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1. Kl 7202119 72 230 Parameters Steady State Disturbance Analysis Parameters Evaporator Process 1 Select Disturbance 2 Select Operation mode 3 Test Range Select only one item stepsize 01 z v Open Loop Closed Loop Feed Flow rate kg min no steps ES v Feed Temperature C 4 Select manipulated varaibles amp their limits Feed Concentration wt only if closed loop mode is selected Reset Limit Coolant inlet Temperature C MY name upper limit lower limit B Coolant Flow Rate 400 100 I Steam Pressure 5 Select Controlled Output ia only if closed loop mode Steam Flow rate is selected Liquid Level Product Concentration Vessel Pressure Product Flow rate 6 Final Step r When ready click the Run button warning r King Saud University Chemical Engineering Department Fig 4 2 SSDSA menu for the evaporator process The menu in Fig 4 1 has six steps that lead to carry out the SSDA analysis procedure as discussed in the following sections 4 2 OPEN LOOP MODE First the user should select one of the four possible disturbances by marking the appropriate check box Let us say the feed temperature Note that the other case studies will have different list of disturbance variables Next mark the open loop check box The third step controls the test range For example if the nominal value for the feed temperature is To 40 C and using step size of 0 1 and number of step
2. 12 PID K 0 6K P P LL qucm mW Revisit Fig 1 13 of chapter one Using the main menu of this figure choose the Forced Circulation Evaporator to get Fig 1 16 and then from this menu choose the second item Single loop control Evaporator to get Fig 6 1 File Edit View Simulation Format Tools jos ns SB mlOcl gt e Evaporator Process Closed Loop P100 kPa Toh E Level m concentration X Pressure kPa z J Flow kg min Set point Fig 6 1 Process flow sheet of closed loop evaporator process This figure represents the closed loop set up for the evaporator process Notice the addition of two new color codes different from the previous figures The light green color code is the designation for the controller in this case using a PID controller to control the outlet concentration of the evaporator process The manipulated variable in this case is the feed steam pressure The light blue color code represents that for the set point The loop pairing is chosen for demonstration purposes The user can simply reconfigure the control loop to link any output to any input presented in the module 93 6 2 1 Selecting the Coon and Cohen Parameters CC Should there be a need for the open loop parameters the reader can simply run the simulation open loop mode To do so double click the PID controller Box green Box and enter zero for all controller parameters as shown in Fig
3. Let us study the cascade control through an example In the main menu shown in Fig 1 13 select Multi stage Flash Desalination This will bring the following submenu a E S Quit Clear Work Space MSF Process Menu Ay Chemical Engineering Department King Saud University Fig 8 1 The MSF Process Menu 109 Selecting Singleloop control in the MSF menu shown in Fig 8 1 will bring up the following Simulink module View Simulation Format Tools D cs Multi Stage Flash Desalination Closed Loop with last stage evel control Multi Stac lash Desalination PID controllerm Fig 8 2 Single loop control for MSF process The module shown in Fig 8 2 illustrates a control loop that regulates the top brine temperature Tgo by manipulating the steam mass flow rate Ws The top brine temperature plays important role in the MSF operation as it affects the production rate Wa significantly Since the distillate product Wa is the main output of the MSF one may try to control the distillate product via manipulating the top brine temperature However the control objective can not be achieved directly Therefore one can work through a cascade loop Selecting cascade control in Fig 8 1 will activate the module shown in Fig 8 3 The module shown in Fig 8 3 contains a cascade control loop The inner loop in that cascade structure is the Tgo W control loop This is the standard loop shown in Fig 8 2 Howe
4. TY Primary Loop Fig 3 7 Cascade control configuration The reasons for using this type of control are as follows e Allow faster secondary controller to handle disturbances in the secondary loop e Allow secondary controller to handle non linear valve and other final control element problems e Allow operator to directly control secondary loop during certain modes of operation such as startup Requirements Secondary loop process dynamics must be at least four times as fast as primary loop process dynamics e Secondary loop must have influence over the primary loop e Secondary loop must be measured and controllable Cascade control can be used when there are several measurement signals and one control variable It is particularly useful when there are significant dynamics e g long dead times or long time constants between the control variable and the process variable 69 CHAPTER 4 STEADY STATE DISTURBANCE SENSETIVITY ANALYSIS 4 1 INTRODUCTION In this chapter we discuss how steady state disturbance analysis can be implemented on PCLAB This procedure is very useful to design the appropriate control structure When controlling a plant or a process with many inputs and outputs it is usually difficult to optimally pair theses variables into multi single loops structure SSDA is a tool that can help in this regard however it can not be implemented on real plant Instead simulation can be utiliz
5. simout Display Floating Scope Outi Scope Stop Simulation Terminator To File To Workspace XY Graph Fig 1 4 SIMULINK Sinks Library 1 4 2 Open Loop Simulation A user now has enough information to generate an open loop simulation The Clock simout step and Transfer function blocks can be dragged to a model mdl workspace as shown in Fig 1 5a Renaming the blocks and variables and connecting the blocks produces the model shown in Fig 1 5b simout Clock To Workspace LE s 1 e P N Transfer Fen To Workspace To Wonepace a Placement of function blocks 16 Clock time manipulated Set point output Transfer Fon b Renaming and connecting of blocks Fig 1 5 Development of an Open loop Simulation The s polynomials in the process transfer function were entered by double clicking on the transfer function icon and entering the coefficients for the numerator and denominator of the polynomials Notice also that the default step used for the step input change is to step from a value of 0 to a value of 1 att 1 These default values can be changed by double clicking the step icon The simulation parameters can be changed by going to the Simulation pull down menu and modifying the stop time default 10 or the integration solver method default ode45 The reader should generate simulations and observe the inverse response behavior of t
6. Au AW Au AW Ay Tpo Toss Ay Tbo Toss Ky Ay Au Ky Ay Au tstart tstart Tp063 2 Tgoss 0 632 Ay Tp063 2 Toss 0 632 Ay t63 2 t63 2 T 163 2 start T 1632 start tstep tstep m O tstep tstart 0 tstep fun 131 Work sheet Effect of Ty on Tuo Initial steady state Tis Wis Boss Toss Positive step change Negative step change A T A Ty New final value of Tgo New final value of Tgo Au A T Au A Ty Ay Thao Toss Ay To TBoss Ky Ay Au Ky Ay Au tstart tstart TB0632 TBoss 0 632 Ay TB0632 Toss 0 632 Ay t63 2 163 2 T 63 2 start T 63 2 fstart tstep step z O tstep tstart O S tstep tstart 132 Work sheet Effect of Bo on Tg Initial steady state Tis Wis Boss Toss Positive step change Negative step change New final value of Tz9 New final value of Tgo Au ABo Au AD Ay To Toss Ay Tao Toss Ky Ay Au Ky Ay Au tstart tstart TB0632 TBoss 0 632 Ay TB0632 Toss 0 632 Ay t63 2 163 2 T 63 2 Cstart T 63 2 fstart tstep tstep O S tstep tstart O S tstep tstart 133 B 4 Single Loop PI Control Tutorial 1 PI Control of an MSF plant Objective To design
7. hy Q Ly B Cy C C The specific enthalpy of Equation 2 60 amp 2 61 are determined from an empirical correlations developed by the author of the original model Here common enthalpy correlations for water are used In the current model water vapor pressure correlations are included in order to calculate the vapor flow rate in 2 66 The proportional controllers 2 69 amp 2 70 are used here where indicated to control the liquid level in the corresponding effects The sensitivity of the enthalpy of the solution is given by empirical relation C in the original model Here it is estimated from enthalpy correlation for brine 2 5 3 Process Parameters and Variables Variable Description Value Units Ay Heat transfer area of 1 effect fi A2 Heat transfer area of 2 effect 4 6 f B Bottom stream of 1 effect 3 315 Ib min B2 Bottom stream of 2 effect 1 715 Ib min C Solute concentration in 1 effect 4 8262 Wt C5 Solute concentration in 2 effect 9 3307 Wt Cr Solute concentration in the feed 3 2 Wt F Feed flow rate 5 lb min hr Enthalpy of the feed Btu lb hi Liquid enthalpy in the i effect Btu lb Hi Vapor enthalpy in the i effect Btu lb 43 Heat transfer coefficient in the i effect Valve coefficient Heat loss in the 1 effect Heat loss in the 2 effect Overhead stream of the 1 effect Overhead stream of the 2 effect Operating pressure in the 1 effect Operating pressu
8. m from where the name of m file comes When using the editor of MATLAB it automatically saves your files with the m extension Otherwise one should be sure to save them with the m extension M files can be in the form of scripts and functions and could be executed in the MATLAB workspace A script is simply a series of MATLAB commands that could have been entered in the workspace When typing the name of the script the commands will be executed in their sequential order as if they were individually typed in the workspace For example let us calculate the volume of an ideal gas as a function of pressure and temperature Type the following commands in the editor and save it as myscript m A sample script file disp Calculating the volume of an ideal gas R 8314 94 Gas constant t input Vector of temperatures K p input Pressure bar le5 v R t p Ideal gas law Plotting the results plot t v xlabel T K ylabel V m43 kmol title Ideal gas volume vs temperature The symbol indicates that this line contains comments The 96 sign and what comes after it in that line will be ignored at the time of execution Return to the MATLAB command window and type myscript Input the required data and see the results 1 3 5 Flow Control MATLAB has several flow control structures that allow the program to make decisions or control its execution sequence These structures are f
9. 11 12 13 14 E Ali and K Alhumaizi Temperature Control of Ethylene to Butene 1 Dimerization Reactor Ind Eng Chem Res 39 pp 1320 1329 2000 E Ali A Ajbar and K Al humaizi Robust Control of Industrial Multi Stage Flash Desalination Processes Desalination 114 pp 289 302 1997 E Ali Understanding Industrial MSF Operation I Stability and Steady State Analysis Desalination 143 No 1 pp 53 72 2002 E Ali Understanding Industrial MSF Operation II Optimization and Dynamic Analysis Desalination 143 No 1 pp 73 91 2002 E Ali A Abasaeed and S Al zahrani Optimization and Control of Industrial Gas Phase Ethylene Polymerization Reactors Ind amp Eng Chem Res 37 pp 3414 3423 1998 K I Alhumaizi Stability Analysis of the Ethylene Dimerization Reactor for the Selective Production of Butene 1 IChemE 78 pp 492 498 2000 Y Cao and D Biss An Extension of Singular Value Analysis for Assessing Manipulated Variable Constraints J Process Control 6 pp 34 45 1996 P Daoutidis and A Kumar Structural Analysis and Output Feedback Control of Nonlinear Multivariable Processes AIChE 40 pp 647 660 1994 P A Galtier A A Forestiere Y H Glaize and J P Wauquire Mathematical Modeling of Ethylene Oligomerization Chem Eng Sci 43 pp 1855 1860 1988 W L Luyben Simple Method for Tuning SISO Controllers in Multivariable Systems Ind Eng Che
10. 13 Using the main menu of this figure choose the Forced Circulation Evaporator to get Fig 1 16 and then from this menu choose the first item on the menu to get Fig 5 1 Fig 5 1 shows the open loop configuration of an evaporator process The blue colors to the left indicate input parameters There are seven of them as defined in the chapter on modeling These include temperature flow rates pressure and the concentrations defining the process The red colored items to the right represent the output parameters that are important to process performance These four parameters represent the level pressure flow and concentration for the evaporator The yellow portion in the middle represent the process itself Observe the green icons on the 76 top left one of which can take you back to the menu and the other to the interactive graphic tool The coloration code is typical for all the case studies available in the software Ivapopeme Fie dit View Simulation Format Tools D amp 39me c e Evaporator Process ra Open Loop 1947 P100 kPa 9 28 F100 kg min Fresh Feed Evaporator Process Fig 5 1 Open Loop Evaporator Process menu Double clicking on any of the input boxes will give you access the seven inputs described earlier For instance if you need to make a change on the feed flow rate to the evaporator double click on the third input box designated by F A Block P
11. 3 1 The output reaction can be recorded and plotted to infer the system parameter The figure shows how estimate the gain time constant and dead time directly from the transient response This procedure is known as reaction curve method Fig 3 1 Output response for a step change for first order system a with time delay b without time delay Accordingly the time constant is estimated directly from the Ge curve while the u static gain is simply Ax 3 5 63 1 0 Similarly when the input variable is stepped the output of an under damped second order system responds as shown in Fig 3 2 From the recorded data it is easy to identify the system parameters as follows M x Static gain k Au 21 A Damping ratio solve exp for d om T Natural period of oscillation r oe 2a Where y 41 ee Fig 3 2 Output response to a step change for second order system 3 2 2 Closed loop Dynamic Analysis The evaluation of system performance simply reflects the ability of a process control loop to regulate some dynamic variable in the process Such regulation is specified through two criteria The first criterion is the system error of the system in maintaining the controlled dynamic variable at the specific value defined by the set u t 64 point Cs The second criterion is the dynamic response of the system to any disturbance of the process or cha
12. 6 2 Simple Mask mask Insert the values of the PID ocntrollers Parameters Proportional gain 0 Integral time 0 Derivative time jo OK Cancel Help Apply Fig 6 2 Block Parameter for changing the PID controller settings Afterward inset a step change in the desired manipulated variable say the steam pressure The step change should be well known value as discussed in chapter 5 Here the steam pressure was stepped by 1 kPa Now run the simulation the usual way and observe the simulation results for the controlled variable which is the product concentration The plot of the response of the controlled variable is shown in the designated scope box given in Fig 6 3 From this response calculate the open loop parameters as discussed in chapter 5 The parameters calculated for this run Le kp Tp and tg are given in Table 6 3 Using these values in the Coon and Cohen formula of Table 6 2 the PID controller settings are calculated in listed in table 6 3 94 Fig 6 3 Plot of Concentration with time for a unit step change in P100 6 2 2 Ziegler and Nichols Method ZN To obtain the parameters for the Ziegler Nichols controller settings it is necessary to make two changes on the closed loop process First double click on the set point icon of Fig 6 1 to obtain Fig 6 4 Change the set point value by highlighting the current value and type 26 3156 set point change of unity Block Parameters Set point i x r Constant Out
13. Ei Activation energy for initiation amp propagation reactions 6000 K E Activation energy for the termination reaction 3000 K F Reactor fresh feed 0 004 m s K Catalyst 1 122 mole nm K gt Catalyst activator for C2 0 1345 mole m K catalyst activator for C 0 0178 mole m Ks Catalyst activator for Cg 0 0028 mole m 38 SCR NL US AH T Catalyst concentration at the fresh feed Product flow rate Inlet coolant temperature Feed temperature Reference temperature Reactor temperature Recycle temperature Heat transfer coefficient times heat transfer area Reactor volume m Cooler volume Coolant flow rate Mixture density Heat of reaction Recycle ratio 1 25 F p 0 0 30 0 25 0 67 0 43 0 27500 500 50 500 500 25000 0 02 mole m m s CC CC CC CC CC cal s C 3 m 3 m kg s Kg m Cal mole 39 2 5 DOUBLE EFFECT EVAPORATOR 2 5 1 Process Description and Flow Sheet A schematic flow sheet of the process is shown in Fig 2 4 A solution of triethylene glycol in water is fed to the first effect at flow rate F solute concentration Cy and temperature T The solution s concentrated in the first effect using steam at flow rate W generating the overhead vapor stream O and the concentrated bottom stream B with solute concentration Cj The bottom stream B is fed to the tube side of the second condenser
14. Phase zz cooling water separator L second effect P gt T2 d condensate mE first effect OT Pi Jt steam Sr Wi condensate cond nsate CEN Product F Cr T Buc iT B C5 T Fig 2 4 Two Effect Evaporator effect at a lower pressure while the overhead stream O is fed to the shell side The bottom stream B which is the product stream leaves the second effect with solute concentration C2 The overhead stream O from the second effect is condensed and released as condensate W and W2 are the liquid holdups whereas Pi 7 and P2 T2 are the pressures and temperatures in the first and second effects respectively A standard modeling procedure was followed to develop a dynamic model for the process using the following assumptions 1 The steam chests tune walls and so on have negligible heat capacity 2 The temperature T is held constant by pressure controller 40 3 The overhead vapor streams leaving each of the effects have negligible solute concentration compared to the respective bottom liquid streams 4 Vapor holdup in each effect is negligible Here assumption 2 is relaxed The stream O is fixed and the temperature T is evaluated such that it respects the algebraic energy balance on the second effect In the original model O is determined from the energy balance on the first effect Here O is determined from the pressure difference between the two effects In addition the bottom stream
15. Wsp Inventory of catalyst in regenerator 3200 27 lb State spent pipe puis Density of catalyst in lift pipe 3 2 Ib ft State definition and numerical values of various process parameters are given in the cited reference The system has three major PI control loops which are set as Control loop ke TI P4 gt Vii 0 1 0 04 AP gt Vi4 0 08 0 03 Fair gt V 0 01 0 0025 57 The process has several equipment and operational constraints as follows Flows OE lt 17 O lt F lt 16 0zF lt 144 0 lt F lt 10 O lt Fs lt 20 Valves 0 lt Vi lt l i 1 14 Vessels P6 lt 39 7 psig P5 lt 39 7 psig Compressor surge limit level 10 Lift air Fsuc Fsur gt 0 Combustion air Fsuc Fsurg gt 0 Wet gas Fsuc Fsur lt 0 Total combustion in regenerator level 9 5 Co sg gt 1 5 Treg gt 1265 F Teye Treg lt 20 F T2 1310 F Cco sg 350 ppm 58 Differential pressure level 8 5 0 lt AP lt 2 0 psi Standpipe level level lower limit 10 upper limit 8 0 lt Ly lt 20ft Riser Temperature level 10 T lt 995 F Furnace Temperature level 9 T lt 1700 F 29 CAHAPTER 3 THEORETICAL BACKGROUND 3 1 INTRODUCTION As mentioned in Chapter 1 and 2 PCLAB deals with exercises that deal with steady state and dynamic analysis of the process The analysis is essential part of the controller design In this chapter the reader will be introduced
16. ale ari ters Ctrl um E Evaporator Process EE open Loop Evaporator Process Show the simulation parameters dialog Fig A3 Selecting the parameters option in the simulation menu item 122 Simulation Parameters E ZU 21 al Simulation Parameters E 090021 Solver Workspace 1 0 Diagnostics Solver Workspace I 0 Diagnostics Simulation time Simulation time Start time 0 0 Stop time 300 Start time 0 0 Stop time 300 Solver options Solver options Type Variable step z ode45 DoimandPrince z Type Variable step ode45 Dormand Prince discrete no continuous states Max step size 2 Relative tolerance 1e 3 ode45 Dormand Prince Max step size a ode23 Bogacki Shampine Initial step size auto Absolute tolerance 1e 6 Initial step size ode113 Adams ode 5s stiff NDF ode23s stiff Mod Rosenbrock ode23t mod stiff Trapezoidal Output options ode23tb stiff TR BDF2 0 x Refine output l Refine factor 1 a Refine factor mf ES IE ox coca nee on Fig A4 the parameter adjustment dialog box A 4 GRAPHICAL TOOL All Simulink modules comprising the case studies allow for visualization of the transient response through the Scope box However the Scope shows only the result of the current simulation Relying solely on the Scope capability the user can not compare the result of different simul
17. c ones 3 1 a c Adding a scalar to an array results in adding the scalar to all the elements of the array at2 Vector and matrix multiplication requires that the sizes match a b c a To perform an operation on an array element by element use a before the operator a b a 2 a 2 l a Some useful matrix functions are det a determinant of a square matrix inv a inverse of matrix rank a rank of matrix eig a eigenvalues and eigenvectors of square matrix poly a characteristic polynomial of matrix svd a singular value decomposition Example 2 Using MATLAB for matrix calculations Enter the example below at the prompt gt gt b 1 2 3 4 hit enter b 12 3 4 c 5 6 7 8 hit enter c 5 6 7 8 gt gt d b c hit enter ans 19 22 43 50 To find the transpose of d type d gt gt d enter ans 19 43 22 50 Example 3 Using MATLAB elementary math functions The software also has several elementary math functions These include trigonometric functions exponential functions and other built in matrix functions like determinant rank and null space Examples of trigonometric and exponential functions are Trigonometric functions gt gt cos 2 hit enter ans 0 4161 gt gt sin pi hit enter ans 1 2246e 16 Exponential functions gt gt exp 1 hit enter ans 2 7183 gt gt log 2 hit enter ans 0 6931 1 3 3 Graphics The program al
