IP01_2 Position_PV_Student_504
Contents
1. Figure 5 Slider Gain for K Figure 6 Slider Gain for Ky Also bring up the Position Error m as well as the Vm V Control Signal scopes Also discuss the effect of varying K and K one at a time on the resulting position error and the commanded voltage applied to your IPO1 or IPO2 DC motor Step 4 To specifically include in your lab report i Make a short table to describe the changes in the system response characteristics t and PO with respect to changes in K and K Note Hold one gain constant while changing the other within the preset range i Does the system response react to how you had theorized in Assignment 2 4 Step 5 Now that you are familiar with the effects of each one of the two controller gains enter in the designed K and K that you have calculated in Assignment 3 to meet the system re quirements Note the values should fall within the slider limits Step 6 After running the simulation with the gains set to their calculated values specify in your lab report the following 1 Does the system response look like what you had expected i What is its Percent Overshoot PO Measure its rise time t Hint To get a better resolution when measuring t decrease the time range under the parameters op tion of the scope iil Do they match the design requirements Step 7 If the simulated response is as expected you can move on to the next Section in order to implement a real time controller2. sees 8 7 3 Simulation of the Servo Plant with PV Controller eene 9 Dido MMC CU VCS t EE 9 7 3 2 Experimental Procedure ert i eene eese perat bonae EXEAT CEN era te eae aeg 9 7 4 Real Time Implementation of the PV Controller serene 11 FE NNI ei men MM MERE 11 7 42 Experimental Procedure scires teenie n esa asg ie 11 8 O BRO TEO a E EEE E E E E EO TE E TAA 14 Append Ac NOMEE ARIE a eta a e ee naive deed eer E RRR 15 Appendix B IPO1 and IP02 Open Loop Transfer Function eene 17 B 1 A Simplified Dynamic Model e eeeeeeeeeeeeeeee eese ee eee tn eee nnnne nen 17 B2 oA More Complete Dynamic Model s Dore eie oed nee Se ghen vad t cu dodpa iem eiua 19 Appendix C Position Controller Design eeeeeeeeeeeeseee eene eene nennen netten nene 21 C 1 Standard Closed Loop System iecit scavbeavsdeeatovaassuedegesesuadayonstesaaveahosagaonnastued quad 21 C 2 Proportional plus Derivative PD Control Scheme eese 22 C 3 Proportional Velocity PV Control Scheme esee 22 Document Number 504 Revision 02 Page i PV Position Control Laboratory Student Handout 1 Objectives In this laboratory session you will become familiar with the fundamentals of control system design using PID types of compensators The challenge of the present lab is to control the
3. in this lab Document Number 504 Revision 02 Page 22 PV Position Control Laboratory Student Handout V x m tO amp gt Gs Xa Figure C 2 Block Diagram of the PV Control Scheme Document Number 504 Revision 02 Page 23
4. During the course of this lab were there any problems or limitations encountered If so what were they and how were you able to overcome them 2 After completion of this lab you should be confident in tuning this type of controller to achieve a desired response Do you feel this controller can meet any arbitrary system requirement Explain 3 Most controllers of this form also introduce an integral action into the system PID Do you see any benefits to introducing an integral gain in this experiment Document Number 504 Revision 02 Page 14 PV Position Control Laboratory Student Handout Appendix A Nomenclature Table A 1 below provides a complete listing of the symbols and notations used in the IPO1 and IP02 mathematical modelling and controller design presented in this laboratory The numerical values of the system parameters can be found in Reference 2 Symbol Description Matlab Simulink Notation Vin Motor Armature Voltage Vm In Motor Armature Current Im Ra Motor Armature Resistance Rm La Motor Armature Inductance Lm K Motor Torque Constant Kt On Motor Efficiency Eff_m Ka Back ElectroMotive Force EMF Constant Km Bont Back EMF Voltage Eemf Jim Rotor Moment of Inertia Jm K Planetary Gearbox Gear Ratio Kg 0 Planetary Gearbox Efficiency Eff_g Ma IPO1 Cart Mass Cart Alone Mcl M IP02 Cart Mass Cart Alone Mc2 M IP02 Cart Weight Mass Mw M Total Mass of the Cart System i e moving parts M P Rack Pit
