouse button Zooms the diagram 100 around the clicked point Pressing the left mouse button and spanning a rectangle Zooms in on the drawn rect angle which is scaled to fit the diagram Clicking on the right mouse b
299. tecture of the Dymola program is shown below Dymola has a powerful graphic editor for composing models Dymola is based on the use of Modelica models stored on files Dymola can also import other data and graphics files Dymola contains a symbolic translator for Modelica equations generating C code for simulation The C code can be ex ported to Simulink and hardware in the loop platforms Dymola has powerful experimentation plotting and animation features Scripts can be used to manage experiments and to perform calculations Automatic documentation generator is provided Simulation Visualization and Analysis Basic Operations Dymola has two kinds of windows Main window and Library window The Main window operates in one of two modes Modeling and Simulation The Modeling mode of the Main window 1s used to compose models and model compo nents The Simulation mode 1s used to make experiment on the model plot results and animate the behavior The Simulation mode also has a scripting subwindow for automation of experi mentation and performing calculations 14 Simulating an existing model Find the model Dymola starts in Modeling mode The model to simulate 1s found by using the Open or Demo commands in the File menu Example models are also found in the libraries Modeli ca or ModelicaAdditions or in other libraries opened by the Library command E MotorDriveTest MotoDriveTest Diagram BEE Q Fle Edt Yew Simsio
300. ted for components and connectors for lines and connections and also for the model itself when no object 1s selected Context menus are also available in the package and component browsers and in the library window Moving objects Objects are moved by pressing down the left mouse button with the cursor over one of the selected objects and then moving the mouse while holding the left button down to the de 114 Moving objects with ar row keys Name and modifiers are set after inserting sired position All selected objects are moved the same distance rounded to a multiple of the grid Note that when connect mode is enabled connectors must be selected first then moved Clicking on a connector followed by an immediate move will draw a connection Selected graphical objects can be moved by pressing the arrow keys The default 1s to move one grid unit as specified in Edit Attributes If the Ctrl key 1s held down the objects are moved half a grid unit If the Shift key is held down the objects move half a gridline five grid units Connections are automatically adjusted after a move operation to make sure that the end points still reach the corresponding connectors Edit Manhattanize can be used to clean up skewed connections Reshaping objects First select an object The object can then be reshaped by moving the handles for example making a component larger or changing the shape of a polygon The object is redrawn w
301. ted models and is thus not a good idea in modeling When using noEvent for performance reasons one should always measure the total CPU time since turning off events can cause a drastic increase in the number of steps This did not occur for this example but no substantial improvements were found and there 1s no rea son to introduce noEvent Examining the average time for block 302 after the change one observes that it 1s not influ enced by this change Thus the overhead for generating events for gt and lt is only mar ginal and no reason for using noEvent On the other hand rewriting the polynomials with Horner s rule decreased the average from 7 to 3 microseconds Even that had marginal influence on the total CPU time in this exam ple One should remember to reset the switch Advanced GenerateTimers false in order to avoid the overhead for the next model Note that this switch is not cleared by clear or Clear All commands Inline integration Inline integration re quires the Realtime op tion In order to increase the simulation speed in particular for real time simulation Dymola provides inline integration Inline integration 1s a combined symbolic and numeric approach to solving differential algebraic equations systems Discretization expressions representing the numerical integration algorithm are symbolically inserted into the differential algebraic equation model The symbolic power of the Dymola tr