18. first output or the output flow rate fourth output The second MV can be used to control product concentration second output Nevertheless the control structure is not well defined Another input other than the coolant temperature shall be examined u LILIA sj S Fig 7 5 Open loop response for a step change in the steam pressure 108 CHAPTER 8 ADVANCED CONTROL STRUCTURES 8 1 CASCADE CONTROL Cascade control is one of the most successful configurations to improve the performances of the single loop feedback control It can provide more effective control by reducing both the maximum deviations and integral error for the disturbances response The concept of cascade control was introduced in chapter 3 The block diagram for cascade control is shown in Fig 3 6 which consists of two control loops the inner and the outer loop The primary also called outer master controller maintains the primary variable say y at its set point by adjusting the set point y of the secondary controller The secondary also called inner slave controller responds both to the output of the primary controller and to the secondary controlled variable y2 The key point in cascade control is the selection of secondary variable Two guidelines must be observed e The secondary variable must indicate the occurrence of an important disturbance e The secondary variable dynamics must be faster than that of the primary variable
19. heat of vaporization of water 80 6 1 0 50 5 9 3 119 9 194 7 339 0 208 0 25 0 46 1 307 9 20 20 4 38 5 Heat transfer coefficient times the heat 6 84 transfer area C m kPa kg min kPa kW Kg min kW kg m kg kg kPa kW kg kW K A is the latent heat of steam which is calculated from a given correlation as a function of the saturation temperature 30 2 3 ETHYLENE POLYMERIZATION REACTOR 2 3 1 Process Description and Flow sheet Polyethylene is considered the world largest produced synthetic commodity polymer The polyethylene reactor process is depicted in Fig 2 2 The Py Py Pip Pro process model was developed by McAuley et al 12 and is given below The major components of the process are a feed gas which is partly combined with the recycled gas before entering the bubbling fluidized bed the other part of the fresh feed gas is used to introduce the Ziegler Natta catalyst b a catalyst feeder c a product withdrawal system which is controlled in order to Fur Fea Fp Fro Im T maintain a constant bed height E f Eis MO inside the reactor d gas Fig 2 2 Polymerization Reactor recycling which includes a cyclone and a compressor e reactor with catalyst disengagement zone Four major components are fed to the reactor The gaseous species are Ethylene monomer Butene comonomer hydrogen and nitrogen The nitrogen is used to carry the catalyst powder and maintain
20. point of 94 C in the set point box run the simulation and observe the temperature closed loop response To change the set point value simply double click the set point box When a new dialog box appears enter your desired value in the space called constant value One can also examine the time response of the other outputs and the steam flow rate At this given values for ke and t does the temperature reach its new set pint exactly Note that the final value of the temperature should be higher than the set point by amount of 0 046 Is the response fast enough 4 Try different larger values for ke at fixed t and re examine the closed loop response Try different larger values for t at fixed ke and examine the closed loop response In which case the response is faster Disturbance test 5 Explore the controller performance for regulatory problem Re enter the temperature set point of step 2 without the decimal digits in the designated box Click the step box of the feed temperature Add 5 to the given value Close the dialog box by clicking ok This step change simulates a sudden increase in the feed temperature Set the controller gain and time integral to zero Simulate the process under disturbance without controller Observe the temperature response 6 Re enter the PI controller parameter values found in step 1 above Click the start button and watch the top brine temperature responds Discuss how the controller improves
21. the interaction is d Ai O indicates strong opposite effect compared to its effect when other loops are open Such input output pairing is potentially unstable and should be avoided Based on the above results RGA pairing rule is pair input and output variables that have positive RGA elements and closets to one To compute the RGA we can do the following steps Step 1 step the feed pressure P100 by amount say 1 kPa with all control loops are disabled and record the reaction curve as shown in Fig 7 5 Step 2 Using the response in Fig 7 5 compute the steady state gain for all outputs as explained in chapter 5 and insert in the RGA matrix as the first column Step 3 Repeat step 1 and 2 for the other inputs say F100 T200 F200 The final RGA matrix is 107 0 018 2 0 0 017 0 35 0 02 104 001 0 2 0 0037 10 7 0 08 1 4 0 0015 0 8 0 0067 0 12 The resulted RGA matrix is thus 0 3161 0 1164 4 19 4 76 0 0505 0 8704 0 332 0 253 0 0906 0 2933 17 99 17 38 0 5374 O28 13 153 13 87 The RGA matrix shows that the system is highly interacting It is obvious that the third and fourth manipulated variables i e F200 and T200 are collinear We can see that they have the same effect on all output but at the opposite direction This is expected because the coolant temperature and its flow has the same thermal effect but at the reverse directions The first MV can be used to control either the liquid level
22. the Polyethylene Process Menu Choose the second item on the menu Polyethylene stable by simply clicking on it This leads to the process flow sheet of the polyethylene process as shown in Fig 5 10 Remember the coloration code discussed earlier still applies Quit Clear Work Space O x Polyethylene Process Menu Chemical Engineering Department King Saud University Fig 5 9 Polyethylene Process Menu 87 Double click on the input parameter of the recycle flow rate F to obtain the Block Parameter icon Then increase this recycle flow from 8500 to 9020 moles s After this is done close the Block parameter icon for the recycle and double click that for hydrogen flow Fy to obtain Fig 5 11 Once this is displayed on your screen use the keyboard to enter 2 2 moles s instead of the 1 16 Press the enter button for the system to accept this entry Now run the simulation as the same way it was done in the first part of the chapter When the run button is pressed PCLAB will run your simulation based on the values of the new parameters that were entered File Edit View Simulation Format Tools Dees e Gas Phase Polyethyelen Reactor eae outputs PM1 PM2 PH2 P T 131 13 Fml mole s 3 51 Fm2 mole s 1 6 FH moles 2 52 FN mole s 2 Fc kg s Temperature C 8500 Fg mole s 293 TEK 3 11e4 Fw mole s Disturbance Polyethylene Fi
23. the regulatory response 7 Repeat step 7 8 using a disturbance of magnitude of 5 in the feed temperature 135 In the case of disturbance rejection does bringing the top brine temperature to its original set point brings also the distillate product to its original set point why not Sampling time test All the above simulation was carried out at a specific sampling time of 5 minute The choice of the sampling time plays an important role in the controller performance To examine such a role change the simulation sampling time Double click the time box and change the sampling time to say 10 Double click the large MSF box When a new simulink model appears double click the signal generator box Update the period to 10 After closing all dialog boxes the new sampling time is activated Run the closed loop simulation steps 4 9 again and observe the effect of the new sampling time on the control performance Idea Innovative user can test different control structure i e different output input pairing Fixing the simulation time If the process response is fast ie the simulation time is larger than the apparent dynamic of the process change the simulation time On the toolbar menu open the simulation and select parameters A dialog box for simulation parameter comes up Change the value of Stop time to your desired value 136 B 5 Single Loop PI Control Tutorial 2 PI Control of an MSF plant Objective To buil
24. to some of the terms that will be encountered in most of the exercises to be performed The modeling of industrial processes usually starts with a balance on a conserved quantity mass or energy Mass and energy balances are very important for the engineer to describe the process mathematically This balance can be written as Total flow rate of Total flow rate of Accumulation rate of mass energy into mass energy out of the mass energy within 3 1 the system system system As we can imagine in writing these balances and all other auxiliary equations we must make use of almost every area of process engineering such as thermodynamics heat transfer fluid flow mass transfer reaction engineering etc This makes the modeling of industrial processes most interesting and challenging After characterizing the system by the model it is then necessary to analyze the behavior of the system in terms of its variables that affect the controlled parameter or the effect of disturbances that surface to affect the controlled parameter with time When these variables are known steps are then taken to keep them in check through the development of control algorithms Applying 3 1 usually results in nonlinear ODE equations which can be linearized and converted into transfer function in the form of First Order with Dead Time FODT y s ke Lo 3 2 w l1 60 ke Second Order with Dead Time SODT y s u
25. values to variables ya 2 b 3 a If no name is introduced result of the expression is saved in a variable named ans atb If you do not want to see the result of the command put a semicolon at the end of it atb You can see the value of the variable by simply typing it a MATLAB is case sensitive This means MATLAB distinguishes between upper and lower case variables In MATLAB all computations are done in double precision However the result of calculation is normally shown with only 5 digits The format command may be used to switch between different output display formats c exp pi format long c format short e c format long e c format short c The c c command clears the command window and homes the cursor clc Remember that by using the up arrow key you can see the commands you have entered so far in each session If you need to call a certain command that has been used already just type its first letter or first letters and then use the up arrow key to call that command Several navigational commands from DOS and UNIX may be executed from the MATLAB Command Window such as cd dir mkdir pwd Is For example cd d matlab toolbox cd c MProgram Files Numerical Methods Chapterl The single quotation mark is needed in the last command because of the presence of blank spaces in the name of the directory 1 3 1 Vectors and Matrices MATLAB is designed to make ope
26. y e FC V b C4K bC K 2 43 Ss FO V b C4K4 b C5 Kg 2 44 y FK QBK V a3C a4C4 K t bC5 K5 Kg Ko cb4C4 K5 K4 2 45 2 46 VC y Fp C T T 00 B PC Ty OPC T T amp V rCAH r AH 2 47 V pC d Qu B pC T T amp UAT Rav Teay pm QOBK V a C K aC a4C4 t b5C t b C4 K 2 48 y a QOpK V a5C Ky a43C5 bC c b4C4 K4 t a4C4K 2 49 y D OBK Via C Ks bi CK t a4C4K5 2 50 where 37 T Tg 2 51 T Rav 2 NE 2 52 cav 2 The dynamic of the outlet temperature of the coolant fluid is not included and alternatively it is obtained by solving the steady state equation WCp T T U A Trey ca 2 53 2 4 3 Process Parameters and Variables Variable Description Value Units Q2 Rate constant for consumption of component C in the m mole s initiation and propagation a4 Rate constant for consumption of component Ci in the m mole s initiation and propagation b2 Rate constant for consumption of component C in the m mole s termination stage b4 Rate constant for consumption of component Ci in the m mole s termination stage Cp Heat capacity of reactor mixture 0 55 cal gm C Cpr Heat capacity of feed 0 55 cal gm C Cp Heat capacity of water 1 0 cal gm C C Butene 1 concentrations 8700 mole m C ethylene concentrations 1065 mole m Cy Ethylene concentration at the feed 25000 mole m
27. 1 The default data method for the to workspace blocks r t u y in Fig 1 12 must be changed from structure to matrix in order to save data in an appropriate form for plotting In conclusion SIMULINK is a very powerful block diagram simulation language Simple simulations including the majority of those used as examples in this textbook can be set up rapidly in a matter of minutes The goal of this module was to provide enough of an introduction to get you started on the development of open and closed loop simulations With experience the development of these simulations will become second nature It is recommended that you perform the simulations shown in this module as well as other exercises to rapidly acquire these simulation skills 1 5 INSTALLING PCLAB For better performance simply copy the PCLAB folder into your local hard disk Then either add this directory to your MATLAB path using the path command or choose to work from the designated directory for PCLAB using the cd command Note that the working directory can be adjusted directly from the menu of the MATLAB Command Window PCLAB works for MATLAB version 5 3 and higher Quit Clear Work Space Process Control Modules R Department of Chemical Engineering King Saud University Help Menu Fig 1 13 Main menu of the PCLAB software 22 To start PCLAB first lunch your MATLAB Once in the MATLAB program use the path browser to change to PCLAB subdi
28. 466 0 5 ton min kJ kg C kJ kg C ton min Kg Kg Bar ton min C C C C C C kJ min C m kJ min C m ton min kg kg ton min ton min ton min ton min m pB pp Orifice width for stage N Density of brine Density of Distillate Latent heat for vaporization Latent heat for vaporization at the temperature Latent heat for steam 3 Calc 1000 Calc distillate Calc Calc m kg m kg m kJ kg kJ kg kJ kg 50 2 7 TWO CSTRs IN SERIES 2 7 1 Process Description and Flow Sheet Consider two CSTRs in series with an intermediate mixer as shown in Fig 2 6 A chemical exothermic reaction of the form of A B takes place in the liquid phase The reaction rate is considered to be first order in the reactant species The feed to the first reactor is a pure species A with volumetric flow rate Q11 at ambient temperature The liquid inside the reactor converts partially to species B The heat released from the chemical reaction is removed by cooling water with volumetric flow rate Qcw1 and temperature Tcwl The outlet of the first reactor has a volumetric flow rate Q1 and temperature T1 and it is mixed with a fresh feed of pure component A The product of the mixer is then fed to another reactor where the same first order reaction takes place Water at ambient temperature is also used to cool the second reactor The outlet flow rates are considered to be driven by the hydrostatic pressur
29. 5 4 Table 5 5 Table 6 1 Table 6 2 Table 6 3 Table 6 4 Table 7 1 Table 8 1 Table 8 2 Page Calculated values of the characteristic parameters for positive step change 77 Calculated values of the characteristic parameters for negative step change 80 Comparison of the values of characteristic parameters 81 Calculated values of the characteristic parameters for 1 step change 81 Calculated characteristic parameters for the polyethylene process 86 Cohen Coon Formulas 88 Ziegler Nichols formula 89 Estimated Parameter values for a PID controller 92 Parameters used for the PID controller 94 Estimated Parameter values for a PID controller 100 Comparison between Feedback and feed forward controllers 110 FFC tuning values 111 iv List of Figures Figure 1 1 SIMULINK Library Browser Figure 1 2 SIMULINK Continuous Blocks Figure 1 3 SIMULINK Sources Library Figure 1 4 SIMULINK Sinks Library Figure 1 5 Development of an Open loop Simulation Figure 1 6 SIMULINK Math Library Figure 1 7 SIMULINK Additional Linear Library Figure 1 8 Block Diagram for Feedback Control of the Van de Vusse CSTR Figure 1 9 Measured Output amp Manipulated Input Responses to a Unit Set point Change Figure 1 10 Transport Delay Icon Figure 1 11 Saturation Element Figure 1 12 Block Diagram with Saturation and Time Delay Elements Figure 1 13 Main menu of the PCLAB software Figure 1 14 Process description help option Figure 1 15 User gui
30. 53 25 25 25 2 25 2 2515 21 25 0 50 100 150 200 250 300 251 0 50 100 150 200 250 300 Time offset 0 Time offset 0 Fig A 2 concentration response to step change in steam pressure 121 A 3 SIMULATION PARAMETER All Simulink modules are simulated by pressing the start button as mentioned throughout the manual In this case the module will be simulated using default simulation parameters To alter the simulation parameter one can simply select parameters from the simulation menu as shown in Fig A 3 This concept is also discussed in chapter 1 section 1 4 2 The user can adjust the simulation time see Fig A4 For example if the simulation length is not enough to capture the full transient response then the Stop time should be increased Moreover in some cases the simulation may crash because the dynamic equations of the process are stiff or hard to integrate In this case the user should try different ODE solver The current solver as it appears in Fig A4 is Dormand Prince Pointing at the solver type box will reveal the available ODE solvers in a drop down menu fashion The user can also adjust the relative and absolute tolerance In general reducing the tolerance will make the ODE easy to solve but the resolution of the simulation plot will degrade The user is also allowed to change the type of the solver from variable step to fixed step vapopen i File Edit View EST 1M Format Tools Digg 9 Ctrl T
31. Feedback Control According to fig 3 4 the following are defindd G H G G s controller transfer function e s s G s final control element valve transfer function G s process transfer function G s disturbance transfer function G n s measurement device transfer function C s controller signal Vm S measured output Ysp S set point e s error PID controller The operating equation for PID controller is C t ceo fena tT E c 3 6 are dt Taking Laplace transform of the above equation we get co x prs Le ros Jes 3 7 T I5 The transfer function for PID controller is 66 6 Kr e ros 3 8 TS The parameter Ke is called proportional gain tp is called the derivative time constant and rris the integral time constant Feed forward system The objective of the feed forward control is to keep the values of the controlled output as its defined values It is configured such that predictive action is taken on the controlled variable thus it does not wait until the effect of a disturbance is already felt in the system but acts appropriately in anticipation of the disturbance Fig 3 5 depicts a typical feed forward control element 16 Disturbance Process Fig 3 5 Feed forward Control configuration Manipulated variable Controlled variable In this control the direct measurement of a disturbance is used to adjust the values of the manipulated
32. KING SAUD UNIVERISTY COLLEGE OF ENGINEERING RESEARCH CENTER Final Research Report No 55 426 PCLAB Manual By Dr Emad Ali 2 1427H 3 2006G Table of Contents Content CHAPTER 1 INTRODUCTION 1 1 Objectives 1 2 What is MATLAB 1 3 Basic Operations and Commands 1 4 Introduction to SIMULINK 1 5 Installing PCLAB 1 6 Overview of PCLAB Structure CHAPTER 2 CASE STUDIES 2 Introduction 2 2 Forced Circulation Evaporator Unit 2 3 Ethylene Polymerization Reactor 2 4 Ethylene Dimerization Reactor 2 5 Double Effect Evaporator 2 6 Multi Stage Flash Desalination 2 7 Two CSTRs in Series 2 8 Fluid Catalytic Cracking Unit CHAPTER 3 THEORETICAL BACKGROUND 3 1 Introduction 3 2 Steady State Analysis 3 3 Dynamic Analysis CHAPTER 4 STEADY STATE DISTURBACNE SENSTIVITY ANALYSIS 4 Introduction 4 2 Open loop Mode 4 3 Closed loop Mode CHPATER 5 OPEN LOOP DYNAMIC ANALYSIS 5 1 Introduction 5 2 First order System s Dynamic analysis 5 3 Second order system Dynamics CHAPTER 6 CLOSED LOOP DYNAMICS 6 1 Introduction 6 2 Controller Tuning 6 3 Testing the ZN and CC PID settings through Simulation CHAPTER 7 MULTIVARIABLE SYSTEMS 7 1 Multi Control Loops CHAPTER 8 ADVANCED CONTROL STRUCTURES 8 1 Cascade Control 8 2 Feed Forward Controller FCC REFERENCES APPENDIX A SPECIAL FEATURES APPENDIX B TUTORIALS iii 86 9 9 9 99 103 103 109 109 114 118 120 126 List of Tables Table 5 1 Table 5 2 Table 5 3 Table
33. To build intuition about designing multi loop PI control and experience the effect of cross loop interaction Process Description For detail description of the process its main variables and schematic of the flow sheet refer to chapter 2 Here we deal the control of at least two controlled variables For the specific polyethylene example the monomer and hydrogen concentrations are controlled by manipulating their corresponding flow rates Tutorial procedure 6 10 11 12 13 At the Polyethylene sub menu select multi loop control A simulink module showing the closed loop process in multi loop mode pops up The first control loop that links the monomer concentration with the monomer feed flow rate The second control loop links the hydrogen concentration with the hydrogen feed flow rate These two control loops are chosen for demonstration purposes The user can alter the control loop structure as desired Compute the controller parameter values for each control loops using the same methods used in the single loop control tutorials Insert the computed values of the controller settings in their designated boxes Explore the controller performance for regulatory problem To do so select an appropriate disturbance from the available list Change the numerical of the chosen disturbance Simulate the process under disturbance with the two controller loops in service Observe the output response Discuss the performance o
34. adily to attain a new steady state value Observe the dead time represented by the flat portion of Fig 5 4 In this region the liquid height in the tank does not change with time In order to read the numerical value of the time during which the system stayed flat choose the first icon on the top left Click this icon to allow you enlarge the scale and read the corresponding value on the x axis as shown in Fig 5 5 The enlarged portion shows the output response beginning after 10 seconds 78 Simulation Parameters Evapopen Exi Tz x Solver Workspace 1 0 Diagnostics Real Time Workshop Simulation time Start time 0 0 Stop time 300 Solver options Type Variable step m ode45 Dormand Prince m Max step size 2 Relative tolerance 1e 3 Initial step size auto Absolute tolerance 1e 6 Output options Refine output Refine factor 1 DK Cancel Help Apply Fig 5 3 Simulation Parameter window for stop time change e ala amp Fig 5 4 Output showing the height of tank versus time The region or period is known as the dead time during which the system does not respond to any input change or disturbance One can then use the plot of Fig 5 4 to calculate the process gain and the time constant as per 3 2 and 3 3 79 Fig 5 5 Part of Output showing the height of tank versus time The gain is defined as the change in output over the change in the input This ra