5. If your response is close to meeting the set require ments try fine tuning the controller gains to achieve the desired response If the system re sponse is far from the specifications then you have to re iterate your design process and re calculate your controller gains K and K as asked in Assignment 3 Document Number 504 Revision 02 Page 10 PV Position Control Laboratory Student Handout 7 4 Real Time Implementation of the PV Controller 7 4 1 Objectives m To implement with WinCon the previously designed PV position controller in order to command your IPO1 or IP02 servo plant F1 To run the simulation simultaneously at every sampling period in order to compare the actual and simulated responses M To change on the fly the two controller gains K and K and observe the effect on the actual position response of your physical IPO1 or IP02 system 7 4 2 Experimental Procedure After having designed your PV controller calculated its two gains satisfying the desired time requirements and checked the position response of the obtained closed loop system through simulation you are now ready to implement your designed controller in real time and observe its effect on your actual IPO1 or IPO2 plant To achieve this please follow the steps described below Step 1 Open only one of the following Simulink models q position pv mqpci ip01 mdl or q position pv mqpci ip02 mdl or q position pv mq3 ip01 mdl or q posit
6. Linear Motion Servo Plants IP01 or IP02 Linear Experiment 1 PV Position Control GSU san TG E T4 INNOVATE EDUCATE IP01 and IP02 Student Handout PV Position Control Laboratory Student Handout Table of Contents Wf MOB FCC HVC S eoe rab pote cae E LU EE DEM EE E ML ED OC as DERE um 1 Z OPISCQUISITES es o reet ema t med tutt est aes ead gale aie SRG Aaa a aedis 1 3 ISI Te PS dde o au presume o cr a Ee e saes Eee o ta osea 1 A Experimental SEIUD us isa epis tie tap ae ances aati A Nd Lets ooi bm s Ie ad M aS Ir edd 2 4 1 NI COBDOBents noi ciae esses sca gets e esae icit de elu A eua eed E O aiT 2 42 MP T E ESEE 2 5 Controller Design Specifications cisiicccass ccesnseavernageasaseceeetseccddesavacayhaveeasecedensseeussaeverasedeeasaes 4 GSTS EA AGS EVN IIMS ceo oue Modes cda RERO Aet DLE wav doch eevee LE Co 5 6 1 Assignment 1 Open Loop Transfer Function 5 6 2 Assignment 2 Open Loop Model Block Diagram eere 5 6 3 Assignment 3 PV Controller DesIgri cinia RES HO Ne ede ter hel apa eios dara 6 T Edge iiic 8 TA Experimental Setup eru Seni PS TREO RSANO ERE EROR EAR E AIR Ada Qe XE VERSER SERA EARS 8 7 1 1 Check Wiring and Connections itas Deed diete teet bere p ed ores quee pdarceps 8 11 2 IPOT Gr TPO2COnfiSUF AOT odore gr edo Res r a dM ree vu O ees deeds 8 7 2 Closed Loop System Actual Requirements
7. a simplified dynamic model is used to derive G s We shall begin by applying Newton s second law of motion to the IPO1 or IP02 system d d aseo Jer 2 xn B 1 Here the inertial force due to the motor s armature in rotation is neglected The cart s Coulomb friction is also neglected The driving force F generated by the DC motor and acting on the cart through the motor pinion can be expressed as F n ut D B 2 mp We now shift over to the electrical components of the DC motor first Figure B 1 represents the classic electrical schematic of the armature circuit of a standard DC motor Document Number 504 Revision 02 Page 17 PV Position Control Laboratory Student Handout O Figure B 1 DC Motor Electric Circuit Using Kirchhoff s voltage law we obtain the following equation d Voc I La 3 on 0 B 3 However since L Rm we can disregard the motor inductance leaving us with V g E mf p COR B 4 m Since we know that the back emf voltage created by the motor E m is proportional to the motor shaft velocity Tm we have Y K a On a R B 5 m Moreover in order to account for the DC motor electrical losses the motor efficiency is introduced to calculate the torque generated by the DC motor T UM K L B 6 Substituting Equations B 5 and B 6 into Equation B 2 leads to uP K ue K u Ka e F MEME RNECRPCERQS B 7 r m mp By considering the rack a