302. tep BooleanPulse SampleTrigger le E gt K Drag for example over Step to the model window and connect it to the motor Step1 Motor1 EN startTime 0 Now it is time to simulate Click on the tab for Simulation Click on the toolbar button Sim ulate to start a simulation GETTING STARTED WITH DYMOLA 57 Angular position To inspect the result we will first look at the angular position of the motor Motor1 flange_b phi Open Motor in the plot selector by clicking on the sign Open the flange_b and tick phi E TestMotor DriveLib TestMotor Plot 1 ES i x m File Edit Simulation Plot Animation Window Help m gj xi je OS NP ER amp vsu ISSR a Vaii 7 Vates Jura Desc Motor Tange bh EjTestMotor 1 14 0 84 N m Cuttorg DEW phi rad Absolut 0 64 Step1 0 4 4 0 24 D BERE SCR 0 0 2 0 4 06 08 1 Ej Modeing V Simulation First we may establish that a positive input signal makes angular position increase The plot looks almost like a straight line However there are some wriggles in the beginning Zoom in use the mouse to stretch a rectangle over that portion of the curve you would like to see We may also plot the angular velocity Motor1 Jm w There is an oscillation which dies out and the velocity becomes constant There is much to be done to validate the model However model validation 1s out of the scope for t
303. th a smaller number of events e g a fast sampled controlled system can be replaced by an equivalent continuous time controller and a pulse width modulated control signal by an average signal Debug facilities when running a simulation When a simulation 1s running 1t 1s possible to open the result file to plot and animate the re sult in order to see that the simulation 1s progressing correctly It 1s also possible to activate these using from these individually before the simulation 1s started using the Debug tab on page 153 or by using the debug monitor when the simula tiong 1s running In order to determine the roots of some problems it 1s possible to enter a simple debug mon Itor for the simulation 1n order to determine how the simulation 1s progressing and to deter mine which variable 1s slowing down the simulation This requires that Microsoft Visual C compiler with DDE support is not selected as compiler since the commands are entered in the DOS window created when using the other compilers See also Compiler tab on page 154 Restore the DOS window and press Ctrl C to get the end of simulation statistics where the simulation 1s number of steps number of function evaluations etc Since parts of this 1n SIMULATING A MODEL 185 Debug commands Integrator error statis tics formation 1s stored internally by the integrators the information might underestimate some of the statistics By pressing Ctrl C
304. the background r Server List C Configuration using License File No FLEXIm Services defined use Configure Services to add services In the Configure Services tab Enter a new service name e g Dynasim License Server Enter the path to the license daemon dymola bin lmgrd exe Enter the path to you server license file dymola insert dymola lic Enter the path to a debug log file anywhere you want Enable Start Server at Power Up and Use Services Click on Save Service 288 Configuration of the li cense server LMTOOLS by Globetrotter Software http 77www globetrotter com Dynasim License Manager M In the Start Stop Reread tab Select the Dynasim license server Click on Start Server In the Server Status tab Click on Perform Server Enquiry and check the output of the log window You should see lines identifying the server processes and what features are available e g DymolaS tandard or DymolaLight Checking the operation LMTOOLS by Globetrotter Software http www globetrotter com of the license server APPENDIX INSTALLATION 289 The FLEXIm logfile Installation without CD Also check the logfile to verify that the server has started and that Dymola features can be checked out The following 1s an example 10 39 20 lmgrd Detecting other lmgrd proce
305. the model Generate an input file for further simulation studies in Dymola this requires an extra step save the generated result file Context menu in plot selector in Dymola as dsu txt All of this 1s accomplished by selecting Generate Result If you also want the result file to be automatically loaded in Dymola select Auto load If the result files become very large it might be useful to reduce the size by introducing a Minimum Dt which is a minimal output interval length e g 0 1 similar but not identical to Interval length in Dymola The choice Minimum Dt requires Matlab 6 1 or later Any modifications of these choices require a new compilation Implementation notes The DymolaBlock only works from Matlab 5 3 Simulink 3 0 Temporary files for compilation are created in dymola tmp and reused from one compila tion to the next When changing mex compiler in Matlab you have to remove the contents of this directory The DymolaBlock rely on a number of callbacks and tags 1n order to allow copying renam ing etc This allows us to store settings for model name parameters and initial values in Simulink s mdl format However manually editing mdl files containing DymolaBlocks 1s not supported neither 1s changing the tag of the DymolaBlock or any of the callbacks asso ciated with the DymolaBlock If Allow multiple copies of block 1s unchecked you should not copy the block Uncheck ing 1t shou