35. aint 2 Lookup Tables 2 Math Operations UT Y y Assign Drag this icon into a m 2 j Model Verification i 2 Model Wide Utilities Bias 21 Ports amp Subsystems 24 Signal Arent F Complex to E 2H Signal Routing u Magnitude Angle Sinks Belu S Sources mc Complex to Realmag Zr User Defined Functions amp 34 Additional Math amp Discrete x Divide Wi Control System Toolbox l Wl Real Time Workshop Dot Product w Wii Signal Processing Blockset 3 lli Simulink Control Design E m BA Simulink Extras Gain d BH Simulink Parameter Eai WA MagitudeAngleto E Wl Simulink Response Optimization z Complex Wii stateflow Math Function Horiz Cat NAN Matriv Canratenation Fig 1 6 SIMULINK Math Library Simulink Library Browser File Edit View Help DS d PID Controller Enter expressions for proportional integral and derivative terms Pel s Ds Commonly Used Blacks Ia Continuous Discontinuities PID PID Controller d PID PID Controller with Discrete Approximate Derivative Logic and Bit Operations Lookup Tables k Math Operations Model Verification 4 Transfer Fen with initial Model Wide Utilities sei outputs Ports amp Subsystems 1 Transfer Fen with initial Signal Attributes oH states Signal Routing en Sinks Zero Pole with initial as 1 outputs 1 sen b Ax Bu State Space with initial y Cx Du outputs Source
36. ameter of F and changing the flow rate from 10 to 9 kg min Fig 5 8 is the graph for the response of the tank to the input forcing function From the graph there is an immediate inverse response before the curve picks up to respond normally Similar to the previous paragraph the parameters of this run are captured and listed in Table 5 2 Level m CNN PAP rs aj Fig 5 8 Output showing the height of tank versus time Table 5 2 Calculated values of the characteristic parameters for negative step change I mw pe e 84 Table 5 2 still shows the concentration output parameter to be the most sensitive with a time constant of 28 8 seconds The gain is seen to be very high reaching 20 1 for a step change of 10 The gain and the time constant parameters in Table 5 3 are different from those in Table 5 2 and 5 1 for an input step change of 10 and 10 It should be noted that the dead time was not affected by the step change because it is intrinsic property of the process Moreover the dead time incorporated by ad hoc method For linear systems the process parameters must have the same absolute magnitude for the same magnitude of step change Therefore the systems dynamics for 10 step change do not exhibit linearity in that region Since linearity is the basis of these calculations further tests need to be carried out to establish the existence of linearity One can also check the process linear behavior throug
37. and test a PI controller of an MSF plant for set point change and disturbance rejection Note In this tutorial the MSF process is considered as an example Similar procedure applies to other case studies Process description For detail description of the process its main variables and schematic of the flow sheet refer to chapter 2 Here we analyze the dynamic behavior of the MSF plant under a single PI control loop All controllers should be designed for a specific level of operation which include specifying an expected or desired value for set point and typical or baseline for important process parameters Here we consider controlling the top brine temperature of an MSF plant The main possible manipulated variable is the steam feed rate to brine heater A standard Proportional Integral control algorithm will be used It is therefore necessary to determine the controller parameters i e ke controller gain and c integral time Next the performance of the controller can be examined through simulation for tracking different set point changes and to reject possible disturbances To simulate real practice the PI control is implemented in discrete time fashion with sampling time of 5 minutes There are several methods for determining the PI parameter values One method is the reaction curve method This method utilizes the process model parameters determined in the previous Open loop Workshop tutorial These values can be fitted in pr
38. ansfer limitation is considered in this system Schematic of the process is depicted in Fig 2 3 The liquid is homogenized by a high re 35 circulation rate around the reactor through a heat exchange used to remove the high exothermic heat of reaction The model uses the Homo and Co polymerization mechanisms suggested by Galtier et al 9 The reaction stages initiation propagation and termination are of first order kinetics with respect to each reactant Initiation and propagation stages KC gt KC nzl 2 32 KC Cy 2 KC nym 2 1 2 33 The rate of initiation and propagation which also represent the rate of disappearance of Can in these stages have the following rate equation 1 2 34 Fa E a gt C gt KC m 0 Termination stage KC Coy KC nmzl 2 35 The chain termination reactions which are assumed to occur in parallel with the growth reactions have the following rate equations E 2 36 un bz C gt KC m 1 The rate constants are defined as follows ey 2 37 36 adb 2 38 Ay Aye p y 2 39 by aye Spiels 2 40 b bbs gt Based on the above assumptions and the assumed reaction kinetics the resulted dynamic model of the dimerization process is presented in the following 1 6 2 4 2 The Process Model V OPC V b C a4C4 b4C4 K5 a4C4K b4C4K4 2 41 P 2 42 perd OBC V a C K K Ki cb C K K44 Kq
39. arameter window will appear as shown in Fig 5 2 Block Parameters F1 kg min x r Constant Dutput a constant m Parameters Constant value 10 Cancel Help Apply Fig 5 2 Block Parameter window for feed flow input JT Note that the current flow rate is 10 kg min To change this number simply use the mouse to highlight the number 10 by right clicking the mouse hold and drag slightly to the right until the number 10 is fully highlighted then release the mouse Now type in the number 11 and press the OK button This way a 10 step increase in the inlet flow is attributed to F After effecting this change press on the run icon or press simulation and then start Note that in this case the 300 seconds allotted may not be enough so click on Simulation then Parameters to get Fig 4 3 Using the parameter menu option see Appendix A 3 the stop time of this run should be changed from 300 seconds to 400 seconds This will enable you to capture enough time for steady state operation Use the same procedure as in changing the value of the Block Parameter window change the run time from 300 to 400 seconds Now run the simulation by pressing on the start button in the simulation menu After the 400 seconds has elapsed the run will be complete Click on the first output icon for level to view Fig 5 4 The input has changed step wise from 10 to 11 kg min The output response of the tank to this change is seen to rise ste
40. ations in one screen For this reason we have added the graphical tool to allow the user to plot his results in a single screen The graphical tool can be activated from any Simulink module by clicking the green box entitled graphical tool By doing so the following window pop up PCM Plot oad Dara Fils ee Plot View Misc Options Look in PClab1 1 xy amp metE i Amoco E fCovP dat E y wd nn good dat Em dimerization fgain dat _wd_wn_bad dat Print Evaporator fitting dat wd wn ood dak Quit gt help fpoles dat FResult dat i fstep E yv dat Ej fzeros yy dat M dat i us dat ut dat uv dat y_nd_nn dat y nd wn dat E CC bad noisy dat y osc dat CC bad nosiy dat Ey wd nn bad dat 123 PEM Plot PCM Plot Data Gis view Misc Options n 0967 100 200 300 50 86 50 84 1 98 50 82 5078 Data Pet View Mec Options 000 300 Fig A5 Plotting Forum Options Before starting the drawing one should save his data containing the results of different simulation in a single matrix The data matrix should have the sampling points in the first column The following subsequent columns should contain the results for diverse simulations After creation of the data file the user starts uploading the data file by choosing oad from the Data menu item see Fig A5a By doing so a new dialog box called Load Data file appears as in Fig A5b pointing at the current PCLAB home di
41. axis will increases allowing more accurate reading of 63 2 3 Repeat step 3 using exactly the same amount of step change AW but with negative value Record your results and compute the dynamic parameters as in the previous step 4 The two steps in the steam flow were both the same in magnitude Are the computed model parameters i e Ky and tp the same for these two steps How why are they different Does the process dynamic behave linearly 5 Repeat steps 3 to 8 for the other process inputs i e Bo recycle flow rate T seawater feed temperature 6 Based on the above analysis can you conclude upon which process input has the most effect on the process temperature Can you determine which process input has the slowest impact on the process dynamics 7 To further assess the linearity of the process dynamics carry out two different but proportional step changes with specific ratio Examine the resulted static gains and time constant Are the calculated process parameters proportional to each others with the same given ratio Ideas Innovative user can test the process dynamics for input functions other than step changes The user can utilize the simulink library to includes pulse sine ramp etc signals 130 Work sheet Effect of W on To Initial steady state Ths Wiss Boss Toss Positive step change Negative step change AW AW New final value of Tso New final value of Tso
42. balance in distillate tray Dy Dy t Vy e Energy balance of condenser tubes Mc ncn a WrCpc y Tr Te n Uy AggATy Uy AppATy Vy y Splitter Wr Rej Wink Brine Heater e Energy Balance equation dT xp M pu Cpg j 23 Bo Cpe Tc CPgoTgo Wh s Additional relations 47 2 74 2 75 2 76 2 77 2 78 2 79 2 80 2 81 2 82 In the above model equations the brine flow and the brine level in each stage are correlated as follows B wL K j pp Pj a P pp jg L Ch 2 83 Similarly the distillate flow is correlated to the distillate level as follows D Cp 4Pp 8Lp j 2 84 The temperature difference used in the above energy balances is defined as follows AT T5 x 0 5 T Tein 2 85 Note that j is computed at Tg while 2 lt is computed at the distillate temperature which is assumed to be equal Tg minus the boiling point rise at the j stage BPRj In the original model 2 4 the physical properties for each stage in the above model i e p Cp U Mc M pp BPR and the vapor pressure P are estimated through empirical correlation Industrial values were used for the plant design parameters such as C h Ap Anc Apr and w Moreover realistic values for the size and number of tubes were used in computing U M and Mgy The definition of all parameters of the model equations is given in the next table 2 6 3 Process parameters and va
43. beled graphical tool shown in the Simulink Module can be used to trigger the plotting forum The usage of the plotting forum is discussed in Appendix A 90 CHAPTER 6 CLOSED LOOP DYNAMICS 6 1 INTRODUCTION A closed loop system normally has a controller together with other hardware components but the key component here is the controller The closed loop response also depends on the transfer function of the system and on the nature of the change Normally the change is divided into two namely set point and disturbance If there is a set point change the feed back controller acts in such a way as to keep the ultimate response as close as possible to the changing set point On the other hand if there is any form of disturbance but the set point remains the same then the feed back controller tries to eliminate the impact of the disturbance or load changes and keeps the ultimate response at the desired set point However the presence of other hardware components could lead to oscillatory behavior and unstable systems Therefore it is important to design controller systems that will eliminate all the instability 6 2 CONTROLLER TUNING Performance of feedback controllers depends on the values of their chosen parameters If these parameters are properly chosen they offer the highest flexibility to achieving the desired controlled response and stability The process of choosing these parameters is known as controller tuning There are thr
44. d intuition about PI tuning by trial and error method and experience the advantage and drawback of such a method Process description For detail description of the process its main variables and schematic of the flow sheet refer to chapter 2 Here we analyze the dynamic behavior of the MSF plant under a single PI control loop In previous tutorial the controller parameters i e ke controller gain and t integral time were determined by the reaction curve method The reaction curve method requires building information about the process model The reaction curve method requires stepping the process Sometimes it takes long time for the process to settle to another steady state value During which disturbances may also occur Moreover some processes may not exhibit regular dynamic similar to that of a first order system For this reason PI controller can be tuned by the continuous cycling method as described here The PI controller is applied in discrete time fashion with sampling time of 5 minute Tutorial procedure 1 Use the same MSF module with single loop control Set controller integral time to zero Therefore the integral action will be disabled Select arbitrary value for ke Similarly select an arbitrary value for the set point Click the start button to simulate the process View the top brine temperature response at the scope box 2 Repeat the previous step repeatedly Each time increase the value of ke gradually Obse
45. d ones 120 A 2 ADDING NOISE TO OUTPUT MEASUREMENT All the simulation results shown in the manual depicted very smooth curves Industrial practice indicates that output signals are always corrupted with noise To add a realistic touch to the PCLAB simulations a feature that allow the addition of measurement noise is adopted in this version of the software As mentioned in the previous section double clicking the yellow box in any Simulink module will open the process parameter dialog box i e Fig A 1 At the bottom of the parameter list appears the noise variance The number of the noise variance equals the number of outputs The order of the noise variance follows the order of the outputs appearance in the Simulink module The user can specify the value of the noise variance which is supposed to be trivial compared to the variance of the measured output Usually noise is a random variable generated from mechanical and electrical sources Since we are dealing with pure simulation the noise is incorporated artificially to the data Fig A 2 shows the response of the product concentration in the evaporator process to 10kPa step change in the steam pressure The left hand side plot depicts the response when no noise is preset while the right hand side plot shows the response with the measurement is corrupted by noise whose variance is 0 001 concenmanon 4 LIE Pepe aal i s 25 35 koncentration 22 BE Pepe aj S 254 25 3 2
46. de help option Figure 1 16 Evaporator menu Figure 2 1 Flow sheet of Forced circulation Evaporator Process Figure 2 2 Polymerization Reactor Figure 2 3 Ethylene Dimerization Reactor Figure 2 4 Two Effect Evaporator Figure 2 5 Flow Sheet for the MSF process Figure 2 5b Single Stage Figure 2 6 Flow Sheet for two CSTRs in series Figure 2 7 Flow sheet for FFCU process Figure 3 1 Output response for a step change for first order system a with time delay b without time delay Figure 3 2 Output response to a step change for second order system Figure 3 3 Typical Feedback control configuration Figure 3 4 Typical Block diagram for Feedback Control Figure 3 5 Feed forward Control configuration Figure 3 6 FFC block diagram Figure 3 7 Cascade control configuration Figure 4 1 Steady State Disturbance Module for Evaporator Process Page 14 15 15 16 17 18 18 20 21 21 21 23 24 24 25 28 31 35 39 43 44 48 51 59 60 61 62 63 64 65 66 Figure 4 2 SSDSA menu for the evaporator process Figure 4 3 SSDSA results for open loop test Figure 4 4 SSDSA menu for the closed loop test case Figure 4 5 Output responses to disturbance in feed temperature when the coolant flow rate is used as manipulated variable Figure 5 1 Open Loop Evaporator Process menu Figure 5 2 Block Parameter window for feed flow input Figure 5 3 Simulation Parameter window for stop time change Figure 5 4 Output showin
47. dicates a drop of more than one ton of distillate water The situation demands a good control system Fig 8 6 illustrates how the process behaves when a single control loop like that shown in Fig 8 2 is involved The PI settings for that loop is ke 50 ky 10 ka 0 The feedback reaction in Fig 8 6 demonstrates an excellent control of the top brine temperature but the product is left without control Although the 112 product is increased the feedback performance is considered poor from control point view pg MA toni iz El a 5 1 al 2 aj 70 Fig 8 6 Product response to disturbance when single loop is involved Now examine Fig 8 7 which shows the process feedback performance when cascade control is installed Here the product flow rate Wa is well maintained at its reference value This is achieved by manipulating the top brine temperature to a new value of 88 C Note that maintaining the top brine temperature at its initial value is not necessary because it is not considered as a desired process output a 3 ER Way eonun o 22 Am S Lo 22 aje S Time offset 0 Fig 8 7 Product response to disturbance when cascade control is involved The user can carry several control analysis on this cascade loop For example one can test the effect of tuning the inner and or outer loop on the overall performance This teaches how these two loops are interacting and hence care should be taken when tu
48. distillate temperature Tpj coolant temperature Tc vaporization rate Vj and stage pressure P Furthermore and in order to minimize the size of the model the liquid levels except that for the last stage and the temperature dynamics in the distillate tray are not included in the modeling The dynamics for the salt concentration is also excluded because they have no direct effect on the other process states except through physical properties of the brine such as density and heat capacity Our simulations revealed that the physical properties vary between 1 and 1 over the plant temperature range due to changes in salt concentration The mass holdup of the cooling brine inside the condenser tubes is assumed constant The following mass and energy equations are written for each stage 2 Stage j except the last stage e Mass balance of brine pool aco edm e PAAR a i 2 71 e Energy balance of brine pool dTg Pa j ApnL Cpn j EXE BCP a Tp ja TB j V Ae j a Uns D 2 72 e Mass balance in distillate tray D D V 2 73 46 e Energy balance of condenser tubes dTe Mc CPc j Ux BoCpc j Tc ja Te U jAgc AT for the rejection section the see water feed Wr is used instead of Bo in 2 74 Last stage N e Mass balance in brine pool dL Pa j Ap Pi By By Vy Wmk Bo e Energy balance in brine pool dT Ds j AngL CDs E m By Cp j Th v4 Taw Vy Ay Cp T5 v zu W Cps Tc T y e Mass
49. disturbances by marking its checkbox Select the closed loop mode Select appropriate step size and number of steps 2 3 4 Select appropriate manipulated and controlled variable pair 5 Run the simulation by clicking the run button 6 Examine the generated plots 7 Discuss your results and make conclusions Additional steps 8 Repeat the above procedure for the same controlled variable but with another manipulated variable 9 Compare the results for the two different manipulated variables and make a conclusion 127 10 The user can reexamine all possible manipulated variables for the same controlled variable and comes up with the best input output pair Additional steps 11 The user can study the multivariable framework by selecting two controlled variable and two manipulated variable simultaneously and run the simulation 12 The user shall examine the results discuss them and draw conclusions 128 B 3 Open loop tutorial Exploring Dynamics of an MSF Plant Case study Objective To study the open loop dynamic behavior of an MSF plant and to fit the step test data to a first order plus dead time model Note In this tutorial the MSF process is considered as an example Similar procedure applies to other case studies Process description For detail description of the process its main variables and schematic of the flow sheet refer to chapter 2 Here we analyze the dynamic behavior of the MSF plant to variatio
50. e SSDSA can be studied for each loop individually and consequently the appropriate structure can be determined This approach however ignores the cross loop interaction Alternatively one can conduct the SSDSA method over all process variables and determine the best design structure However the method is based on steady state behavior only Moreover it is designed for a specific disturbance variable and hence may not necessarily work for other disturbances Another way to design a multivariable system is to use the concept of loop interaction A Multivariable process is said to have interaction when process input affect more than one process output The degree of interaction can be quantified by the so 106 called Relative Gain Array RGA Let K be the steady state gain matrix of the process Let K be the transpose of the inverse of the steady state gain matrix K en K The elements of the RGA can be obtained as follows The most important properties of the RGA are as follows 1 The elements of the RGA across any row or down any column sum up to 1 2 Ajj is dimensionless 3 The value of A is a measure of the steady state interaction a j 1 implies that u affects y without interacting with the other control loops The system is completely decoupled b j 0 means that uj has absolutely no effect on yi Thus y can not be controlled by uj c O A 1 means an interaction exists the smaller Aj the larger