8. ch Pr Tip Motor Pinion Radius r_mp Nop Motor Pinion Number of Teeth N_mp Top Position Pinion Radius r pp Ns Position Pinion Number of Teeth N pp B Equivalent Viscous Damping Coefficient Beq as seen at the Motor Pinion Document Number 504 Revision 02 Page 15 PV Position Control Laboratory Student Handout Symbol Description Matlab Simulink Notation Torque Generated by the Motor Torque Applied by the Motor on the Motor Pinion Cart Driving Force Produced by the Motor Armature Rotational Inertial Force acting on the Cart Armature Inertial Torque as seen at the Motor Shaft Motor Shaft Rotation Angle Motor Shaft Angular Velocity Cart Linear Position Percent Overshoot Peak Time Continuous Time Laplace Operator Undamped Natural Frequency Damping Ratio Proportional Gain Velocity Gain Table A 1 IPO1 and IP02 Model Nomenclature Document Number 504 Revision 02 Page 16 PV Position Control Laboratory Student Handout Appendix B IP01 and IP02 Open Loop Transfer Function This Appendix derives the mathematical modelling of your IPO1 or IPO2 The resulting linear model will provide us with the open loop transfer function of your IPO1 or IP02 which in turn will be used to design an appropriate controller Equation 1 defines G s the open loop transfer function of your IPO1 or IP02 system G s is derived in the following two sub sections B 1 A Simplified Dynamic Model In a first approach
9. equirements The following hint formulae are provided 1 Hint formula 1 PO 100 L i 23 ii Hint formula 2 T am M e 24 Document Number 504 Revision 02 Page 7 PV Position Control Laboratory Student Handout 7 In Lab Procedure 7 1 Experimental Setup Even if you don t configure the experimental setup entirely yourself you should be at least com pletely familiar with it and understand it If in doubt refer to References 1 2 3 4 and or 5 7 1 1 Check Wiring and Connections The first task upon entering the lab is to ensure that the complete system is wired as fully described in Reference 2 You should have become familiar with the complete wiring and connections of your IPO1 or IP02 system during the preparatory session described in Reference 1 If you are still unsure of the wiring please ask for assistance from the Teaching Assistant assigned to the lab When you are confident with your connections you can power up the UPM You are now ready to begin the lab 7 1 2 IP01 or IP02 Configuration In case you use the IP02 for this laboratory this experiment is designed for an IP02 cart without the extra weight on it However once a working controller has been tested the additional mass can be mounted on top the cart in order to see its effect on the response of the system As an extension to the lab the first PV controller design could be modified in order to account for the additiona
10. ewton s second law of motion to the motor shaft Document Number 504 Revision 02 Page 19 PV Position Control Laboratory Student Handout a J E a T 1 B 13 m dt m Moreover the mechanical configuration of the cart s rack pinion system gives the following relationship 8 B 14 Substituting Equations B 13 and B 14 into Equation B 12 provides the following expression for the armature inertial force n KJ d x t F a un B 15 mp Finally substituting Equations B 9 and B 15 into Equation B 11 and rearranging results in the following dynamic equation for the system 2 2 N K J rg nK Nn KK g n Ky K V t _ m pl 8g g m t mye L8 8 m t m M ME xn ee z Po Ry B 16 m mp mp m mp Equation B 16 expresses the system motion with a single second order differential equation in the cart position Finally applying the Laplace transform and rearranging yields the desired open loop transfer function for the IPO1 or IP02 system such that G s mp Ve E V K dt qx POSSE ub Rod Ame Bd m ZU ui g mS n g Nn t m eq m ib 5 Document Number 504 Revision 02 Page 20 PV Position Control Laboratory Student Handout Appendix C Position Controller Design This section deals with the design of a closed loop controller in order to control the position of your IP01 or IP02 on a quick and accurate manner C 1 Standard Closed Loop System Figure C 1 below depicts a sta
11. gnals but that would be less convenient to take accurate measures Step 5 Once your results are in agreement with the desired design requirements and your response looks similar to the one displayed in Figure 8 below you can move on and begin your report for this lab Remember that there is no such thing as a perfect model and that your calculated controller gains K and K were based on a theoretical and ideal plant model ETT position pv mqpci ip 2Meas 0 and Sim 2 Resp 0 E Ini xl File Edit Update Axis Window Background Colour Text Colour Text Font 4_positio Meas 0 and Sim 2 Resp 0 q_positio Meas 0 and Sim 2 Resp 1 _positio Meas 0 and Sim 2 Resp 2 Figure 8 Actual and Simulated Position Responses to a Square Wave Setpoint Step 6 However in order to perfectly meet the chosen design requirements i e t and PO of the closed loop system any controller design will usually involve some form of fine tuning which will more than likely be an iterative process At this point you should be manually fine tuning your K and K based on your findings above i e from Assignment 3 question 5 and the previous table based on experimental observations in order to ensure your response matches perfectly the system requirements Document Number 504 Revision 02 Page 13 PV Position Control Laboratory Student Handout 8 Post Lab Questions 1