306. ting for the Mod elica language Any syntax errors are reported in the message window Settings Defines settings that affect the editor Insert Presents a submenu with common Modelica constructs This makes it easier to enter Modelica code Edit function call Inside a function call this allows you to modify the arguments using a modifier window Selected Class Allows you to open the selected class or its documentation Documentation Class documentation consists of a one line description and a larger documentation text This information as well as full model path 1s shown in the documentation layer 126 Documentation layer of a model viewing Copy Select All Find Goto line Edit Source Ctrl C Ctra Ctrl F Ctri G E Revolute ModelicaAdditions MultiBody Joints Revolute Read Only Documentation TES EEN Eile Edit Simulation Plot Animation Window Help l x l d amp M mev as a Fh 2i gt eSHElo i Name Revolute Path ModelicaAdditions MultiBody Joints Revolute Interfaces Description Revolute joint 1 degree of freedom used in spanning tree Joints Joint where frame b rotates around axis n which is fixed in frame a The joint axis has an additional 1 flange where it can be driven with elements of the Modelica Mechanics Rotational library The Revolute relative angle q rad and the relative angular velocity qd rad s are used as state variables y P
307. tio for the gearbox model please consult Info for the model Set ratio to 100 as indicated It means that the motor load rotates 100 times slower than the DC mo tor The library Modelica Mechanics Rotational Sensors contains a sensor for angles GETTING STARTED WITH DYMOLA 59 The completed motor drive E MotorDrive DriveLib MotorDrive Diagram amp File Edit Simulation Plot Animation Window Help l x He NI DOoQGAZZ S5 i nszi sm mHimEL Dv B E Modelica DJ Modelica dditions i Unnamed f DriveLib controller position motor E e E Jt 105 gearbox 100 J 10 Components EjDriveLib MotorDrive motor gearbox load phiload positionerror controller peofiyd B v p A To test the model MotorDrive for normal operation we need to define a reference for the position This can be done in different ways A simple approach is to add a signal source di rectly to MotorDrive However we may like to use MotorDrive also for other purposes If we would like to use the drive as a component we could add a connector for the reference as we did for the electric DC motor model However here we will take the opportunity to show another useful way namely use of extends We will develop a new class say Motor DriveTest which extends MotorDrive Select MotorDrive in the package browser and se lect Edit Extend From in the context menu
308. tion For large systems the actual writing of the file can take substantial time this can be checked by deselecting storing of States Derivatives Outputs and Auxiliary Variables see Output tab on page 152 and then re running the simulation In this case no result file will be generated By looking at the logfile it is possible to compare the time to normal simula tions For very nice problems the interpolation of the solution in order to generate the result file can also take substantial time This can be reduced by decreasing the number of output points or the increasing the interval length see Simulation Setup on page 150 If using an integrator with fixed step size it 1s necessary to enter a non zero value for the Fixed Inte grator Step in this case Events and chattering The first step to ensure that events are efficient 1s to examine the number of events in the log of the simulation If the number of events is small compared to the number of steps the simulation 1s not slow because of events A large number of state events can be caused by chattering e g solving the model model Chattering Real x start 0 3 equation der x sign x 0 2 time end Chattering After 0 25 seconds the sign function will switch back and forth between positive and nega tive Activating Output Debug Information see Output tab on page 152 will generate a log where the expression x 0 2 time
309. tion 9 53 Capacitance F Resistance Ohm Potential at Potential at Potential at The matrices may be in any order on the file If a matrix 1s missing a default matrix 1s used If a matrix has dimension 0 0 the matrix 1s just 1gnored It 1s allowed to supply only a subset of the parameters or initial values of state variables If a parameter or state variable name is provided which is not present in the model Dymosim prints a warning message and ignores this variable This feature is useful e g when a simulation run should be performed Voltage drop between the two pins Voltage drop between the two pins the pin V Current flowing into the pin A p v n v p v n v the pin V Current flowing into the pin A the pin V culated according to the fo and defaul and iary variables to determine a consistent se lowing procedure other variables t setting the number of to the number of a non linear t of initial conditions the following optimization problem is solved value i DESIRED i scale i 2 under the constraint that the differentia equation is fulfilled In most cases weight i 1 is sufficient v due is not close to zero the scaling is based on the If these values V s with an input file from a previous run of a slightly different model 212 1 Simulation result file dsres mat On the Dymosim result fi