51. e gain parameter to be negative If it is negative then the next steady state value will be lower than the initial steady state and the curve will be seen to fall to the new value as in the cases of pressure and concentration However if the gain is positive then the response curve rises and settles at a higher new value The time constant is a measure of how fast a particular parameter responds to an input forcing function The concentration parameter has the smallest time constant and therefore it is the most sensitive to changes in the inlet flow The pressure and the flow both respond within the same magnitude of time 82 All the parameters show the same value for the dead time except the outlet flow This 1s the time it takes before the parameters start or begin to respond to the forcing function Probably this dead time is inherent in the system The analysis can also be done by storing the raw data to a workspace which could be used in other software like EXCEL or the MATLAB itself To achieve this double click the output icon whose data you wish to store before starting the run For instance if you wish to store the data of the level in the tank then double click the first output icon of Fig 5 1 Doing so will open for you the window similar to Fig 5 4 but without any plots Then click on the sixth icon on the top left Properties Next click on the Data History icon to get Fig 5 7 Now mark the box of Save data to
52. e in each tank thus it related to the square root of the liquid holdup inside the reactor Fig 2 6 Flow Sheet for two CSTRs in series 2 7 2 The Process Model The following modeling equations are taken from 7 State variables are used to describe the process variables The definition of the states is given in section 2 7 3 Qu Ci Tii Xx Q Kadxn 2 86 xi Qu C x Ky xx 2 87 xjX4 K x x AH Q T 7x4 UA x3 x4 2 88 V axa Qon Toni 7x4 UA GG x4 2 89 x Q Ky x Ky Xs 2 20 XX O Ch x Kp X56 Kad x X 2 91 XU KyxjxgAH Qi x7 K As G6 x7 UA x7 xg o V 2X8 Qu Too Xg UA x7 xg 2 93 Additional relations K k exp E RT 2 94 Ky ko exp E RT 2 95 2 7 3 Process parameters and variables Variable Description Value Units Ci Feed concentration for component A 20 mole m Ci Feed concentration for component A 20 mole m E R Activation energy 600 K Ky Orifice constant for valve 1 0 16 m s Kv Orifice constant for valve 2 0 256 m s ko Pre exponential factor 2 7x10 l s k Reaction rate in CSTR 1 1 s kp Reaction rate in CSTR 2 1 s On Feed rate for CSTR 1 0 339 m s 52 Qui Feed rate for mixer Oud Cooling water feed rate to CSTR 1 QaaA Cooling water feed rate to CSTR 1 Tu Feed temperature to CSTR 1 Ti Feed temperature to CSTR 2 Tewi Cooling water temperature to CSTR 1 Tew2 Cooling water temp
53. e main menu has two Help option s buttons namely process description and user guide amp tutorial The help documents can be accessed online using typical web browser The first help option fig 1 14 provides online information about case studies such as flow sheet modeling equations and typical values of the process parameters These pieces of information can be accessed by double clicking the desired case study name The second option fig 1 15 has two sub options which provide overview of PCLAB and procedure for carrying out certain tutorials By clicking one of the case studies a sub menu will appear See for example Fig 1 16 which shows a typical sub menu for the forced circulation process This submenu allows the user to select a specific tutorial within several exercises that are ordered as follows 1 Open Loop 2 Closed Loop PID control 24 Multi Loop PID control Feed Forward Control Steady State Disturbance Analysis Qu Uv d US System Identification Evaporator MENU Quit Clear Work Space Evaporator Process Menu Chemical Engineering Department King Saud University Fig 1 16 Evaporator menu The aforementioned exercise focuses on the following objectives e Modeling of the process e Controller design and tuning e Sensitivity analysis and system identification The Tutorial is organized in such a way as to lead the user to the proper understanding of process dynamics First the process i
54. e manipulated variables listed in Step Box 4 as the candidate one Let the candidate manipulated variable be the coolant flow rate The user has the choice to either change the upper and lower permissible values for the candidate manipulated variable or leave them at their default values See for example Fig 4 4 Note that the user can restore the default values for the upper and lower limit any time by simply clicking the reset limit button After the user finishes marking the required checkboxes in the SSDSA menu he can simply click the run button in Step Box 6 The result for the above specification is shown in Fig 4 5 73 Dee kK AAS PHP DEWA kK AAS PHD ed Ternperature C b Fig 4 5 Output responses to disturbance in feed temperature when the coolant flow rate is used as manipulated variable By inspecting the output response in Fig 4 5a we can observe that the controlled variable C is well maintained at the nominal value Note that a red color is used for the controlled variable to distinguish it from the other uncontrolled outputs Because the evaporator pressure is not controlled it increases as expected with disturbance but this time with a larger magnitude On the other hand the feedback control helped in making the output flow rate changes slightly with disturbance More important is the response of the manipulated variable The red lines in the right plot of Fig 4 5b shows the upper and lower limits
55. e than those of the feedback controller Nevertheless FFC is expected to provide much superior performance than that of the feedback The unsatisfactory performance of the FFC may contributed to the accuracy of the estimated parameters in Table 8 2 fu gl DSHS 58 1 gt amp FeedForward Controller mask Feedforward controller Insert the design parameters Tp Td Kp Kd Parameters Plant gain Kp P100 kPa E idi Plant time constant Tp Level m 62 Set point Disturbance gain Kd for concentration Feed forw 475 gt l controlle a disturbance time constant T d concentration 96 Feedback Control Switch on 1 off 0 1 gt Pressure kPa Cancel Help gt F200 kg min gi Flow kg min T200 C Evaporator Process Ready 10095 ode45 Fig 8 9 FFC structure for Evaporator process showing the parameter dialog box 116 Iponcentrgtion yes Sec o p etl amp l 264 26 2 26 25 8 25 6 254 252 amp X 0 150 200 0 50 10 Time offset 0 a concentration 24 BER P aje 8 26 2 26 H 25 8 5 25 6 25 4 0 50 100 150 p Time offset 0 0 b oncentnationy A Bee PeP alm amp TEN p 50 100 150 200 Time offset 0 c Fig 8 10 Process response to step change in the feed concentration 117 REFERENCES l 10
56. easuia ill 3 Aa ape Gbhe Ala GA GI wey ilua dhai Gedy Lad uua Asli 5 Sail old anol JE Yalea cea aal allo Anal ya pall Qua yes lall 9 aal GU uai Lely eal oll Gull Li Qld ay Call Gull y lidi Sansa Saill ohe dalled aba Gull yanai LS aileall 5 Aa iioll 3 ial ALY Aui g AS yall il gall ia daai Sail Glee ix CHAPTER 1 INTRODUCTION 1 1 OBJECTIVES The PCLAB software is developed based on MATLAB tools and functions including SIMULINK a graphical simulation Toolbox Therefore the aim of this chapter is to introduce the student to MATLAB and SIMULINK as well as explain the basic operations and installation of the PCLAB software A brief description of MATLAB and SIMULINK will be presented further information can be found in printed document or online documents provided by MATLAB Inc 1 2 WHAT IS MATLAB MATLAB is developed by Math Works Inc It contains over 200 mathematical subprograms that enables the engineer to solve a broad range of mathematical problems including complex arithmetic eigen value problems differential equations linear and non linear systems and many other special functions MATLAB is a powerful tool that is widely applied to solve many problems in process control and dynamics In order to be able to fully apply PCLAB one must be familiar with MATLAB commands A few examples of the MATLAB commands are given below to familiarize the user with the software and as one practices he becomes exposed to more and more c
57. eated for a lower pressure and flashes to give off water vapor The vapor then passes through a wire mesh demister to remove any entertainment brine droplets and onto a heat exchanger where the vapor is condensed and drips into a distillate tray The process is then repeated all the way through the plant as both brine and distillate enter the next stage which is at a lower pressure The concentrated brine is divided into two parts as it leaves the plant a blow down which is pumped back to the sea and the recycle stream Reject Flow Condenser tubes Sea water feed Steam Distillate trays Distillate Makeup Condensate x Recycle Bri DUM Blowdown Brine Heater Recovery section Rejection Section Fig 2 5 Flow Sheet for the MSF process 45 2 6 2 The Process Model The design and analysis T T ct E Cj of process operation requires the use of a rigorous model of the D EE MSF plant A first principle H model for a 22 stages MSF plant P t V was developed and validated 2 The specific plant consists of 3 rejection section stages and 19 Fig 2 5b Single Stage recover section stages In the following a summary of the developed model is given Each plant stage is shown in Fig 2 5b The process is therefore defined by nine variables brine pool height L brine flow rate Bj salt mass fraction Xj brine temperature T j distillate flow rate Dj
58. ecified disturbance with a set of particular outputs and all the inputs except those used as manipulated variable are fixed The numerical solution is carried out using fsolve m function of MATLAB Further discussion and analysis of this tool will be discussed in a later chapter 3 3 DYNAMIC ANALYSIS The word dynamic conveys the idea of a time variation which can result from a number of unspecified or unknown influences the word variable simply relates the capacity to vary from these influences In process control we are interested in those dynamic variables which require regulation in some industrial application Typical examples are temperature pressure flow rate level force light intensity and humidity Dynamic analysis can be performed in open loop model and closed loop mode 3 2 1 Open loop Dynamic Analysis In open loop dynamic analysis no control algorithm is involved Therefore the dynamic response of a process variable to forced input variation can be studied 62 Dynamic response is a measure of the systems reaction as a function of time in correcting transient inputs or adjusting to a new set point In this case the dynamic analysis is useful to understand the dynamic behavior of a process and to characterize the process dynamic parameters such as time constant damping factor period of oscillation and dead time When a FODT process is subject to a step change in its input variable it responds as shown in Fig
59. ed to perform the task Referring to the menu of the Evaporator case study in Fig 1 16 clicking on the steady state disturbance analysis button brings up the following window File Edit View Simulation Format Tools D eos EVAPORTAOR PROCESS Steady State Disturbance Analysis The outputs L2 C2 P2 F2 F200 kg min P100 kPa F100 kg min Evaporator Disturbance Fig 4 1 Steady State Disturbance Module for Evaporator Process Fig 4 1 shows that the process has three inputs and four possible disturbances The procedure will focus on investigating the static effect of any disturbance or any combination of disturbances on the process outputs in open loop mode This means that the inputs will remain fixed during the test This is known as the open loop test It 70 reveals which process output is affected the most and which one is affected in nonlinear fashion One can also run the test in closed loop mode In this case an output should be selected as the controlled variable and a corresponding input should be selected to be the manipulated variable The test will then examine the effectiveness of the chosen input to maintain the controlled variable at its nominal value in steady state when the process is under the influence of a range of disturbance values To start the procedure one can simply click on the green button or the start button on Fig 4 1 By doing so the following SSAD menu pops up
60. edefined tuning formula such as the Coon and Cohen formula Record your result Coon and Cohen formula k L 0948 24 no 0 30 3 0 7 G I p 9 20 0 1 5 ke Tp If no dead time is observed approximate the settings by 1 k k Tj T Tutorial Procedure 1 At the main menu of the PCCL select the MSF case study In the sub menu select MSF with single loop control A new simulink window that shows the MSF in 134 closed loop mode pops up Make sure that the controller parameters are set at zero When the controller parameters are zero the process will operate in open loop mode i e without a controller Click the start button to simulate the process View the process response at the scope box and record the initial set point of the top brine temperature To setpoint If the simulation need adjustment follow the instruction under fixing the simulation time at the end of this handout 2 Enter the value of the controller gain and time integral computed in step 1 above in the designated boxes Note that the reciprocal of the time integral multiplied by the sampling time should be entered in the KI box Enter the initial set point value in the set point box Rerun the simulation by clicking the start button Watch the closed loop response in the scope box The output response shall remain at the recorded value above Set point test 3 Explore the controller performance for set point change Enter a new set
61. ee general approaches that are used in the controller tuning process These are Time integral performance criteria Use of simple criteria such as one quarter decay ratio and Semi empirical rules which have been proven in practice In this section use is to be made of the semi empirical rules to tune the controller parameters on some of the examples in the exercises The two main semi empirical rules used here are those of Cohen and Coon also known as the process reaction curve method derived from open loop systems The other is the Ziegler and Nichols method derived mainly from closed loop systems The Cohen Coon tuning method requires the response of an open loop system to an input step change The response generates a process reaction curve which can adequately be represented by a first order system with dead time From the generated curve the static gain the time constant and the dead time can all be estimated and used in the rules summarized in Table 6 1 to find the controller parameters 9 The Ziegler Nichols is based on frequency response analysis It requires the generation of two key process parameters from a closed loop system with a proportional controller The two parameters are obtained by increasing the gain of the proportional controller until the closed loop system exhibits sustained oscillations of constant amplitude The period of these oscillations is defined as the ultimate period Pa The controller gain at which these
62. endix A e The Saturation block in the Simulink modules is used to limit the input values between upper and lower constraints The user can change the default values for the constraints by simply clicking the saturation block and insert the new values 102 CHAPTER 7 MULTIVARIABLE SYSTEMS 7 1 MULTI CONTROL LOOPS In chapter 6 the concept of single feedback control loop was discussed Usually all chemical processes particularly the case studies presented in PCLAB have several process outputs It is common practice that each input output pair is linked through a single control loop Therefore the overall control system of a typical process or plant will contain multi single control loops This idea is the scope of PCLAB exercise that will be discussed in this section Refer again to Fig 1 16 one can simply choose the multiloop control option By doing so the following Simulink window pops up Evaporator Process Multi Closed Loop Steal 100 lode4S Fig 7 1 Evaporator Process with two control loops Fig 7 1 shows two independent control loops One loop pair the output concentration with the steam pressure and the other loop pairs the liquid level with the coolant flow rate These two loops are chosen arbitrary simply for demonstration purposes This means that the user can create as many control loops as the number of process outputs which is four in this case study Moreover the user can change
63. enter the temperature set point of step 2 obtained in previous Workshop Tut msf2 in the designated box Click the step box of the feed temperature T When the dialog box pops up enter 5 for step time O for initial value 5 for final value and 5 for sample time Close the dialog box by clicking ok This step change simulates a sudden increase in the temperature of the seawater feed stream Set the controller gain and time integral to zero Simulate the process under disturbance without controller Observe the process response Re enter the PI controller parameter values found in step 2 above Click the start button and watch the temperature responds Compare the results with those obtained in the previous workshop i e when the PI controller was tuned using reaction curve method The controller settings found in step 2 above are for set point change Repeat the same procedure but for disturbance rejection To do so set the set point at the initial value reported in the previous Workshop Step the feed temperature as in step 5 Repeat step 2 till the ultimate values are obtained Are the new ultimate values exactly the same as those found in step 2 Repeat steps 3 to 6 using the new controller settings only if they were different than these computed previously What conclusion can you make about the control performance using the continuous cycling tuning method 138 B 6 Multivariable PI Control of Polyethylene Reactor Objective
64. erature to CSTR 2 UA Heat transfer coefficient times the transfer area for CSTR 1 UA Heat transfer coefficient times the transfer area for CSTR 2 Vin Cooling jacket volume for CSTR 1 Vi Cooling jacket volume for CSTR 2 x Liquid holdup in CSTR 1 X2 concentration of component A in CSTRI X3 Temperature in CSTRI X4 Temperature of coolant in CSTR1 Xs Liquid holdup in CSTR 2 Xe concentration of component 4 in CSTR2 X7 Temperature in CSTR2 Xg Temperature of coolant in CSTR2 AH Heat of reaction heat heat 0 261 0 45 0 272 300 0 300 0 300 0 300 0 0 35 0 35 1 0 1 0 4 4891016 0 0840220 362 99526 327 56042 5 4931641 0 0503550 362 99495 335 44732 5 3 m s 3 m s 3 m s 3 m s 3 m s mole m K K m mole m K K m K mole 53 2 8 FLUID CATALYTIC CRACKING UNIT 2 8 1 Process Description and Flow Sheet Fluid Catalytic Cracking FCC is one of the most important units in the petroleum refining industry for the conversion of heavy gas oil to gasoline and light hydrocarbons The performance of the FCC units plays major role on the overall economics of petroleum refineries FCCU receives a number of hydrocarbon feed streams with different molecular weight distribution from several refinery units and cracks the heavier components in these streams to more valuable lighter ones Sp mam fractionator Furnace F lt ce Da 7 a Z mio mgp op Fig 2 7 Fl
65. es User Defined Functions zl Additional Math amp Discrete Tl Control System Toolbox E W Real Time Workshop ij Wl Signal Processing Blockset gi Simulink Control Design e WI Simulink Extras E WI Simulink Parameter Estimation i BH Simulink Response Optimization Wii Stateflow 2 E 2 2 2j 2 2 2 2 2 2j 2d 24 2 2 Integrator State Space Transfer Fen Transport Delay Variable Transport Delay Zero Pole Fig 1 2 SIMULINK Continuous Blocks Selecting the Sources icon yields the library shown in Fig 1 3 The most commonly used sources are Clock which is used to generate a time vector and Step which generates a step input rary er File Edit View Help k DB dAa oC Band Limited White Noise The Band Limited White Noise block generates normally distributed random numbers that are suitable for use in continuous or hybrid systems l Simulink Commonly Used Blocks Continuous Discontinuities Discrete Logic and Bit Operations Lookup Tables Math Operations Model Verification Model Wide Utilities Ports amp Subsystems Signal Attributes Signal Routing Sinks Sources User Defined Functions i Additional Math amp Discrete Wi Control System Toolbox Wi Real Time Workshop BH Signal Processing Blockset m M Simulink Control Design Bl Simulink Extras i Wl Simulink Parameter Estimation E lli Simulink Response Optimization Ini Wii stateflow C
66. es designing only one parameter used as a de tuning factor for all control loops However the resulted controller performance is conservative since the de tuning factor is determined such that it provides tradeoff between stability and performance Another design method is the Sequential Loop Closing SLC 11 In this case the loops are tuned individually but closed one after another so that interaction caused by closing a previous loop is accounted for during tuning the current loop One drawback of such method is that interaction is taken care of in one direction only This means that interaction brought by closing a current loop into all previous loops is not accounted for Discussing these methods is out of scope Nevertheless users are encouraged to use the PCLAB platform to test these various procedures reported in literature and compare them 7 1 2 Control Structure Design As mentioned earlier control configuration which means selecting the controlled variables and their appropriate manipulated variables in multiloop s framework is an important design step for any successful control system The control of a process with many variables can also be handled through multivariable control approach which requires advanced control strategies The latter is out of the scope of the PCLAB There are several techniques available for control structure design 5 The SSDSA method discussed in chapter 4 can also be used for control configuration Th
67. esponses depicted in Fig 6 9 and 6 10 the only conclusion we can draw is that both methods provided excellent guesses for the values of the controller parameters In feedback control systems controllers do not only act to keep responses as close as possible the desired set point changes but they also try to eliminate the impact of load changes from achieving the desired set point changes Having already looked at how effectively our controller settings can cope with set point change will an incoming disturbance sway the system from achieving the desired set point Fig 6 10 Response of Evaporator Process to set point change using Ziegler Nichol settings 100 To find out the set point is maintained at its original value of 25 316 and a disturbance introduced Using Fig 6 1 any of the input parameters blue can act as a disturbance In this case the feed flow F was chosen as the disturbance parameter The flow was increased by a step change of 0 1 kg min This is done by double clicking on the F icon to obtain a block parameter from where the change is effected Fig 6 11 shows the open loop response of the concentration to this disturbance The open loop response shows the concentration rising from the value of 25 316 96 to a new steady state value of 26 36 without limitation Fig 6 12 and 6 13 show the controlled responses to a 0 1 kg min step change in F the feed flow rate Note how in both responses the concentration