12. igh frequency noise which is moreover amplified during differentiation causes long term damage to the motor To protect your DC motor the recommended cut off frequency is 50 Hz Document Number 504 Revision 02 Page 11 PV Position Control Laboratory Student Handout IP02 PV Position Control Experiment vs Simulation EOF UPM Voltage Limit IP02 MOPCI Ky hi s2 zetafwotstwot2 Position Setpoint m Switch IPO1 or IP02 Plant Model v k e s 2 zelafwefetwci 2 Derivative Filter Initializing 100 i _ T 0 00 lode4 up Figure 7 Diagram used for the Real Time Implementation of the PV Controller Step 2 Before compiling the diagram and running it in real time with WinCon you must enter your previously designed values of K and K in the Matlab workspace To assign K and K type their value in the Matlab command window You are now ready to build the real time code corresponding to your diagram by using the WinCon Build option from the Simulink menu bar After successful compilation and download to the WinCon Client you should be able to use WinCon Server to run in real time your actual system Before doing so manually move your IP01 or IP02 cart to the middle of the track i e mid stroke position and make sure that it is free to move on bo
13. ins K and K are both set by slider gains Check that the signal generator block properties are properly set to output a square wave signal of amplitude 1 and of frequency 2 3 Hz s z s_pv_position ETE Ele Edit view Simulation Format Tools Help WinCon Dsus 238 52 2 hmt S gt nom of IP01 and IP02 Position Control PV Controller Simulation 1 Position Error m Position Setpoint m EE I oo 4063 4 409 7 e Square Wave w Slider Gain Amplitude Slider Gain Ready 100 lodei Figure 4 Simulink Diagram used for the Simulation of the PV Control System Step 2 Before you begin you must run the Matlab script called setup lab ip01 2 posi tion pv m This file initializes all the IPO1 or IP02 system parameters and configuration variables used by the Simulink diagrams Step 3 Ensure that the Simulink simulation mode is set to Normal Click on Simulation Start from the Simulink menu bar and bring up the Position Response m scope As you monitor the position response adjust K and K using the slider gains as depicted in Figures Document Number 504 Revision 02 Page 9 PV Position Control Laboratory Student Handout 5 and 6 Try a variety of combinations and note the effects of varying each gain one at a time on the system response lt Kp m Slider Gain
14. introducing this zero the closed loop transfer function would no longer match the standard form of Equation C 2 Therefore the design formulae derived from Equation C 2 would also no longer exactly apply to the thus obtained closed loop transfer function and it would become more challenging to analytically design a controller that can exactly meet the user defined time specifications In our case adding an integral gain i e I to the forward path does not have to be considered since the open loop transfer function as seen in Equation B 17 is already of type 1 i e it has a pole located at the origin of the s plane i e s 0 C 3 Proportional Velocity PV Control Scheme To work around the undesired zero introduced by a PD controller this laboratory involves designing a Proportional Velocity i e PV position controller for the IPO1 or IP02 servo plant Such a controller introduces two corrective terms one is proportional by K to the position error and the other is proportional by K to the velocity or the derivative of the actual position of the plant Coincidentally the characteristic equations of the PV and PD controller closed loop transfer functions are equal Equation C 5 below expresses the PV control law where x is the reference signal i e the desired position to track d VD K e 7x amp xo C 5 Figure C 2 below depicts the block diagram of the PV control scheme as it will be implemented