310. tion Inertia F2 Clutch iN FB OnewayClutch po Qui Brake dl IdealPlanetary IdealGearR2T ap GeatEfficiency ar Gear sir Position Accelerate Large icon view z Fixed Torque RelativeStates Components are dragged from the package browser to the diagram layer and connected The component hierarchy is shown in the component browser Graphics editing tools ola Dyna odeling Laboratory Diagra x amp imulation Plot Animation Window Help 8 xi INDOGVA LS im 2 le BSR Bho zl Package browser Examples Interfaces Ep Inertia HldealGear E LoldealPlanetary pyldealGearA2T Spring Diagram layer Inertial La Inertia2 SpringD N imm i immi o o E IdealG Um 1 Uer Fised1 0 ce Damper 29 SpringD amper Components E Inertial E IdealGeart Fixedl By double clicking on a component a dialog for giving the name of the component and its parameters are shown WHAT IS DYMOLA 17 E Dymola Dynamic Modeling Laboratory Diagram Simulation Elot mation E SpringDamperl in Unnamed Inertia2 SpringD N nn Idealearl 1 The model browser allows opening a component for inspection of the documentation or the model itself for example by looking at the underlying Modelica code which 1s shown in the Mo
311. tion Window Help 18 xi le El amp M2 CQ O A SB m inu 7 Modelica J ModelicaAdditions Unnamed 7 DriveLib MotorDriveTes m pue Step controller positi motor h load ElMotoDriveT est 4 o m M MotorDrive DriveLib MotorDrive gaii ml r startTime Tiz0 5 loai phiload positionerror controller Stepl Modelica text of a model H Eie Edit Simulation Plot Animation Window Help 81 x lus SMV m A2 2 Hr SIunits ngle q final fixed startValueFixed SIunits AngularVelocity qd final fixed startValueFixed E interfaces SIunits ngularAcceleration qdd Joints SIunits ngle qq aiit Prismatic Real nn 3 Real sing Real cosq alte Screw gt axis phi q i Ed y x bearing phi 0 define states Modelica dditions MultiBody Joints Revolute qd der q TreeJoint ModelicaAdditions MultiBo add der qd axis bearing equation f rotation matrix nn n sqrtin n qq q q0 PI 180 sing sin qq sf Modeling y Simulation Z A Class documentation Two levels of documentation is available in the documentation layer or in the component or connector modifier windows if the author of the model has provided it If no documenta tion 1s available in the model Dymola will search the base classes
312. trix mn n sqrtin n qq q qO PI 180 sing sin qq Bl bearing sil Modeling y Simulation Pa Graphical components and connections are by default indicated by icons inserted into the the text Using the context menu it possible to show the corresponding Modelica text DEVELOPING A MODEL 125 Undo CtrleZ Redo Ctrley Cut Ctrl g Copy Ctrl C Paste Ctrl Select All Ctrl Find Ctrl F Goto line Cul G Expand Highlight Syntax Settings Insert Edit function call Selected Class Context menu Pressing the right mouse button presents a context menu with common text operations Most of these operations are also available in the Edit menu Undo Redo Undoes and redoes the last editing operation in the text editor Same as Edit Undo and Edit Redo Cut Copy Paste Copies text between the clipboard and the editor Delete Deletes all text in the editor Select All Selects all text in the Modelica text layer Find Find and replace text in the text editor Enter the text you search for and press OK Goto Line Sets cursor at specified line and scrolls window if necessary ExpandSelects the expansion level Normally graphical components and connections are represented with icons in the corresponding Modelica text By editing the expand level you can you can see these and also the contents of the annotations Highlight Syntax Scans the text in the editor and applies syntax highligh
313. ts component hierarchy allows inspection of model details but does not change the root model or permit editing The contents of the package browser and the component browser is by default sorted ac cording to order of declaration 1n the enclosing class Clicking on the header line sorts the contents in alphabetical order Clicking a second time restores declaration order Modified classes are marked in red in the package browser until they are saved A package and all classes inside it is marked read only if the Modelica file 1s read only Package browser context menu Pressing the right mouse button in the package browser presents a menu with the following choices A similar menu is presented when pressing the right mouse button in the compo nent browser Open Library Window Creates a new library window see below Open Class in This Window Opens the class of the selected class in this window Open Class in New Window Opens a new main window with the selected class Check Checks the selected class for errors See Edit Check on page 140 Search Searches the selected class for all classes or components matching a search pat tern See File Search on page 134 Close Closes an open hierarchy and all lower levels Info Displays extended documentation for the selected class HTML documentation will be used if 1t 1s available both for the standard packages and for classes written by users You can also use What s