68. f the multi loops control system Do both controlled variable return back to their set points rapidly and smoothly Try to increase the controller gain or time integral of the second loop and rerun the closed loop simulation What do you observe And Why Change the upper and lower limit of the feed flow rates To do so point the mouse on the PID subsystem press the mouse right button and select look under mask When a new dialog box appears double click the saturation box and change the upper and lower limit values Close the dialog box Rerun the simulation for a larger value for the disturbance and observe the closed loop response of both outputs Do you observe any sign of input saturation If yes do you observe any offset in the output responses Now increase the integral time for the second loop 10 times and rerun the simulation Do you observe any improvement in the control performance Is the performance of the other loop get affected by retuning What do you conclude ideas 14 Look in the literature and or books for tuning formula that apply for multi loop PID control and try to implement it on this process 139 15 In the above tests the control pairing was predefined It is more rigorous to pair the control loops based on Relative Gain Array RGA To do so follow the following steps First compute the steady gain matrix as follows k k pT if pT Qc k k pC f pC Qc Compute the inverse of the transpo
69. ffect of disturbance is possible disturbances and their felt by the system measurement 2 Itis unsatisfactory for slow systems 2 Itis insensitive to modeling error 3 It may create instability in the closed 3 Itis insensitive to parameter changes loop response All case studies of the PCLAB contain feed forward design tutorial For demonstration purposes we will examine the feed forward controller design for the evaporator process Refer to the evaporator menu shown in Fig 1 16 and select the feed forward controller The following Simulink module shall appear 114 Iw 770 File Edit View Simulation Format Tools Due steam Pressure F100 kg min Set point for concentration Feed forward Pils dgimit controller F200 kg min Flow kg min Evaporator Process T200 C Fig 8 8 feed forward Controller Structure for the Evaporator Process Fig 8 8 depicts a single FFC loop linking the disturbance C feed concentration with the steam pressure It should be noted this structure is not unique The user can create or replace it with another FFC loop According to the design equation discussed in chapter 3 the feed forward control block require the determination of the static gain and time constant for the manipulated variable and disturbance variable These values can be inserted directly into the feed forward block as sho
70. for the coolant flow rate which is set at 400 and 100 respectively The white line represents the response of the coolant flow rate to disturbances in order to maintain C at nominal value For large disturbances i e when the feed temperature exceeds 55 C the coolant flow should be reduced slightly below the lower limit in order to reject the effect of the disturbance However at feed temperature below 30 C the coolant flow rate must be increased by many folds especially below 25 C to maintain the required operation Low feed temperature requires higher steam pressure to provide enough heat of evaporization which in turn increases the process temperature As a result large amount of coolant flow is needed to absorb the extra heat and to cool down the vapor 74 One can conclude that the coolant flow rate is a good manipulated variable for controlling the product concentration at moderate to high disturbances in the feed temperature However the coolant flow is recommended at low feed temperature The user can test other candidate manipulated variable and can also repeat the procedure for the other controlled variables At the end the user can build up a satisfactory control structure for the process ie can select the appropriate input output pairing configuration The SSDSA can be studied for each loop individually and consequently the appropriate structure can be determined This approach however ignores the cross loop interactio
71. g 5 10 Process Flow Diagram of the Polyethylene system After the run is complete double click on the last red icon to the right of your screen the temperature T to get Fig 5 12 The graph shows the plot of output bed temperature versus time for a typical second order system The nature of the graph resembles that of Fig 3 2 Applying the definitions used in the Figure A is found by subtracting the steady state height T from the maximum reading of 122 65 C as shown in Table 5 5 B is similarly calculated as the ultimate value of the response Then the ratio of A B gave the overshoot The period is also calculated by taking the time elapsed between two consecutive crests Using the equations and the appropriate figures of Chapter 3 Table 5 6 was generated The overshoot is the ratio of the maximum amount by which 88 the response exceeded its ultimate value to the ultimate value of the response It is related to the damping factor through the equation shown in the Table It increases with decreasing and as approaches 1 the overshoot takes the value of zero and the system response is described as being critically damped m Constant Output a constant m Parameters Constant value 1 6 DK Cancel Help Fig 5 11 Block Parameter for hydrogen flow FH moles s E BIET PJP Alta lt aj Fig 5 12 Simulation Results of the Open Loop Polyethylene Reactor The system seems to have a
72. g the height of tank versus time Figure 5 5 Part of Output showing the height of tank versus time Figure 5 6 Output showing the change in concentration with time Figure 5 7 Level Properties window for saving data to a workspace Figure 5 8 Output showing the height of tank versus time Figure 5 9 Polyethylene Process Menu Figure 5 10 Process Flow Diagram of the Polyethylene system Figure 5 11 Block Parameter for hydrogen flow FH moles s Figure 5 12 Simulation Results of the Open Loop Polyethylene Reactor Figure 6 1 Process flow sheet of closed loop evaporator process Figure 6 2 Block Parameter for changing the PID controller settings Figure 6 3 Plot of Concentration with time for a unit step change in P100 Figure 6 4 Block Parameter for changing the set point Figure 6 5 Block Parameter for PID controller Figure 6 6 System responses to set point change at gain of 320 Figure 6 7 System response to set point change at gain of 350 Figure 6 8 Expanded Closed loop response of concentration to set point change Figure 6 9 Response of Evaporator Process to set point change using Cohen Coon settings Figure 6 10 Response of Evaporator Process to set point change using Ziegler Nichols settings Figure 6 11 Effect of Feed Flow disturbance on concentration in open loop System Figure 6 12 Effect of feed flow disturbance on concentration in closed loop system with Cohen Coon settings Figure 6 13 Effect of feed flow dist
73. h testing the plant for step changes of specific proportional magnitudes In this case the calculated process parameters should have the same proportional magnitudes Otherwise the process is said to behave nonlinearly Table 5 3 Comparison of the values of the characteristic parameters 10 step change 0 089 46 5 io In order to establish this linearity the step changes were reduced by ten orders of magnitude Instead of an increment of 1 kg min on the flow rate an increment of 0 1 kg min was made The module is simulated and the corresponding process parameters were estimated as shown in Table 5 4 The step change was then doubled to an increment of 0 2 kg min using the same procedure outlined above Table 5 4 was produced In this region an approximation of linearity can be assumed because the values of the gains are close to each other at 0 058 and 0 06 m min kg respectively while the time constants are also close to 30 seconds 85 Table 5 4 Calculated values of the characteristic parameters for 196 step change Step Change Step Change 0 1 kg min 0 2 kg min 0 9604 0 9604 0 9662 0 9729 0 0058 0 0125 0 632AL 0 00367 0 0079 Lo 0 632AL 0 9641 0 9683 0 9641 0 9683 Em x 5 3 SECOND ORDER SYSTEM DYNAMICS Let us now look at the open loop response of second order systems These systems are known to have differential equations of the form given in 3 3 The Laplace transform of this differentia
74. he output with respect to a step input change Use the subplot command to place the process output y on the top plot and the manipulated input u on the bottom plot If desired change the default simulation stop time by selecting the parameters pull down menu 1 4 3 Feedback Control Simulation The Math icon from Fig 1 2 can be selected resulting in the functions shown in Fig 1 6 Additional icons can be found by selecting the Simulink Extras icon in Fig 1 1 Selecting the Additional Linear icon from this group yields the set of icons in Fig 1 7 The most useful icon here is the PID Controller Any icon can be dragged into the 17 untitled model workspace In Fig 1 8 we show the preliminary stage of the construction of a control block diagram where icons have been dragged from their respective libraries into the untitled model workspace Simulink Library Browser R i l x File Edit View Help DERA 8 8 rt C s LC Cts Add Add or subtract inputs Specify one of the following a string containing or for each input port for spacer between ports e g 1 b scalar gt 1 A value gt 1 sums all inputs 1 sums elements of a single input vector Wi snark 3 2 Commonly Used Blocks lul 2 Continuous z 2 Discontinuities 2 Discrete 2 Logic and Bit Operations ILI e 2 Algebraic Constr
75. hirp Signal Clock Constant Counter Free Running Counter Limited Digital Clock all oll e es ll ll A s ol e f en s o 9 untitled mat From File From Workspace Ground Pulse Generator Ramn Fig 1 3 SIMULINK Sources Library 15 The Sinks icon from Fig 1 1 can be selected to reveal the set of sinks icons shown in Fig 1 4 The one that we use most often is the To Workspace icon A variable passed to this icon is written to a vector in the MATLAB workspace The default data method should be changed from structure to matrix appropriate form for plotting W Simutink Library Browser Wok in order to save data in an 8 8 Hl 8 8 8 Dd uda Display Numeric display of input values File Edi View Help DW Simulink 2 Commonly Used Blocks S Continuous 2 Discontinuities 2 Discrete 2 Logic and Bit Operations 2 Lookup Tables 2 Math Operations 2 Model Verification 2 Model Wide Utilities 2 Ports amp Subsystems 2 Signal Attributes gt H User Defined Functions H H Additional Math amp Discrete Wi Control System Toolbox Wl Real Time Workshop Wi Signal Processing Blockset Wil Simulink Control Design Wi Simulink Extras BD Simulink Parameter Estimation BD Simulink Response Optimization DW Stateflow Ready ii y luntitied mat
76. hroughout the project duration I would like to emphasize the benefit and advantage of this program which enables the scientist and scholars to manifest their research ideas into realistic application viii ABSTRACT A user manual for the Process Control Laboratory PCLAB software is composed The PCLAB is a MATLAB based computer program that simulates certain chemical processes for dynamic analysis and control The manual consists of eight chapters and two appendices The manual is organized such that the first chapter gives and overview of the MATLAB basic functions SIMULINK and PCLAB The second chapter introduces the user to the case studies which comprises of seven common industrial processes Brief theoretical background regarding dynamic analysis and control is discussed in chapter three Chapter four addresses the steady state disturbance sensitivity analysis Chapter five and six cover the open loop and closed loop dynamic analysis respectively Chapter seven addresses the control of multivariable systems while chapter eight investigate advanced topics such as cascade and feed forward control configuration oaa y Abe uuaigll eua pall gle aisi gall OY uuu Sail Glee ji geal pal ea iaall Gils alae ai Diss s cal gll Abed Gye cass Cy SS Lead aSaill 5 calipall gS sa Aust pal laL Glileall slSlaa cies ees Ga Rai ltl lll Gl OY ot cot dignas GOEL ea 3 Ge JS apt I Gull aig 5 43 bill Deal e335 ai CAI cau ul 5 Agu jall Sila pall GuLuls
77. iption For detail description of the process its main variables and schematic of the flow sheet refer to chapter 2 Here we analyze the static behavior of the MSF plant to variation in the process inputs disturbances This shows how the measured variable responds at steady state to a range of changes in the feed conditions This analysis is essential for understanding the disturbance detrimental severity and nonlinearity effect on the process Specifically the steady state behavior of the distillate product W4 Blow Down flow Bp Top brine temperature Tpo last stage level and temperature Lg22 Tp22 can be examined in the simulink module Launching the SSDSA simulation module At the main menu of the PCCL select the MSF case study In the sub menu select steady state disturbance analysis A new simulink window that shows the MSF in open loop mode pops up One typical steady state operating condition for the input variables is shown in the corresponding boxes of the block diagram Record these steady state values on the work sheet To launch the SSDSA menu simply click the start button Tutorial Procedure 1 Select one of the available disturbances by marking its checkbox 2 Select the open loop mode 3 Select appropriate step size and number of steps 4 Run the simulation by clicking the run button 5 Examine the generated plots 6 Discuss your results and make conclusions 126 B 2 SSDSA Closed loop tuto
78. k Parameter similar to Fig 6 4 was obtained The set point value was stepped from 25 316 to 26 316 by typing the new value Press the enter button to complete this operation Now double click the PID controller icon to get the PID Block Parameter similar to Fig 6 5 Then using the curser to highlight the parameter spaces enter the values for Proportional gain Reset time gain and Derivative time gain for the Cohen Coon settings as given in the last three rows of Table 6 4 Press enter and run the simulation to produce Fig 6 9 Note in the response shown in Fig 6 9 the CC proportional gain is divided by two because the original value produced very oscillatory response Repeat the same steps for the Ziegler Nichols settings to produce Fig 6 10 For the same set point change Fig 6 9 shows the product concentration rising to as high as 26 81 Then after two decays it settled at a steady state value of 26 316 96 showing no offset at all The figure gave a rise time of about 60 seconds and a response time of close to 500 seconds Fig 6 10 produced almost a similar response There was an overshoot but no decay with a similar rise time to that of Fig 6 9 but a faster response time of about 300 seconds Not only did both settings produce similar responses but also the final steady state concentration values of 26 316 for Cohen Coon settings and 26 315 for the Ziegler Nichols settings are in very good agreement 99 Judging from the r
79. l equation yields a second order transfer function given by the equation below WS _ yy __KP 5 4 za ED u s TS 2 7 5 1 Where y s is the system output u s is the input forcing function Ky is the system gain ty is the natural period of the system Gis the damping coefficient Second order systems occur in nature Such systems are said to be inherently second order They can be derived from a multi capacity system such as two first 86 order systems in series through which material or energy flow Many closed loop systems also exhibit second order behavior In this chapter the dynamic behavior of these systems is to be studied based on step changes in the input forcing function When there is an input forcing function the response of these systems follows that of the transfer 5 4 The key parameter of this equation is the damping factor Depending on the value of the damping factor the system can be overdamped critically damped or underdamped Fig 3 2 shows a typical output response of an under damped second order system to a step change in the input From the data generated by simulating the system its characteristic parameters can be calculated as shown in the Figure In this case the Polyethylene Reactor example is to be used to make the necessary parametric calculations To do this revisit Fig 1 13 and choose the Polyethylene example on the menu by clicking on it to get Fig 5 9 The figure shows
80. m Proc Des Dev 25 pp 654 660 1986 J M Maciehowski Multivariable feedback Design Addison Wesley Workingham UK 1986 K B McAuley D A McDonald and P J Mclellan Effects of Operating Conditions on Stability of Gas phase Polyethylene Reactors AIChE J 41 pp 868 879 1995 R C McFarlane R C Reineman J F Bartee and C Georgakis Dynamic Simulator for a Model IV Fluid Catalytic Cracking Unit Comp Chem Eng 17 pp 275 300 1993 R B Newell and P L Lee Applied Process Control A Case Study Prentice Hall Sydney 1989 118 15 R B Newell and G Fisher Model Development Reduction and Experiment Evaluation for an Evaporator Ind Eng Chem Proc Des Develop 11 pp 213 223 1972 16 G Stephanopolous Chemical Process Control Introduction to Theory and Practice Prentice Hall NJ 1984 17 C Yi and W Luyben Evaluation of Plant Wide Control Structures by Steady State Disturbance Sensitivity Analysis Ind Eng Chem Res 34 pp 2393 2405 1995 119 APPENDIX A SPECIAL FEATURES A 1 PROCESS PARAMETERS As discussed in chapter 2 each case study is comprised of differential equations with pre specified parameter s values Some key process parameters which are believed to have important effect on the process behavior are made accessible for modification To access these parameters one can simply double click on the process flow sheet shown inside the yellow box i
81. monomer 116 17 mole m Cy Concentration nitrogen 166 23 mole m Cy Concentration of hydrogen 105 78 mole m Cpui Heat capacity of monomer 11 cal mole K Cpm Heat capacity of co monomer 24 cal mole K Cpu Heat capacity of hydrogen 7 7 cal mole K Cpu Heat capacity of nitrogen 6 9 cal mole K Cp Heat capacity of recycle gas and water 18 0 cal mole K Cp Heat capacity of polymer 0 85 cal g K E Activation energy for propagation 9000 cal mole F Catalyst flow rate 2 0 kg s Fw Cooling water flow rate 5 6x10 mole s F recycle flow rate 8500 mole s Fm Monomer flow rate 131 13 mole s Fin co monomer flow rate 3 51 mole s Fy hydrogen flow rate 1 6 mole s Fy nitrogen flow rate 2 52 mole s ka Deactivation rate constant 0 0 1 s kp Propagation rate constant for monomer 85 0 L mole s kp2 Propagation rate constant for co monomer 3 0 L mole s Mw Water holdup in the heat exchanger 2x10 mole M Cp Thermal capacitance of the reaction vessel 14x10 kcal K Op Polymer outlet rate 3 6434 kg s P Total pressure 20 0 atm Pm Partial pressure of monomer 8 67 atm 33 Pin Partial pressure of co monomer 3 39 atm Py Partial pressure of nitrogen 4 8525 atm Pu Partial pressure of hydrogen 3 0875 atm R Ideal Gas constant 82 6x10 atm mole T Bed temperature 82 G Ty feed temperature 25 C rm reference temperature 87 Ke Toi Temperature of recycle stream before cooling 136 C g Temperature of recycle stream after cooling 51 7 e Tu Cooling water te
82. mperature before cooling 20 C y Cooling water temperature after cooling 35 2G Y Number of moles of catalyst site mole 5 849 mole AH Heat of reaction 894 cal g The system has two internal built in PI control loops which are set as Control loop ke TI Pt gt Bt 10 10 T gt Tw 3 20 34 2 4 ETHYLENE DIMERIZATION REACTOR 2 4 1 Process Description and Flow Sheet FT Ethylene Catalyst 1 B Q T BQ T Q T Ethylene Butene Co C 3 Fig 2 3 Dimerization Reactor The catalytic dimerization of ethylene is considered to be one of the most promising methods for producing butene 1 the first member of the even numbered linear 1 alkenes which have diversified applications This process uses a homogeneous titanium based catalyst which demonstrates high dimerization activity coupled with excellent selectivity to butene 1 at moderate pressure 20 30 psia and temperature 50 60 C The dimerization reaction is regarded as a degenerate ethylene polymerization reaction and therefore the formation of heavier oligomers is expected The industrial ethylene diemrization reactor is operating in liquid phase at bubble point conditions Fresh ethylene and homogenous catalyst are fed continuously to the reactor where the exothermic reaction is removed by means of external loop equipped with a cooler The dimerization reactor considered in this study is assumed to be a liquid phase perfectly mixed reactor i e no mass tr
83. n Alternatively one can conduct the SSDSA method over all process variables and determine the best design structure T5 CAHAPTER 5 OPEN LOOP DYNAMIC ANALYSIS 5 1 INTRODUCTION Of the seven systems that were defined in chapter 2 some follow the response of first order systems others follow that of second order systems and yet others follow those of higher order systems In this chapter we will practice the responses of some of these systems to input manipulations or disturbances The response of an output parameter to changes in an input parameter with time is referred to as system dynamics Normally the input parameter must behave in a certain defined fashion like step ramp or sinusoidal As discussed in the previous chapter dynamic analysis can be performed on an open loop model as well as on a closed loop model For systems that mimic first order dynamics system parameters like gain time constant and dead time can be computed These parameters are typical to system response to a step change in the input Here it is intended to perform the computations of these parameters using the PCLAB software described in chapter one This will provide a hands on application and will enable the reader to calculate the parameters that characterize the system 5 2 FIRST ORDER SYSTEM S DYNAMIC ANALYSIS In order to run the software recall how you were instructed to lunch PCLAB in chapter one Follow the same steps till you arrive at Fig 1