15. ion pv mq3 ip02 mdl depending on your model of MultiQ i e MultiQ 3 or MultiQ PCT and if your plant is an IPO1 or IP02 Ask the TA assigned to this lab if you are unsure which Simulink model is to be used in the lab You should obtain a diagram similar to the one shown in Figure 7 The model has 2 parallel and independent control loops one runs a pure simulation of the PV controller connected to the same plant model as the one developed in Assignment 2 of the pre lab section The other loop directly interfaces with your hardware and runs your actual IPO1 or IP02 servo plant To familiarize yourself with the diagram it is suggested that you open both subsystems to get a better idea of their composing blocks as well as take note of the I O connections Check that the model manual switch for the position setpoint generation correctly selects the signal coming from the signal generator block called Square Wave Also check that the signal generator block properties are properly set to output a square wave signal of amplitude 1 and of frequency 2 3 Hz Moreover your model sampling time should be set to 1 ms i e T 10 s A CAUTION The velocity signal used in the control inner loop of the actual IP01 or IP02 plant is obtained by first differentiating the position signal e g encoder counts or potentiometer voltage and then by low pass filtering the obtained signal in order to eliminate its high frequency content As a matter of fact h
16. l weight 7 2 Closed Loop System Actual Requirements As already stated in the pre lab session this lab requires you to design a Proportional plus Velocity PV controller to control the position of your IPO1 or IP02 cart with the following performance specifications 1 The Percent Overshoot should be equal to 10 96 PO 10 i e 0 59 i The time to first peak should be 150 ms t 0 15s These specifications are the same as the ones you previously used in the pre lab session to calculate the corresponding PV controller gains K and K Document Number 504 Revision 02 Page 8 PV Position Control Laboratory Student Handout 7 3 Simulation of the Servo Plant with PV Controller 7 3 1 Objectives F1 To simulate witha Simulink diagram your IPO1 or IP02 model and to close the servo loop by implementing a Proportional plus Velocity PV position controller M To change during the simulation the two gains K and K of the PV controller and observe the effect on the position response 7 3 2 Experimental Procedure If you have not done so yet you can start up Matlab now and follow the steps described below Step 1 In Simulink open a model called s position pv ip01 2 mdl This diagram should be similar to the one shown in Figure 4 It includes a subsystem containing your IPO1 or IP02 modelled plant as well as the PV controller two feedback loops In order to be conven iently changed on the fly the two controller ga
17. nd pinion and the gearbox mechanisms the motor angular velocity can be written as a function of the cart linear velocity as expressed by Document Number 504 Revision 02 Page 18 PV Position Control Laboratory Student Handout d K x t T Aso B 8 m r mp Therefore substituting Equation B 8 into Equation B 7 and rearranging leads to d F n K n K Va mg E aX f B 9 C 2 m mp Finally substituting Equation B 9 into Equation B 1 applying the Laplace transform and rearranging yields the desired open loop transfer function for the IPO1 or IPO2 system such that r nK K G s mp g m t RaM T np S TU K n KK B Ra m S m eq m mp B 10 B 2 A More Complete Dynamic Model However as a second analysis a more accurate but also slightly more complex dynamic model can be used to derive G s In the previous analysis the inertial force due to the motor s armature in rotation has been neglected Therefore our dynamic model will be more accurate if it considers it Taking into account such an inertial force as seen at the cart and applying Newton s second law of motion together with the D Alembert s principle Equation B 1 becomes a d M qx F FQO B x B 11 As seen at the motor pinion the armature inertial force due to the motor rotation and acting on the cart can be expressed as a function of the armature inertial torque Nn KT uS g g al ai r mp B 12 Applying N