314. ts from different domains Current tools are generally weak in treating multi domain models because the general tools are block oriented and thus demand a huge amount of manual rewriting to get the equations into explicit form The domain specific tools such as circuit simulators or multibody pro grams cannot handle components of other domains in a reasonable way There 1s traditionally too large a gap between the user s problem and the model description that the simulation program understands Modeling should be much closer to the way an en gineer builds a real system first trying to find standard components like motors pumps and valves from manufacturers catalogues with appropriate specifications and interfaces Equations and reuse Equations are used in Modelica for modeling of the physical phenomena No particular variable needs to be solved for manually because Dymola has enough information to decide that automatically This 1s an important property of Dymola to enable handling of large models having more than hundred thousand equations Modelica supports several formal 1sms ordinary differential equations ODE differential algebraic equations DAE bond graphs finite state automata Petri nets etc The language has been designed to allow tools to generate very efficient code Modelica models are used for example in hardware in the loop simulation of automatic gearboxes which have variable structure models Such models have so f
315. twice in rapid succession you will enter a debug monitor pressing Ctrl C once more will terminate the simulation The following commands are available Command name abbreviation Action continue c continue simulation qui t q stop simulation log 1 log event true le t give help for commands starting with activate logging of events log norm true In t activate logging of dominating component log singular true 1s t log and continue if singular systems Of the log commands log event true and log norm true are the most important It 1s also possible to use log event false to turn it back off Setting log event true makes it possible to activate logging of events at the right time and without seeing the log for non linear sys tem of equations It can be used to determine 1f there are any problems with chattering Setting log norm true makes it possible to determine which variable 1s causing an adaptive integrator e g Dassl to be slow In the end of simulation statistics 1t will include statistics for each variable indicating Column Indicates Limit stepsize How often has the error in the component ex ceeded the tolerance and forced the integra tor to reduce the stepsize Dominate error How often has the component dominated the error estimate How often has the error contribution from the component exceeded 10 of total
316. two layers are graphical The icon layer represents the class when it is used as a component or connector in another model that is the diagram layer displays the icon layer of its components The surround ing background of the icon layer is light blue when editing is possible The diagram layer shows the major contents of the class 1 e components connectors and connections decorated with additional graphical primitives The surrounding background of the diagram layer is light grey when editing 1s possible The other two layers use a textual representation The documentation layer shows the one line description of the class plus the longer info text that gives a complete explanation of its behavior These texts are available when browsing classes and components It 1s also used for automatically generated HTML doc umentation The Modelica text layer shows simple declarations of local constants parameters and variables and the equations of the class Components with graphical representation are by default hidden Connectors are typically placed in the diagram layer of a model Public connectors are also shown in the icon layer to assist the graphical layout of the icon and to make it possible to connect to the component Protected connectors are only shown in the diagram layer DEVELOPING A MODEL 111 Diagram layer of an edit E MotorDriveTest MotorDriveTest Diagram Rm ES window File Edit Simulation Plot Anima