84. n affects only the output concentration Now we repeat the simulation but with both control loops activated using the PI settings listed in table 7 1 The result is shown in Fig 7 3 4 concentration a TPA aij amp 35 30 Fig 7 3 Closed loop response to disturbance in feed concentration Fig 7 3 illustrates that the response of the process is unstable despite the existence of the control system This finding is not surprising because the loops were tuned independently ignoring their interaction It is true that each loop will perform excellently when the other loop is open However when both loops are active the cross loop interaction is magnified causing poor and even unstable process dynamic behavior A possible remedy is to fine tune both control loops For example if we cut down the PI settings of Table 6 1 by factor of 4 we obtain the results shown in Fig 7 4 ajm 7j aj 50 100 150 200 ao Fig 7 4 Closed loop response to disturbance using improved PI settings There is no doubt that the resulting feedback response is much enhanced however it still suffers from oscillation One can keep fine tuning the PI setting till desired performance is obtained 105 Alternatively one can use other tuning methods available for multi control loops system Among these methods is the Biggest Log Modulus BLT proposed by Luyben 10 The attractive feature of this procedure is simplicity since it includ
85. n any given Simulink module Figure A 1 shows an example of accessing the process parameters for the evaporator process SingleblstkedBlock mack D Sug im p amp Sel he necersary parameter fot te Evaporator procerr a 1 The intial condition Tor the states Level ILL Concentration C2 and Evaporator Pro Poses P3 2 Some of the process physacal parameters such as heal capacity hest Fic Tot open Loop ESSERE 3 nome variance 0 for no noue Tor definition and nominal values of the process stasti end parameters click on the Help bar Parameter Ae level m ose Viii convenes Y inia Bir mur Meat capacity kwako min Han capaci L four Heat hamia com kW 6 04 e Latent heat kwkg min o cea Hep Rody 1008 dett Fig A 1 Accessing the process Parameter dialog Box Specifically the dialog box for the evaporator process contains that the initial value of the states the heat capacity of the fluid the overall heat transfer coefficient and the latent heat of the steam The user can change the value of the designated process parameter directly However the user must run the simulation for open loop mode for enough long time to assure that the process reaches a new steady state The new steady state values of the process states must be recorded in a separate sheet The user should then access the process parameter box again and replace the initial value of the states with the newly obtaine
86. n in the process inputs This show how the measured variable responds in time to changes in the feed conditions This analysis is essential for understanding the dynamic characteristic of the process and for controller design Specifically the trend of the distillate product Wa Blow Down flow Bp Top brine temperature Tpo last stage level and temperature Lp22 Tp22 can be examined in the simulink module Launching the open loop simulation module At the main menu of the PCCL select the MSF case study In the sub menu select MSF or MSF with level control A new simulink window that shows the MSF in open loop mode pops up One typical steady state operating condition for the input variables is shown in the corresponding boxes of the block diagram Record these steady state values on the work sheet To examine the steady state value of the outputs at this operating condition simply click the start button Watch the output trend by clicking the designated scope icon to monitor the measured process variables For clear view of the output trend the plotting scale shown in the scope can be adjusted either by clicking the left button of the mouse on the edge of the data curve or by clicking the auto scale button in the toolbar menu Tutorial Procedure 1 Step the steam flow W by a specific amount say AW click the start button and watch the temperature responds until it reaches a new steady state value Record the step in the steam flow a
87. nd the new Top Brine Temperature steady state value on the work sheet Note To step a specific input simply double click the step function box that corresponds to the desired input A new dialog box called Block parameters appears at which you can change the numerical value of the step input by entering a non zero value for the final value You can also set the time at which the step change starts Pressing ok will close the dialog box and save the changes Some of the case studies do not have a designated step block In this case one can still impose step changes by directly clicking the desired input block As a result a block parameter dialog box pops up allowing the user to alter the value of the specific input variable 129 2 Compute the steady state gain the dead time if applicable and the response time as described in the work sheet To estimate the final steady state value of the process output from the trend shown in the scope simply draw a square around the end of the simulation using the left button of the mouse This will expand zoom in that specific region To get more precise value for the steady state point at the curve and click the left button This will increase the resolution of the y axis Similarly to better estimate 555 expand the region at which y63 2 occurs using the same technique just described Pointing the mouse on the curve and clicking the left button once more the resolution of y axis and x
88. nes that we often use are Transfer Fen and State Space R amp Simulink Library Browser ce File Edit View Help De Continuous simulink Continuous Wi Simulink 2 Commonly Used Blocks Continuous Discontinuities k H Discrete 2 Logic and Bit Operations 34 Lookup Tables m 2 Math Operations 2x Model Verification m 2 Model Wide Utilities H Ports amp Subsystems 2 Signal Attributes ren monty Commonly Used Blocks tH Discontinuities Discrete Logic and Bit Operations 24 Signal Routing Lookup Tables 35 Sinks m Sources Math Operations 35 User Defined Functions amp 34 Additional Math amp Discrete Model Verification BD Control System Toolbox t x Mi Real Time Workshop Model Wide Utiities Wii Signal Processing Blockset E w Wi Simulink Control Design BM Simulink Extras a Mii Simulink Parameter Estimation ll Simulink Response Optimization Wii stateflow Ports amp Subsystems Signal Attributes Signal Routing TIE belt iP Sink Ready Fig 1 1 SIMULINK Library Browser 14 y File Edit view Help Dg a Derivative Numerical derivative du dt zi Wi Simulink 2x Commonly Used Blocks Continuous Discontinuities Discrete Logic and Bit Operations Lookup Tables Math Operations Model Verification Model Wide Utilities Ports amp Subsystems Signal Attributes Signal Routing Sinks Sourc
89. nge of the process control loop set point The system error is a measure of the inherent error between the system set point value and the actual value of the dynamic variable maintained by the system The desired value of the dynamic variable in the process is referred to as the set point Generally a set point Csp is expressed with some allowable deviation AC about the nominal value Thus when control has been achieved the actual value of the dynamic variable may be in the range from Csp AC to Csp AC Of course the wider the allowable deviation the easier the control is to achieve Note that this deviation can never be less than the inherent system error Feedback control loop The regulation of a specific dynamic variable is usually carried out in feed back fashion as shown in fig 3 3 4 Fig 3 3 Typical Feedback control configuration The feedback controller is the component of the feedback loop that issues control commands to the process via the final control element based on e the deviation of the process measurement from its desired set point value The way the controller calculates the type of command signal to be issued for any given value of e is what differentiates one controller from another To consider all dynamic elements of a feedback controller the following block diagram is usually used 65 E Eod l Fig 3 4 Typical Block diagram for
90. ning such loops One can also test how the overall control loop performs when 113 disturbances enter the process This teaches him how cascade loop in comparison to conventional loop can improve the feedback performance Innovative users can create similar cascade control structure for the other case studies and examine their performance 8 2 FEED FORWARD CONTROLLER FFC Feed forward control attempts to enhance the performance of the single loop feedback control by making use of an additional measurement of process input as shown in Fig 3 5 The implementation block diagram for FFC is shown in Fig 3 6 and the design equation is given by 3 12 and 3 13 Feed Forward should be used when feedback control does not provide satisfactory performance and a measured feed forward variable is available Comparison between the feedback and feed forward controllers is listed below Table 8 1 Comparison between Feedback and feed forward controllers Advantages disadvantages Feed Forward 1 acts before the effect of a disturbance 1 Requires identification of all possible has been felt by the system disturbances and their measurement 2 Is good for slow systems 2 Can not cope with unmeasured 3 It does not introduce instability in the disturbances closed loop response 3 Sensitive to process parameter variation 4 Require good knowledge of the process model Feedback 1 Does not require identification of all 1 It waits until the e
91. oefficients for the numerator and denominator polynomials Notice also that the default step used for the step set point change is to step from a value of 0 to a value of 1 at t 1 These default values can be changed by double clicking the step icon The simulation parameters can be changed by going to the Simulation pull down menu and modifying the stop time default 10 or the integration solver method default ode45 19 Double click the PID controller box and enter the controller tuning parameters of kc 1 89 and x1 1 23 by entering P 1 89 and I 1 89 1 23 in the default PID Controller block and run the simulation by clicking the start button Generate Fig 1 9 by typing the following on the command window subplot 2 1 1 plot t r t y xlabel t min ylabel y mol I subplot 2 1 2 plot t u xlabel t min ylabel u min 1 1 5 T T T 1L 3 o Es al g 0 5 A g 0 5 I I I 1 2 3 4 5 6 7 8 9 10 t min 3 2b 4 E 531b 7 0 ji L 1 L 1 1 1 1 1 0 1 2 3 4 5 6 7 8 9 10 t min Fig 1 9 Measured Output amp Manipulated Input Responses to a Unit Set point Change 1 4 4 Other Commonly Used Icons Often you will want to simulate the behavior of systems that have time delays The Transport Delay icon can be selected from the Continuous library shown in Fig 1 2 The transport delay icon is shown in Fig 1 10 Our experience is
92. olute concentration of C2 The vapor is usually condensed with water Water is used as the coolant Steam d P 19 Fio0 Too Feed Product FC T FCT Fig 2 1 Flow sheet of Forced Circulation Evaporator Process 2 2 2 The Process Model T up ee dt 2 1 C n HC PC t 2 2 2 3 y or F4 F5 dt Additional relations 28 T 0 5616P 0 3126C 48 43 T 0 507P 455 0 P F F4 F4 Qho0 41C 1 X Tioo 0 1538 P00 90 0 Qi00 FiooA UA Too T2 Q200 F599Cp T591 T200 UA T3 0 5 T200 T201 F Q3o9 UA 0 16 F F 2 2 3 Process Parameters and Variables 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 Variable Description Value Fi Feed flow rate 10 0 F2 Product flow rate 2 0 F Circulating flow rate 50 0 F4 Vapor flow rate 8 0 F5 Condensate flow rate 8 0 C Feed composition 5 0 C2 Product composition 25 0 T Feed temperature 40 0 T2 Product temperature 84 6 29 Units kg min kg min kg min kg min kg min Percent Percent C C T3 L2 P2 F100 Tio0 P100 Q100 F200 T200 UA Vapor temperature Separator level Operating pressure Steam flow rate Steam temperature Steam pressure Heater duty Cooling water flow rate Cooling water inlet temperature Cooling water outlet temperature Condenser duty Mass holdup in the separator Solute holdup Constant Latent
93. ommands When the software is loaded to the computer memory the prompt gt gt is displayed The program is in an interactive command mode If an expression is entered with the correct syntax it is processed immediately and the result displayed on the screen The tutorials below are intended to introduce the reader to MATLAB so as to give the students handy experience with the features that are essential to understanding and evaluation of the software 1 3 BASIC OPERATIONS AND COMMANDS The four elementary arithmetic operations in MATLAB are done by the operators and where stands for power operator For example type the following and then press Enter key and observe the result 243 4 1 1 5 The operator is for left division For example try 2 4 2M Example 1 Using MATLAB as a calculator At the prompt type 432178765 gt gt 4321 8765 hit enter Ans 13086 Or try to solve the expression 2 3 4 5 1 5 11 gt gt 2 3 4 5 1 5 11 hit enter ans 18 2 MATLAB easily handles complex and infinite numbers sqrt 1 Ans 0 1 00001 Both and j stand for the complex number that is square root of 1 unless another value is assigned to them Also the variable pi represents the ratio of the circumference of a circle to its diameter 1 e 3 141592653 If an expression cannot be evaluated MATLAB returns NaN which stands for Not a Number The equality sign is used to assign
94. or if while and switch which we describe briefly below If else end The if command enables the program to make decision about what commands to execute x input x ifx gt 0 y x 2 end You can also define an else clause which is executed if the condition in the if statement is not true x input x if x gt 0 yemas else y x 2 end for end The for command allows the script to cause a command or a series of commands to be executed several times k 0 for x 0 0 2 1 k k y k exp x end while end The while statement causes the program to execute a group of commands until some condition is no longer true x 0 while x l y sin x x x 0 1 end switch case end When a variable may have several values and the program has to execute different commands based on different values of the variable a switch case structure is easier to use than a nested if structure a input a switch a case 1 disp One case 2 disp Two 10 case 3 disp Three end Two useful commands in programming are break and pause You can use the break command to jump out of a loop before it is completed The pause command will cause the program to wait for a key to be pressed before continuing k 0 for x 0 0 2 1 if k gt 3 break end k k l y k exp x pause end 1 3 6 Data Export and Import There are different ways you can save yo
95. oscillations occur is referred to as the ultimate gain K It is these two parameters that are used in conjunction with the equations of Table 6 2 to arrive at the tuned parameters for use in the controller These two semi empirical methods will be used to calculate Controller parameters for a PID controller on the Evaporation process The values obtained will be compared with each other and used to run the processes mentioned in order to draw conclusions on the superiority 1f any of one method over the other Table 6 1 Cohen Coon Formulas 16 Controller Controller Gain Reset time Derivative Time Type Kc TI Tp ses PI 1 BE td 30 4 2 K t T K 10 127 T t a P in 1 6 4 id ee m PE E Ke T Da H K ty 3 4r T t Lp 11 pA Let us now revisit Fig 1 13 Using the same steps described in chapter 5 the open loop response for the evaporator process could be used to obtain Table 5 5 and the values of this table for the gain time constant and the dead time are plugged into the equations of Table 6 1 to obtain the Cohen Coon controller parameters Another way of obtaining the open loop parameters of Table 5 5 is to run the single closed loop module in an open loop mode fashion as discussed in the following sections 92 Table 6 2 Ziegler Nichols Formula 16 Controller Type Controller Gain Reset time Derivative Time Kc TI TD P K 0 5K PI K 0 45K P T
96. outlet flow rate F2 will decrease One can also observe that the solute concentration C2 received the highest magnitude impact Moreover all outputs are altered inearly with the temperature variation Thus the user 72 can learn how the process operation and product quality may get seriously influenced when the feed temperature is changing freely El eure NZ ZS sl Sh Parametere Steady State Disturbance Analysis Parameters Evaporator Process oe 2 Select Operation mode 3 Test Range chew kan Fes miesat unus TOT v Feed Temperature C 4 Select manipulated varaibles amp their limits Feed Concentration wt only if closed loop mode is selected _ Reset Limit Coolant inlet Temperature C MY name upper limit lower limit 3 I Coolant Flow Rate 100 ha so Steam Pressure 5 Select Controlled Output only if closed loop mode Steam Flow rate is selected Liquid Level M Product Concentration Vessel Pressure Product Flow rate 6 Final Step r When ready click the Run button warning r King Saud University Chemical Engineering Department Fig 4 4 SSDSA menu for the closed loop test case 4 3 CLOSED LOOP MODE In this test mode the user should unmark the open loop checkbox and mark the close loop checkbox instead Furthermore the user needs to specify a controlled variable Let us choose for example the output concentration C In addition the user should select one of th
97. ow sheet for FFCU process The FCCU as Shown in Fig 2 7 consists of two major processes a reactor and a regenerator In the reactor cracking reaction occurs and coke is deposited on the catalyst The reaction product is passed to the main fractionator for heat recovery and separation into various product streams The spent catalyst is sent to the regenerator section where the coke is burnt by excess of oxygen to form carbon monoxide and carbon dioxide The gaseous products of the combustion reaction leave the regenerator section through the cyclones as stack gas The regenerated catalyst is recycled to the reactor 54 The catalyst is transferred back and forth between the reactor and regenerator through the catalyst U bend Air is injected at the bottom of the regenerator lift pipe to assist the circulation of the catalyst Further detailed description of the process can be found in 13 2 8 2 The Process Model The process dynamic equation can be found in the previous reference 13 The model equations are lengthy that we believe not to include them 2 8 3 Process Parameters and Variables Variable Description Value Units Type Co Concentration of carbon monoxide in 37 ppm State output stack gas Coz Concentration of Oxygen in stack gas 0 ppm State output Cigi Weight fraction of coke on 0 0008475 ICFM State output regenerated catalyst Ca Weight fraction of coke on spent 0 0078 ICFM State output catalyst Fsucca Combus
98. put a constant r Parameters Cancel Help Fig 6 4 Block Parameter for changing the set point This way a set point change is introduced Press the enter button to apply this change to the process Now double Click the block parameter for the PID controller icon For the proportional band enter the value 320 by highlighting the current value and typing on it Then change the settings for the reset time and the derivative time to read zero as shown in Fig 6 5 95 Block Parameters PID controllerm Ep x Simple Mask mask Insert the values of the PID ocntrollers m Parameters Proportional gain Integral time D Derivative time 0 Cancel Help Fig 6 5 Block Parameter for PID controller Again run the simulation the usual way and observe the result shown in Fig 6 6 It portrays the response of a set point change in concentration As the concentration rises to the new set point the response starts to oscillate but slowly the oscillation dies away and begins to stabilize like a typical second order system discussed in the previous chapter Since the oscillation is not a sustained one it is necessary to make a second guess of the proportional gain To do this again double click the light green PID Controller representation to get Fig 6 5 When you obtain the Block Parameter icon change the value of the proportional gain from 320 to 350 Press the OK button and
99. rapidly rose to approach the value of the open loop response but was quickly brought back to the set point value of 25 316 Just like the set point response the two graphs of the closed loop system showed responses different from that of the open loop response Note the similarity between the responses of Fig 6 12 and 6 13 The response controlled by the ZN settings settled faster with a response time of about 250 seconds as against 500 seconds for the CC settings In both cases the disturbance swiftly increased the concentration as shown in the beginning of the two graphs but the controllers acted immediately to bring back the concentration to the set point value of 25 316 As concluded earlier the controller setting parameters of both Cohen Coon and Ziegler Nichols are equally effective Fig 6 11 Effect of Feed Flow disturbance on concentration in open loop system 101 Fig 6 12 Effect of feed flow disturbance on concentration in closed loop system with Cohen Coon settings Fig 6 13 Effect of feed flow disturbance on concentration in closed loop system with Ziegler Nichols settings Remarks e The green box labeled Go to menu exists in the Simulink modules can be used to switch between the active Simulink module with the current active sub menu e The green box labeled graphical tool exists in the Simulink modules can be used to trigger the plotting forum The usage of the plotting forum is discussed in App
100. rations on matrices as easy as possible Most of the variables in MATLAB are considered as matrices A scalar number is a 1 x 1 matrix and a vector is a 1 x n orn x 1 matrix Introducing a matrix is also done by an equality sign m 1 2 3 4 5 6 Note that elements of a row may be separated either by a space or a comma and the rows may be separated by a semicolon or carriage return 1 e a new line Elements of a matrix can be called or replaced individually m 1 3 m 2 1 7 Matrices may combine together to form new matrices n m m o n n The transpose of a matrix results from interchanging its rows and columns This can be done by putting a single quote after a matrix m m 7 8 9 A very useful syntax in MATLAB is the colon operator that produces a row vector v 1 4 The default increment is 1 but the user can change it if required yw 1 0 5 4 8 1 2 1 11 A very common use of the colon notation is to refer to rows columns or a part of the matrix w 5 w 1 w 2 3 4 7 w 2 8 end Two useful array functions are size which gives the size of the array and length which gives the maximum length of the array size w length w 1 3 2 Array Arithmetic Multiplying a scalar to an array multiplies all the elements by the scalar ya 1 2 4 2 4 4 0 5 5 2 a Only two arrays of the same size may be added or subtracted b ones 3 a b
101. re in the 2 effect Temperature in the 1 effect Temperature in the 2 effect Feed temperature Wall temperature Heat transfer coefficient Liquid holdup in the 1 effect Liquid holdup in the 2 effect Latent heat of vaporization of water 1 7824 1 7 1 6 25 7 5 225 160 190 qi 5 2345 30 35 948 Btu minF ft Btu lb Btu lb Lb min Lb min psi psi F F F F Btu minF ft Lb Lb Btu lb 44 2 6 MULTI STAGE FLASH DESALINATION 2 6 1 Process Description and Flow Sheet In a typical MSF plant shown in Fig 2 5 we can distinguish between three basic sections heat rejection section heat recovery section and the brine heater On leaving the first warmest rejection stage the feed stream is split into two parts reject sea water which passes back to the sea and a make up stream which is then recycled back to the flash section of the last stage A recycle stream which is drawn from the last stage passes through a series of heat exchangers its temperature rises as it proceeds towards the heat input section of the plant Passing through the brine heater the brine temperature is raised from the feed temperature at the inlet of the brine heater to a maximum value approximately equals to the saturation temperature at the system pressure The brine then enters the first heat recovery stage through an orifice thus reducing the pressure As the brine was already at its saturation temperature it will become superh
102. rectory The user can select and load the desired data file or navigate through other directories for his desired data file Next the user can select plot all var as in Fig A5c which in turn draws all the data stored in the loaded file as shown in Fig A5d Alternatively one can chose plot selected var which brings up the window shown in Fig A5e By inserting the number 2 to select the third column of the loaded data file the plotting forum will be filled out by the response of the corresponding data signal If one tends to plot all results in a single box then he should use the plot selected var option Every time the user selects a specific variable index it will be plotted in the 124 screen on top of the previous plot Repeating this procedure will draw all variables in a single plotting box The menu toolbar of the plotting forum has additional options such changing the axis scale changing the foreground and background colors adding labels clearing the forum and a pointer The latter can be used to point at a specific point of the plot and grip its local value 125 APPENDIX B TUTORIALS B 1 SSDSA Open loop tutorial Exploring Steady State Behavior of an MSF Plant Case study Objective To study the steady state disturbance sensitivity analysis of an MSF in the open loop mode Note In this tutorial the MSF process is considered as an example Similar procedure applies to other case studies Process descr
103. rectory Then type mainmenu at the MATLAB command prompt this will take you to the itemized menu of PCLAB from which you can select the case study you want to work on Fig 1 13 shows the main menu of PCLAB 1 6 OVERVIEW OF PCLAB STRUCTURE PCLAB is interactive simulation software for process control analysis and training The process control module contains several exercises that cover basic concept of process dynamic and control These exercises can be carried out on simulated processes that are very common in the chemical engineering industry such as distillation columns reactors and evaporators The exercises are unified for all case studies This means that the user can choose a relevant case study and work on the pre designed exercises PCLAB is based on menu structure that allows the user to navigate through various case studies each of which has its own submenu that comprises the designated exercises By practicing on these tutorials the user then learns different aspects of dynamic analysis and control design The structure of the software is designed in a user friendly menu driven framework such that the process engineer can easily navigate through the various parts of the program carry out simulation experiments visualize the results and draw conclusions on the effect of different design parameters and control configurations There is a Main menu Fig 1 13 that allows the user to choose from different case studies The ca
104. rerun the simulation Observe the response on your screen similar to Fig 6 7 Notice that this time around the concentration rises to the new set point but with a sustained oscillation of constant amplitude This occurs only at the proportional band settings of 350 The value then becomes our K From the figure the period of the sustained cycling is taken as the average time of two successive crests To do this the graph of Fig 6 7 is expanded using the left top most icon to drag and enclose an expanded region with the help of the mouse to obtain Fig 6 8 The time interval for a complete cycle was found to 94 seconds Therefore P was assigned the value of 94 seconds Using the equations of Table 6 2 the values for the controller parameters were then calculated and allocated to the PID block parameter The calculated controller parameter values for the two methods are shown on Table 6 3 96 Table 6 3 Estimated Parameter values for a PID controller E Cohen Coon Method Ziegler Nichols Method Fig 6 7 System response to set point change at gain of 350 97 Fig 6 8 Expanded Closed loop response of concentration to set point change For the sake of rigid response the controller parameters are re defined in the software The gain ke is maintained as is but the reset time is defined as integral gain ky k t and the derivative time as derivative gain kp k tp The modified parameters are listed in table 6 4 This iss
105. response falls rapidly to a new level of concentration as against the rise in the level of the tank Using the same methodology the gain for the concentration icon was calculated as 7 03 min kg This means for a unit step change in the input flow the concentration falls seven percentage points From this it is clear that process gains can be negative The time constant was calculated as 17 05 seconds The concentration response is therefore seen to be 2 7 times faster than the level response Table 5 1 Calculated values of the characteristic parameters for positive step change Tp k Lu m que er 10 mw ws ws p Table 5 1 was generated for all the four output parameters that were calculated using the procedure above The graphs of the outputs were plotted separately and the 81 values of K tp and ty were all calculated from the graphs based on 10 change in the input flow D210 aja 8 Fig 5 6 Output showing the change in concentration with time If K is large the system becomes very sensitive and a small change in the input forcing function will result in a very large response The output concentration has the largest gain and therefore a small change in the input flow will result in a big change in the concentration On the other hand The outlet flow has the smallest gain of 0 033 so if large changes are made in the input flow the outlet flow will not be unduly disturbed It is possible for th
106. riables Variable Description Value Units Ap Cross sectional area for the brine chamber 1260 m Anrp Heat transfer area for condenser tube at the rejection 7919 1 m sections Anc Heat transfer area for condenser tube at the recover 77314 8 m sections B Inter stage Brine flow rate Calc ton min Bo Recycle brine flow rates 217 257 ton min 48 Bp Cpa Cpg Teo blow down flow rates Orifice contraction coefficient Discharge coefficient for the distillate tray Heat capacity for the brine in the condenser tube Heat capacity for the brine in the flash chamber Distillate flow rate Gravitational constant Orifice height Orifice discharge coefficient Brine level distillate level Liquid holdup for the condenser tube Liquid holdup for the brine heater Total number of stages Vapor pressure Reject flow rate Reference temperature Sea Water feed temperature Brine temperature condenser temperature Steam temperature Top brine temperature Overall heat transfer coefficient for the condenser tube Overall heat transfer coefficient for the brine heater Vapor rate ton min Salt concentration distillate product flow rate Seawater feed flow rate respectively Steam flow rate Make up flow rate Orifice width 49 29 3 0 625 1 0 Calc Calc Calc 9 8 0 11 0 68 Calc Calc 23654 0 34736 09 22 Calc 95 35 0 35 Calc Calc 98 1 93 35 49 5 Calc Calc 19 2 143 816 2 452 48
107. rial Exploring Steady State Behavior of an MSF Plant Case study Objective To study the steady state disturbance sensitivity analysis of an MSF in the closed loop mode Note In this tutorial the MSF process is considered as an example Similar procedure applies to other case studies Process description For detail description of the process its main variables and schematic of the flow sheet refer to chapter 2 Here we analyze the closed loop static behavior of the MSF plant to variation in the process inputs disturbances This show how the measured variable responds at steady state to a range of changes in the feed conditions while certain inputs are used as manipulated variables i e allowed to vary to compensate counteract for the disturbance effect This analysis is essential for understanding the ability and efficiency of the chosen manipulated variable to control the process Single loop and multiloops can be investigated Launching the SSDSA simulation module At the main menu of the PCCL select the MSF case study In the sub menu select steady state disturbance analysis A new simulink window that shows the MSF in open loop mode pops up One typical steady state operating condition for the input variables is shown in the corresponding boxes of the block diagram Record these steady state values on the work sheet To launch the SSDSA menu simply click the start button Tutorial Procedure 1 Select one of the available
108. rve the temperature closed loop response at each new value of ke When you observe a continuous cycling of the temperature response with steady amplitude record the following information The ultimate controller gain ku The ultimate gain is the controller gain at which the continuous cycling is observed The ultimate period T The ultimate period is the period of oscillation for the obtained continuous cycling Using these ultimate values compute the PI parameters as follows ke k 2 2 ki 1 2TJT Where T is the sampling time For clear capturing of the ultimate period of oscillation you may need to zoom in onto specific portion of the temperature response shown in the scope box To zoom in simply point on the temperature curve press the left button of the mouse draw a rectangular around the region to be zoomed release the mouse button An expanded plot of the zoomed in region 137 will appear in the scope from which you can estimate the cycling period Clicking the mouse once more will increase the axis resolution even more allowing for better estimation of the numerical value Enter the computed values of the controller settings in their designated boxes Explore the controller performance for set point change Enter a value in the set point box run the simulation and observe the temperature closed loop response Repeat the simulation for other set point values Explore the controller performance for regulatory problem Re
109. s User Defined Functions e Additional Math amp Discrete Wi Control System Toolbox m Wi Real Time Workshop Bal Signal Processing Blockset E Wii Simulink Control Design E M Simulink Extras 2 Additional Discrete 2 Ad 2 Zero Pole with initial states fr p p p e f p E s E a E E E A i Lr Additional Sinks 2 Flip Flops 2 Linearization 3 Transformations WH Simulink Parameter Estimation EA Ready Fig 1 7 SIMULINK Additional Linear Library 18 The labels names below each icon can easily be changed The default parameters for each icon are changed by double clicking the icon and entering new parameter values Also connections can be made between the outputs of one icon and inputs of another Fig 1 8b shows how the icons from Fig 1 8a have been changed and linked together to form a feedback control block diagram It should be noted that the form of the PID control law used by the SIMULINK PID Controller icon is not the typical form that we use as process control engineers The form can be found by double clicking the icon to reveal the following controller transfer function representation while we normally deal with the following PID structure P ke l Ker D gt keb Setpoint Fig 1 8 Block Diagram for Feedback Control of the Van de Vusse CSTR The s polynomials in the process transfer function were entered by double clicking on the transfer function and entering the c
110. s B and D are used to control the liquid holdups W and W 2 5 2 The Process Model ays F B O dt dC W F C C 04 dh Mioa Opt Os h Q L dW Tz B O y 4C dt B C C O C oh O H h T C B h h OQ 2 Additional relations h f MIN aC BC C 2 41 2 54 2 55 2 56 2 57 2 58 2 59 2 60 H fT 2 61 Q U A To 7T Wr 2 62 Q U A T T 2 63 L h A T T 2 64 Ly hy5 4 Ty T5 2 65 O k VR P 2 66 Fahy 2 67 P f T 2 68 Level Controllers Bj By ka n W 2 69 B By koa r W2 2 70 Notes The current model is different than the original one in the following aspects e The overhead flow out of the first effect is defined in the original model by the heat transfer equation which can be calculates as the amount vaporized at the given temperature of the first effect In this model it is defined by the pressure difference between the two effects 1 e 2 66 42 W The overhead flow out of the second effect is defined in the original model by the heat balance equation around the second effect 2 59 In this model it is defined as manipulated variable The temperature of the second effect is fixed in the original model Here it is given by 2 59 after modification as follows dh ah 0 H hy 4 oF 20H M aC oh Cy By hy
111. s developed for steady state predictions Since chemical process systems do not reach steady state instantaneously accurate modeling must capture both the steady state and transient behavior of the system The transient behavior is the time dependent trajectory of an output in response to a particular input or class of inputs After that control synthesis is the nest step where the control structures are selected and tuned Finally the designed controlled system is analyzed for proper performance Future versions of the software can examine advance control algorithms such as Internal Model Control IMC as well as Model Predictive Control MPC 25 The sub menu in Fig 1 16 has additional navigation buttons The process description button allows the user to access a document file containing the description of the current active selected case study The yellow button simply closes the current submenu and returns the user to the main menu PCLAB also includes additional features which will be discussed as we progress in the manual 26 CHAPTER 2 CASE STUDIES 2 1 INTRODUCTION In this chapter the modeling of the basic case studies representing the heart of the chemical engineering industry is undertaken Tutorials and exercises that can be carried out upon these case studies will be discussed in other chapters These modules case studies are clearly defined and all involved parameters are explained It is important to unders
112. s of 10 then the disturbance value will have the following range during the test 71 Increasing the number of steps at the same step size will increase the temperature range to be covered The above values for the step size and number of steps cover a 50 range which is good enough from practice point of view Decreasing the step size will help in producing smoother response curves but it will decrease the overall range Therefore if one decreases the step size for better resolution he should also increase the number of steps to maintain the same operating range It should be noted though that smaller step size requires higher computational load In the open loop mode steps 4 and 5 must be by passed If you by mistake marked one of the boxes in step 4 or 5 you will receive an error message which will be displayed in the warning box Now press the run button and look at the results shown in Fig 4 3 DaW S kAAs PPD Fig 4 3 SSDSA results for open loop test Fig 4 3 illustrates how the four main process outputs respond at steady state to changes in the feed temperature from 20 to 60 C It is obvious that the liquid level in the separator unit is not affected by this type of disturbance Thus in the open loop mode the user can gain information about the directional magnitude and nonlinearity effect of a disturbance For example as a directional effect both Cz and P will increase when the feed temperature increase while the
113. se of the gain matrix G G Compute the RGA as follows Suf S95n S5 82rp RGA 2 8r2 8 2 Srv If the off diagonal elements of the RGA are negative or positive close to 0 5 then the process is highly interactive Therefore decentralized control may not perform well Pair the controlled variable and manipulated variable so that the corresponding relative gain row element is positive and as close to one as possible According to this analysis does the pairing suggested by the RGA in consistent with the pairing used in the above tests 140
114. se studies covered by the current version of PCLAB are as follows Forced Circulation Evaporator Polyethylene Reactor Fluid catalytic Cracking Unit Ethylene Dimerization Process Double Effect Evaporator Two CSTR in Series Multi Stage Flash Desalination Plant BOY A ae ee p d 23 These basic case studies represents the heart of the chemical engineering industry can be used in combination with the exercises to generate a whole lot of scenarios that will enhance the understanding of the basics of control process analyses E 17190253 U23c1TU ton Microsoit interner E49 Ur 21 Working OL Eef AProcess Control Module Microsoitintenner ploren Plassey 0222 E Jex Fie Edit View Favorites Tools Help a File Edit View Favorites Tools Help Q O x Oh JO serch Se Favortes GM meda M Q O h9 Oh JO serch y Favortes Gi media 62 Address D MATLAB PClab1 1 help Processes htm Eo Links z Address Bl DAMATLABIPCIabI 11 helplUsereTut htm Be m Z List of the Case Studies For detailed information about each case study click on the desired process Forced Circulation Evaporator m Wastewater Treatment Process Ethylene Dimerization Mllti stage Flash Desalination MSF Ethylene Polymerization M gt Two Effect Evaporators Fluid Catalytic Cracking Unit OA 1 My Computer Fig 1 14 Process description help option Fig 1 15 User guide help option Th
115. so has outstanding graphic capabilities It can be done with automatic scaling or within defined scales as shown in the example below gt gt x 10 1 10 gt gt plot x 2 figure gt gt plot x x 2 figure 1 3 3 1 Plotting graphs 2 D Graphs Functions with one independent variable can easily be visualized in MATLAB x linspace 0 2 y x exp x plot y plot x y grid grid xlabel x ylabel y title y x exp x gtext anywhere plots y versus their index plots y against x adds grid lines to the current axes removes the grid lines adds text below the x axis adds text besides the y axis adds text at the top of the graph places text with mouse text 1 0 2 1 0 2 places text at the specific point You can use symbols instead of lines You can also plot more than one function in a graph plot x y x x sin x Also more than one graph can be shown in different frames subplot 2 1 1 plot x x cos x subplot 2 1 2 plot x x sin x Axis limits can be seen and modified using the axis command axis axis 0 1 5 0 1 5 Before continuing clear the graphic window clf Another easy way to plot a function is fplot x exp x 0 2 The function to be plotted may also be a user defined function 1 3 4 Scripts and Functions The programs written in the language of MATLAB should be saved with the extension of
116. speed of response to the inner loop one can step change the steam mass flow rate with all loops disabled As mentioned in chapter 6 disabling the control loop is achieved by settings all PID parameters to zero in the designated boxes i e PID controller for Tgo and PID controller for Wa Introducing a step change in the steam mass flow rate result in the reaction curve depicted in Fig 8 4 The curve indicates that the Tgo W loop has a time constant of 20 minutes It is hard to estimate the response speed of the Wa Tpo loop because the top brine temperature can not be stepped independently Nevertheless the effect of Ws on Tso is direct and its time constant controlled by the heat capacitance of the brine re boiler On the other hand the effect of Tso on Wa is transmitted through the 19 flash stages This means that the time constant would be the accumulation of mass and heat 111 capacitance of all stages According to this reasoning it is evident that the speed of response for Tpo W is faster than that for Wa Tpo POG a00 a2 aja a X 0 Time offset 0 Fig 8 4 The open loop response for Tp to step change in Wg Fig 8 5 demonstrates how the process responds to a disturbance of 5 C in the feed temperature of the sea water without control r Uu a P eje alia 8 22 21 20 o wp 18 Time offset Fig 8 5 Product response to disturbance in feed temperature The result in
117. sure Reactor fractionation pressure Regenerator Pressure Wet gas compressor suction pressure Regenerator cyclone temperature Reactor temperature 56 60 9656 60 9656 14 5719 14 5719 0 0 1 1275 60 1634 1 1275 10 1596 246 25 32 1 14 6421 35 2159 40 5944 32 8244 23 3244 29 6707 22 4988 1279 2 992 6582 Ib s Ib s Ib s Ib s Ib s mole s Ib s Ib s Ib s Ib s Ib s Ib s ft mole Psia Psia Psia Psia Psia Psia Psia psia F algebraic Algebraic algebraic algebraic algebraic Algebraic Algebraic Algebraic Algebraic algebraic Algebraic Algebraic Algebraic state Algebraic State State state algebraic State State State State State Treg Regenerator bed temperature 1286 4 F State Ti Fresh feed temperature to furnace 460 9 F Input T Fresh feed temperature to reactor 667 2611 F state T Furnace firebox temperature 1607 6 F State Ve Combustion air blower suction valve 1 Input position V Combustion air blower vent valve 0 Input position Vg Lift air blower vent valve position 0 Input Vo Spill air valve position 0 Input V List air steam valve 0 4313 Input Vi Wet gas compressor suction valve 0 95 Input position Vi Wet gas flare valve position 0 Input Vis Wet gas compressor vent valve 0 Input position Via Stack gas valve position 0 612 Input W Inventory of catalyst in reactor 101696 89 Ib state Wreg Inventory of catalyst in regenerator 273763 07 Ib State