317. ty if the model class should not be in serted into a package Existing modifiable packages are available in a drop down list DEVELOPING A MODEL 131 Creating a new model Use separate files for concurrent develop ment Name of new model Description mooo Partial Extends optional m Insert in package optional zi Cancel File New Package Creates a new package as for creating new models the user 1s asked for package name a short description optional base class to extend from and the name of an optional parent package Dymola supports two ways of storing packages Saving the package as a single file All models etc of the package are stored in this file This alternative 1s recommended for small packages Saving all models etc of a package in separate files The package itself 1s stored as a di rectory 1n the file system plus a file called package mo which stores package documen tation and other annotations This alternative is recommended for large packages Saving the contents of a package in separate files supports multiple developers concurrently working on the package editing different models of course When a version management system 1s used storing models as separate files allows version control on a per model basis Note the storage format can be changed by Edit Attributes after the package has been created see Edit Attributes on page 140 or
318. umentation 112 parameter 79 118 clear all 134 295 clear log 137 clipboard 136 closeModel 179 color 124 commands convertClass 272 convertClear 275 convertElement 273 convertModifiers 273 comment 240 attribute see class description 76 initialization file 143 compiler GNU C 154 Microsoft Visual C 154 283 292 on UNIX 154 setup 154 troubleshooting 154 291 WATCOM C C 154 component 17 attributes 120 browser 109 library 48 size 113 115 140 computer algebra 78 connection 75 115 138 creating 121 connector 75 nested 122 protected 111 visibility 111 context menu 47 109 113 114 116 122 continue line 173 continue simulation 150 continuous run of animation 170 ControlDesk 227 coordinate system 113 140 specification 113 copy 138 copy to clipboard 136 create script 137 creating a model 50 crossing function 85 current selection 114 cut 138 D DAE 78 204 high index 78 data flow modeling 77 DC motor 42 DDE Dymola commands 233 Dymosim DDE server 234 extended gui 236 hot linking variables 236 requesting variables 235 setting parameters 235 simulator commands 235 debugging models 153 182 declarations 35 125 default graphics 124 delete 138 delete key 115 143 deleting objects 115 demo 24 134 dense output 202 203 204 der operator 34 description 127 descripti
319. uments thus avoiding the need for parenthesis in macros that are familiar to a C programmer The parenthesis are sometimes redundant and can be removed by going to the parameter dialogs of the corre sponding components Prefer convertElement over convertModifiers even for parameters and only use convert Modifiers when there is a need for more than a one to one conversion of parameters 274 convertClear The command convertClear clears the translation tables How to build a convert script In order to convert a model using one library to another it is recommended to begin con struct a conversion script for the library Even if the script is not complete after converting one model it can be reused for the next model and only amend it with additional lines for the additional library components in that model If a library developer restructures a Model ica library it is recommendable to construct such a script Below it 1s explained how to construct a convert script and how to amend it for additional models For clarity assume that we would like to convert a drive train model myOldModel that uses components in the model library Drive Trains to a model myNewModel that in stead uses the components in the library Modelica Mechanics Rotational 1 2 Copy my OldModel mo to myNewModel mo Make a local conversion script say Convert mos Depending on what you are converting start as follows If you have a script for conve
320. utton Returns to the previous zoom level Limits defined with menu command Plot Range are also used in the context File menu File Export Image Saves PNG image of active plot window excluding window borders and menubar The user 1s prompted for a file name Plot menu The plot menu includes commands to load results create and edit plots and diagrams The most common plot commands are available in the tool bar Ie E P3 AUH When plotting there must be an active plot window If the active plot window has multiple diagrams one of the diagrams 1s active and the plot commands are directed to this diagram Plot Open Result Reads the result from a simulation made with Dymola to allow variables to be plotted Note that the result of a simulation 1s automatically opened Plot New Plot Window Creates a new active plot window which 1s initially empty Plot New Diagram Creates a new active diagram in the active plot window Plot Delete Diagram Deletes the currently active diagram Plot Rescale Rescales the current diagram so that the full range of all plotted variables 1s shown If the diagram has not been zoomed in rescaling is performed automatically when new variables are selected for plotting 160 Signals tab of the plot window setup Plot Erase Curves Erases all curves in the active diagram If automatic rescaling is enabled the diagram is res caled to the default scale Plot Toggle Grid Enable