118. tand the mathematical development of the models as they represent the basis to which the exercises will be referred to The mathematical models developed here for each case study are core to the process transfer functions that will be used with differing controller algorithms and are classical examples from literature As listed earlier these case studies are 8 Forced Circulation Evaporator 9 Polyethylene Reactor 10 Waste Water Treatment Unit 11 Ethylene Dimerization Process 12 Double Effect Evaporator 13 Two CSTR in Series 14 Multi Stage Flash Desalination Plant 22 FORCED CIRCULATION EVAPORTOR UNIT 2 2 1 Process Description and Flow sheet The forced circulation evaporator is a common processing unit in sugar mills alumina production and paper manufacture This process is used to concentrate a dilute liquor by evaporating its solvent usually water as shown in the Fig 2 1 A feed stream with solute of concentration C mass percentage is mixed with high volumetric recycle flow rate and fed to a vertical evaporator heat exchanger The solution will pass through the tube A saturated steam is used to heat up the mixture by condensing on the outer surface of the tubes The liquor which passes up inside the tube 27 boils and then passes to a separator vessel In the separator the liquid and vapor are separated at constant temperature and pressure The liquid is recycled with some being drawn off as product with s
119. that simulations can become somewhat flaky if 0 is entered for a transport delay We recommend that you remove the transport delay block for simulations where no time delay is involved 20 Transport Delay Fig 1 10 Transport Delay Icon Manipulated variables are often constrained to between minimum 0 flow for example and maximum fully open valve values A saturation icon from the Nonlinear library can be used to simulate this behavior The saturation icon is shown in Fig 1 11 uH Saturation Fig 1 11 Saturation Element Actuators valves and sensors measurement devices often have additional dynamic lags that can be simulated by transfer functions These can be placed on the block diagram in the same fashion that a transfer function was used to represent the process earlier It should be noted that icons can be flipped or rotated by selecting the icon and going to the format pull down menu and selecting Flip Block or Rotate Block The block diagram of Fig 1 8 has been extended to include the saturation element and transport delay as shown in Fig 1 12 rie r u Setpoint manipulated I 44172634472 s p FID pt Set point 5244 420s 5 3821 Add PID Controller Saturation Transfer Fen YF output Transport Delay Fig 1 12 Block Diagram with Saturation and Time Delay Elements 2
120. the desired column pressure In this process the bed temperature is controlled by manipulating the feed temperature of the cooling water The total pressure is controlled by manipulating the bleed flow And the bed height is regulated by the discharge system The discharge system operates periodically i e the outlet flow valve opens every time the bed level exceeds certain limit 31 2 3 2 The Process Model dC V E Fw xmb 7 Ry ac Vea oc Pin mB Ry dC Ve US F x B Ry dC ae N XyB dY qon Ra hal Op B M Cp B Cp Z HF HG HR HT HP t dT M Cp s F Cp 2 1 eb Cpl T P Cy t Cy Cy Cy RT P ENT P AP a F Cp T i T 0 SUAL T yy Tpi T4 T HF FCP m Fu2P u2 Fx Qu FyCpy XT T4 HG F Cp T T HT F B Cp T Ty HP 0 Cp T T HR M Ry MT O My Rus My Ry E T MTyef E R Ry Cy Y ke E 1 T l Tyef E R Ryo Cur k pre 32 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 2 24 2 25 2 26 2 27 2 28 2 29 2 30 Cp gt x Cp 2 31 2 3 3 Process Parameters and Variables Variable Description Value Units de Active site concentration 0 548 mole kg By Mass of the polymer in the bed 70 0 tonne B Bleed flow rate 10 39 mole s Cui Concentration of monomer 297 06 mole m Cu2 Concentration of co
121. the loop pairing for example one can choose one of the available inputs 1 e F100 F1 F200 T200 as the manipulated variable instead of P100 to control the product concentration The modifications discussed above can be carried out by simple mouse operations 103 However it is suggested that only expert users can do so The concept of selecting appropriate controlled variables manipulated variables and pair them together is known as control structure design This issue will be discussed later in this section 7 1 1 Tuning of Multi Control Loops As far as tuning is considered the user can tune each loop independently using the procedure discussed in chapter 6 Following the Ziegler Nichols procedure used in chapter 6 for each loop and with the aid of Table 6 2 the calculated PI settings are listed in table 7 1 Note that the ZN method is applied to each loop while the other loop is in open mode Table 7 1 Estimated Parameter values for a PID controller Next we examine the performance of the two control loops system Let us introduce a disturbance in the form of a step change of magnitude 0 296 in the feed concentration C The process response in open loop mode i e with both controllers are disabled 1s shown in Fig 7 2 Xl Neyen ops ajsj j aj 5 Time offset 0 Fig 7 2 Open loop response to disturbance in feed concentration 104 It is obvious from Fig 7 2 that the variation in the feed concentratio
122. tio is given by 5 1 for the liquid level 5 1 Where Lo is the initial level of the tank and Lss the final tank level Fo is the initial flow and F the final flow This gives a value of 0 089 m min kg as the steady state gain This value of the gain tells us that the for a ten percent change in the input flow rate the liquid level in the storage tank of the evaporator process will change by about 9 percent Or for a unit step change in the input the tank level will increase by 0 089m Similarly the time constant tp of the process can also be calculated from the graph Refer to Fig 3 1 to refresh your memory on some of these calculations To do this calculation the change in the output from the initial steady state to the final steady state value is calculated through 5 2 below 5 2 80 AL is calculated as 1 05 0 961 to get 0 089m Now apply 5 3 to get the level of the tank at one time constant Lip Ly 0 632 AL 21 017248 5 3 Double click on the first red output icon to revisit Fig 5 4 Then use the icon with binoculars to auto scale your plot Now use the three zoom options to the top left of your plot to vary the y axis until you read the height of 1 017m Note the corresponding reading on the x axis as 46 5 seconds This gives you the value of p for the process Now look at the output concentration icon by double clicking on it Enlarge the graph to obtain Fig 5 6 Notice how the concentration
123. tion air blower inlet suction 49465 ICFM algebraic flow Fsucla Lift air blower inlet suction flow 11750 ICFM algebraic Fsucwg Wet gas compressor suction flow 19011 ICFM algebraic Fsurca Combustion air blower inlet surge 45100 ICFM constant flow Fsurla Lift air blower inlet surge flow 9571 6 ICFM algebraic Fsurwg Wet gas compressor surge flow 11700 ICFM constant Fair Air flow rate into regenrator 75 5375 Ib s algebraic Fi Flow of wash oil to reactor riser 13 8 Ib s input Fy Flow of diesel to reactor riser 0 0 Ib s input F Fresh feed flow rate to reactor riser 126 Ib s input F4 Slurry flow rate to reactor riser 5 25 Ib s input Fs Fuel flow rate to furnace 34 Ib s input 55 Fui Fu Fy Lsp Prip Pi P P4 Ps Ps T cyc Combustion air blower throughput Combustion air flow to regenerator lift air blower throughput Combustion air flow to regenerator spill air flow to regenerator Wet gas flow to the vapor recovery unit Flow through combustion air blower suction valve Flow through combustion air blower vent valve Flow through lift air blower vent valve Flow through wet gas compressor suction valve Flow through wet gas compressor vent valve Flow through wet gas compressor anti surge valve Level of catalyst in standpipe Amount of gas Pressure at bottom of lift pipe Combustion air blower suction pressure Combustion air blower surge pressure Lift air blower discharge pressure Reactor Pres
124. ts r267 41 s 3 3 3 2 STEADY STATE ANALYSIS From 3 1 we conclude that the analysis of a process control system requires an understanding of the overall system behavior and the reflection of this behavior in the properties of the system elements These properties are highlighted during steady state conditions where the accumulation term in the above equation goes to zero The state variables do not change with time and the input is then directly related to the output This leads to the definition of the steady state gain as K Change in output Change in input 3 4 This relation is useful to determine the effect of manipulated and load variables on the controlled variable of a process Thus the relation characterizes the effect that a change in an input variable has on an output variable Implicit in this characterization is the fact that changes in the controlled variable can be calculated by summing up the changes in all the manipulated and load variables multiplied by a constant gain coefficient This superposition applies only to linear systems Steady state models are frequently used to determine set points for controllers whose measured variables are dynamic multiple input computed variables They are used to adjust the set points of unit operations performance variable 3 2 1 Steady State Disturbance Sensitivity Analysis Steady state disturbance analysis is a tool developed by Yi and Luyben 17 to study the controllabili
125. ty and further the control structure of a given process It is more suitable for nonlinear processes where the effect of process disturbance on the plant steady state operating condition is investigated Steady State disturbance sensitivity analysis can be carried out in two modes Open loop Closed loop 61 In the open loop mode steady state disturbance analysis illustrates how much a chosen process output changes at steady state for various different values of a given disturbance when all the manipulated variable are fixed at their corresponding steady state values In this case the severity and nonlinearity of the disturbance impact on a certain process output can be investigated Moreover one can compare the effect of the designated disturbance on several process outputs and find out which one is the most influenced In the closed loop mode the steady state disturbance sensitivity analysis ssdsa demonstrates how much a specific input or a group of inputs should change to keep a controlled output or group of controlled outputs at its set point at steady state for various values of a given disturbance while the other inputs are fixed Given certain constrains on the inputs one can select the most appropriate input to regulate a specific output under the influence of a particular disturbance The steady state disturbance analysis SSDA is obtained by solving the static version of the process model for different values of a pre sp
126. ue is also discussed in chapter 1 section 1 4 3 It should be noted that the negative process gain and consequently proportional gain is the result of the increase decrease behavior of the output input concentration Steam Pressure pair The error signal used in the PID controller is based on the negative gain concept i e e y y Therefore if one wishes not to use negative values for the PID settings which is the common practice in industrial application then the definition of the error signal should be reversed This modification can be easily handled but we prefer to overlook it because we are simply dealing with simulations Table 6 4 Parameters used for the PID controller Cohen Coon Ziegler Nichols o 9 4 om TI k tp 406 2 2421 98 6 3 TESTING THE ZN AND CC PID SETTINGS THROUGH SIMULATION Using the values obtained in Table 6 3 the response of the process to set point changes and disturbances was tested To do this the parameters to be used are recalculated to satisfy the requirement of the software The values of these parameters are as given in Table 6 4 If these parameters are used and the response is unsatisfactory highly oscillatory the rule of thumb is to divide k by two and recalculate the other parameters by this new definition for the software This is repeated until a satisfactory response is achieved For the set point change double clicking on the set point icon of Fig 6 1 The set point Bloc
127. ur data in MATLAB Let us first generate some data a magic 3 b magic 4 The following command saves all the variables in the MATLAB workspace in the file fl mat save fl If you need to save just some of the variables list their names after the file name The following saves only a in the file 2 mat save f2a The files generated above have the extension mat and could be retrieved only by MATLAB 11 To use your data elsewhere you may want to save your data as text save f3 b ascii Here the file 3 is a text file with no extension You can load your data into the MATLAB workspace using the Load command If the file to be loaded is generated by MATLAB carrying mat extension the variables will appear in the workspace with their name at the time they were saved clear load fl 12 1 4 INTRODUCTION TO SIMULINK SIMULINK is an interactive programming environment within MATLAB which provides graphical interface to MATLAB programs The program is user friendly and one can run simulations of linear and nonlinear systems interactively The system can then be analyzed and the results easily visualized by simple click and drag of mouse operations Although the standard MATLAB package is useful for analysis of linear systems SIMULINK is far more useful for the simulation of control system It enables the rapid construction and simulation of control block diagrams In order to make it eas
128. urbance on concentration in closed loop system with Ziegler Nichols settings Figure 7 1 Evaporator Process with two control loops vi 67 68 69 70 T3 T3 74 74 75 711 79 80 83 84 84 85 89 90 90 9 9 93 93 93 96 96 97 97 98 99 Figure 7 2 Figure 7 3 Figure 7 4 Figure 7 5 Figure 8 1 Figure 8 2 Figure 8 3 Figure 8 4 Figure 8 5 Figure 8 6 Figure 8 7 Figure 8 8 Figure 8 9 Open loop response to disturbance in feed concentration Closed loop response to disturbance in feed concentration Closed loop response to disturbance using improved PI settings Open loop response for a step change in the steam pressure The MSF Process Menu Single loop control for MSF process Cascade Control Structure for MSF process The open loop response for Tego to step change in Ws Product response to disturbance in feed temperature Product response to disturbance when single loop is involved Product response to disturbance when cascade control is involved Feed forward Controller Structure for the Evaporator Process FFC structure for Evaporator process showing parameter dialog box Figure 8 10 Process response to step change in the feed concentration vii 100 101 101 104 105 106 107 108 108 109 109 111 112 113 Acknowledgment The investigator would like to thank the general directorate of research center at the college of engineering for their support continuous follow up and patience t
129. variable to achieve a desired output value The controller is the active element that receives the information from the measured parameter and takes appropriate action to adjust the values of the manipulated variable Consider the open loop systems to be in the form of y 5 G s u s G s d s 3 9 67 Let y be the desired set point for the controlled variable y s G s u s G s d s 3 10 The feed forward controller is therefore G s u s 5 y ie G s IG y d s ps 3 11 And the block diagram with FFC looks Feedforward control R Gp O y mechanism Therefore fus pedi G k G Kc _ ky TS 1 G k Gel p Process Fig 3 6 FFC block diagram 3 12 3 13 68 Cascade Control A cascade or multi loop control is a way of minimizing a disturbance that enters a slow process It has two sets of controllers a primary and a secondary Instead of adjusting the final control element such as a valve the output of a primary controller is the set point of a secondary control loop Thus cascade control uses the output of the primary controller to manipulate the set point of the secondary controller as if it were the final control element The block diagram for a cascade controller is shown in Fig 3 7 16 d d ry e y X u Gq es Ga P Gon gt G gt Y Secondary Loop
130. ver the set point of this loop is adjusted from an outer loop which is the one designated for controlling the distillate product Hence the outer loop has W as its controlled variable and 77 as its manipulated variable Cascade control can use the standard PID feedback controllers in the two loops The secondary loop must have the proportional mode but it does not require the reset mode Integral model may be used in the secondary controller if it is desired to suppress completely the disturbance entering the primary or when the primary controller is not in operation sensor not functioning or calibrated etc Derivative modes are not 110 advised in the secondary loop since the derivative action is designed to overcome some lag in the controller loop and if applied to set point changes may result in excessive valve motion and overshoot The cascade controller is tuned in a sequential manner The secondary controller is first tuned satisfactorily before the primary is tuned Conventional tuning guidelines for PID such those discussed in chapter 6 apply for both control loops Is File Edit View Simulation Format Tools D S E8 Multi Stage Flash Desalination Cascade Closed Loop with last stage level control PID controller SN for TBO PID controller for Wd Fig 8 3 Cascade Control Structure for MSF process For satisfactory cascade control application the inner loop must have faster dynamics To check the
131. very large time constant of 11515 seconds The static gain of 26 5 seems to be equally large This shows that the system has very large capacitance Good design engineers are able to reduce these parameters so that the system can have quick response Other parameters that can be calculated from the graph are the rise time and the response time Since the system took a response time of 2 29x10 seconds to reach its ultimate value with equally large value of the rise time found to be 22 200 seconds then the system is expected to have large capacitance The system seems to have a very large time constant of 11515 seconds The static gain of 26 5 seems to be equally large 89 This shows that the system has very large capacitance Good design engineers are able to reduce these parameters so that the system can have quick response Other parameters that can be calculated from the graph are the rise time and the response time Since the system took a response time of 2 29x10 seconds to reach its ultimate value with equally large value of the rise time found to be 22 200 seconds then the system is expected to have large capacitance Table 5 5 Calculated characteristic parameters for the Polyethylene Process Bop s 2x 27a y 2x u Remarks e The green box labeled Go to menu shown in the Simulink Module can be used to switch between the active Simulink module with the current active sub menu e The green box la
132. wn in Fig 8 9 The dialog box for the feed forward controller shown in Fig 8 9 can be activated by double clicking the feedforward controller icon In order to complete the FFC design one needs to determine the value of the FFC parameters i e kp ka Tp and tg these parameters can be computed using the reaction curve method discussed in chapter 3 and implemented in chapter 5 By step testing the product concentration to pre defined changes in the steam pressure and feed concentration the following were estimated Table 8 2 FFC tuning values C P100 ky 0 018 Tp 64 s C Cl kg 4 75 147 22 s 115 Next we insert these values in the feed forward parameter block and test the process for a step change of 0 2 in the feed concentration C Fig 8 10 illustrates the process response to the load change Part a of the figure shows how the product concentration moves away from its nominal value when no controller of any type is involved Part b demonstrates that the product concentration performance can be improved when a typical feedback controller is used A typical PI controller is used with the controller gain and integral time magnitudes are set to the values found by Ziegler Nichols method as listed in table 6 3 The last part of the figure depicts the process performance when FFC is implemented using the tuning values listed in Table 8 2 One can observe that the FFC response has less overshoot and faster settling tim
133. workspace and give it a variable name Choose Matrix for Format box Click on Apply or OK to continue Make your run or simulation as described earlier and continue The stored data can be viewed on MATLAB command window by typing the variable name at the prompt option of MATLAB The data will be stored in MATLAB workspace as a matrix under the chosen variable name the data can be saved for further analysis or plotting General Data history Tip try right clicking on axes v Limit rows to last 5000 Save data to workspace 50 100 150 200 n DK Cancel Help Apply Fig 5 7 Level Properties window for saving data to a workspace 5 2 1 Nonlinearity Analysis Approximating the process dynamics by a first order system is based on that assumption that the physical process responds linearly to input variation However 83 this is not true for most chemical processes except at a very narrow operating region Therefore it is necessary to use small process perturbation in order to obtain faithful process parameters i e static gain and time constant However the input perturbation should be large enough to create reasonable signal to noise ratio In this sense the appropriate procedure for identifying the process parameters 1s a trial and error This will be explained in the next paragraphs Now let us see what happens when the step change is 10 This is done the same way by invoking the Block Par
134. y for learning SIMULINK the reader is taken through different tutorials The goal of the tutorial is to introduce the use of SIMULINK for control system simulation The tutorials are divided into sections namely Background Open loop Simulations Closed loop Simulations 1 4 1 Background The first step is to startup MATLAB on the machine you are using In the Launch Pad window of the MATLAB desktop select SIMULINK and then the SIMULINK Library Browser This is done through the steps below 1 In your PC double click the MATLAB icon As a result a MATLAB command window pops up and becomes ready for operation 2 Change the operating directory to the subdirectory under which a specific tutorial exist by typing At the MATLAB command prompt the following gt gt cd C workshop simulink MPC This will put you in the subdirectory designated for Model predictive simulations Or gt gt cd C workshop simulink ident 13 This will put you in the subdirectory designated for identification simulations Or gt gt cd C workshop simulink phlink This will put you in the subdirectory designated for pH process simulations etc While in the SIMULINK Library Browser number of options are listed as shown in Figure 1 1 Notice in this figure that Continuous has been highlighted this will provide a list of continuous function blocks available Selecting Continuous will provide the list of blocks shown in Figure 1 2 The o

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