321. vative annotation follow the normal lookup rules of Modelica First order derivative The inputs to the derivative function of order 1 are constructed as follows First are all inputs to the original function and after all them we will in order append one derivative for each input containing reals Theoutputs are constructed by starting with an empty list and then in order appending one derivative for each output containing reals As an example consider the following function foo0 input Real x input Boolean linear input Real z output Real y algorithm 250 if linear then y z tX else y z sin x end if annotation derivative fool end foo0 function fool input Real x input Boolean linear input Real z input Real der x input Real der z output Real der y annotation derivative order 2 foo2 algorithm der y der z if linear then der x else cos x der x end fool This implies that given the following equation y t foo0 x t b z t we know that y t fool x t b z t X t Z 0 A more complex example involving records and matrices is record R Real M 2 2 Real x 2 end R function recordFunction input R x output Real y 2 algorithm y 7xX M x x annotation derivative recordFunction d end recordFunction function recordFunction d input R x input R der x output Real der y 2 algorithm der y x M der x xtder x M x x Since A B A B A B
322. wice to calculate the reaction torque in the coupling and it 1s sufficient to select the angle and velocity of either inertia as state variables The constraint leads to a linear system of simultaneous equations involving angular accelerations and torques A symbolic solution will contain a determinant of the form J Jn The tool thus automatically deduces how inertia 1s transformed through a gearbox 78 Advanced modeling features The modeling power of Modelica 1s great Some of the more powerful constructs are sum marized below Vectors matrices and arrays Modeling of for example multi body systems and control systems is done conveniently with matrix equations Multi dimensional arrays and the usual matrix operators and matrix functions are thus supported in Modelica The modeling of continuous time transfer function 1s given below as an example It uses a restricted model called block having inputs and outputs with given causality The polynomi al coefficients in ag ajs aps are given as a vector ag a4 An partial block SISO Single Input Single Output block input Real u input output Real y output end SISO block TransferFunction extends SISO parameter Real a 1 1 Denominator parameter Real b 1 Numerator protected constant Integer na size a 1 constant Integer nb max na size b 1 constant Integer n na 1 System order Real bO na cat 1 b zeros na nb Zer
323. window borders The image is identical to the image shown in the window so the size and representation can be changed by first resizing the window Exported 1mages are included in the command log File Export Animation Saves the current animation window in AVI Audio Video Interleaved animated GIF or VRML format To export an animation in AVI format the user must select small file size which may incur some loss of image quality due to compression or large file size without loss of quality It 1s also possible to change the frame rate 1 e the number of image frames per second File size 3 Frame rate 20 fps a Cancel To create animated GIF images Dymola requires that GIF Construction Set from Alche my Mindworks has been installed on the computer Environment variable DYMOLAGI FCON must point to the executable program and Dymola must be started afterwards File Export Setup HTML Sets up options for exporting HTML See HTML documentation on page 129 File Export HTML Exports comprehensive model and library documentation in standardized HTML format ac cording to the options in File Export Setup HTML See HTML documentation on page 129 File Save Log Saves the contents of the command log window to file The user 1s prompted for a filename The contents of the command log can be saved in three different formats DEVELOPING A MODEL 137 HTML log with embed
324. would like to have pin p in the top position To flip the component use Edit Flip Vertical A rotating inertia component 1s to be found in Modelica Mechanics Rotational Drag and drop such an inertia component Name it Jm and set the inertia parameter J to 0 001 Now all model components are in place Components are connected by drawing lines be tween connectors To connect the resistor to the inductor point at the right connector of the resistor the small white square and drag to the left connector of the inductor The resistor and the inductor are now connected and the graphical result 1s a line between them When connecting the voltage source and the resistor break the line by clicking at an intermediate point There is a possibility to obtain automatic Manhattanize of connections Select the connection Edit Manhattanize Draw all connections Note that we could have drawn a connection between two components as soon as we have the components and we have not to wait until all model components are in place Finally we have to introduce a signal connector for the voltage control and a flange connec tor corresponding to the shaft of the motor so the motor can be connected to an environ 54 The icon of the electri cal DC motor Toolbar for editing ment We would like to place the icon of the connectors at the border of the grid of the drawing pane because the icon of a model component also includes the connectors The connecto
325. xpression STRING STRING terminate STRING STRING Expressions expression simple expression if expression then expression else expression simple expression m m logical expression logical expression logical expression logical expression logical term or logical term logical term logical factor and logical factor logical factor not relation relation arithmetic expression rel op arithmetic expression rel op Want lt n ts n es arithmetic expression add op term add op term add op 4 LLLI term factor mul op factor mul op xm ms 244 factor mar primary primary primary UNSIGNED NUMBER STRING false true expression list component reference function call expression list expression list expression list name IDENT name component reference IDENT array subscripts component_reference function call function arguments function arguments expression list named arguments named arguments named argument named argument named argument IDENT expression expression list expression expression array subscripts subscript subscript subscript wen expression comment string comment annotation stri
326. y Dymola Pressing the Verify compiler setup button performs several tests and reports any potential problems See also Troubleshooting on page 290 154 Realtime tab of Simula tion Setup Realtime tab H Experiment Setup General Translation Output Debug Compiler Realtime simulation Synchronize with realtime Slowdown factor fi Load result interval s 05 Inline integration Implicit Runge Kutta Order Iz wi Optimize code for step size por Store in model Cancel Activating items in this tab requires the real time simulation option of Dymola and that you use MicroSoft Visual C with DDE as compiler Synchronize with realtime This enables soft realtime simulation with frequency of about 20Hz running under Windows For hardware in the loop simulation see the section on other simulation environments Slowdown factor This makes it possible to simulate 1n scaled realtime Load result interval s How often the result file should be loaded Online plots are up dated this often Inline integration Select inline integration method The implicit methods are important for real time integration of stiff systems 1 e models with time scales faster than the For the higher order methods it is possible to select order and for all implicit methods the code 1s optimized for one step size which should be given here This step size should be the same as the fixed step size w
327. y Dymola and compiled the block 1s automatically customized according to the model s input output and top level parameters Model re organization The Simulink model must then be slightly modified to fit into the RT LAB framework Blocks that should run in real time must be grouped according to computational node and input and output blocks e g scopes are grouped into a console block This procedure 1s described in more detail in the RT LAB documentation The figure below shows a master block which 1s the primary block of the real time com putation In addition to the DymolaBlock which contains the entire plant model an OpSim ulationInfo block has been added to make signals for effective step size computation time communication time and a counter of overruns In this example all the signals are multi plexed into a single channel to the console OTHER SIMULATION ENVIRONMENTS 229 An RT LAB master block AE File Edit View Simulation Format Tools Help De tee 2 m Nomal Heo mme Nb Overruns Rst Overrun s Ground Effective step size OpSimulationinto Signals side Acceleration j aw velocity dinal Speed lateralSpeed DymolaBlock Ready 100 lodel yy In a cluster with several computational nodes one node 1s designated as master and other real time nodes are designated as slaves Structurally the slave blocks are similar to the master block The controlli

Dymola User's Manual - Department of Computer Science

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