18. ndard closed loop position control system with a unity feedback loop Xa Vin x gt G s G s Controller Plant H s a Figure C 1 Standard Closed Loop Position Control System For such a closed loop system as represented in Figure C 1 the closed loop transfer function T s is given by the following well established equation x5 GG x 3 1 G G GG HG C 1 Equation B 17 expresses a plant model that has no zero and 2 poles i e second order denominator in s Moreover in order to design controllers satisfying given performance requirements the control theory provides approximate design formulas which are based for quadratic lag systems with no zero on the following standard equation Ko dc n T s RT ec LH C 2 s 20 sto where Kac is the system s DC gain The characteristic equation of the closed loop transfer function expressed in its standard form by Equation C 2 is as follows 51420 s o C 3 Document Number 504 Revision 02 Page 21 PV Position Control Laboratory Student Handout C 2 Proportional plus Derivative PD Control Scheme In the classical sense a Proportional Derivative i e PD controller has the following transfer function G s K Ks C 4 As expressed by Equation C 4 placing such a controller into the forward path would result in introducing a zero in the closed loop transfer function As a result of
19. ning of the IPO1 or IP02 open loop transfer function G s in Assignment 1 derive a block diagram to represent such a transfer function In other words represent as Document Number 504 Revision 02 Page 5 PV Position Control Laboratory Student Handout individual blocks the basic mechanical and electrical equations that you use to determine G s The resulting block diagram should have an overall closed loop transfer function identical to the one found in Assignment 1 2 Finally using the IPO1 or IP02 model parameter values listed in Reference 2 evaluate the IPO1 or IP02 open loop transfer function G s that you previously found Determine the plants pole s zero s and DC gain 6 3 Assignment 3 PV Controller Design You will need the PV controller gain values calculated in this pre lab assignment for the in lab real time implementation of the PV position controller for your IPO1 or IP02 system The PV controllers 2 parameters i e K and K will allow the closed loop system to meet the two time requirements as previously set by the user Hint If supplied with this handout Appendix C offers a possible implementation of PV controllers Oth erwise refer to your in class notes In order to determine and calculate K and K answer the following questions 1 Perform block diagram reduction of the PV control scheme applied to G s as presented in if Appendix C has been supplied with this handout Obtain the o
20. position of your IPO1 or IP02 linear motion servo plant At the end of the session you should know the following m How to mathematically model the IPO1 and IP02 servo plants from first principles in order to obtain the open loop transfer function in the Laplace domain m How to design and simulate a Proportional Velocity PV position controller to meet the required design specifications m How to tune your PV controller gains and their effect on the closed loop system dynamic response m How to implement your controller in real time and evaluate its actual performance 2 Prerequisites To successfully carry out this laboratory the prerequisites are 1 To be familiar with your IPO1 or IP02 main components e g actuator sensors your power amplifier e g UPM and your data acquisition card e g MultiQ as described in References 1 2 3 and 4 ii To have successfully completed the pre laboratory described in Reference 1 Students are therefore expected to be familiar in using WinCon to control and monitor the plant in real time and in designing their controller through Simulink ii To be familiar with the complete wiring of your IPO1 or IP02 servo plant as per dictated in Reference 2 and carried out in pre laboratory 1 3 References 1 P01 and IP02 Linear Experiment 0 Integration with WinCon Student Handout 2 IP01 and IP02 User Manual 3 MultiQ User Manual 4 Universal Power Module Use
21. r Manual 5 WinCon User Manual Document Number 504 Revision 02 Page 1 PV Position Control Laboratory Student Handout 4 Experimental Setup 4 1 Main Components To setup this experiment the following hardware and software are required Power Module Quanser UPM 1503 2405 or equivalent m Data Acquisition Board Quanser MultiQ PCI MQ3 or equivalent m Linear Motion Servo Plant Quanser IPO1 or IP02 as shown below in Figures 1 and 2 respectively Real Time Control Software The WinCon Simulink RTX configuration as detailed in Reference 5 or equivalent For a complete and detailed description of the main components comprising this setup please refer to the manuals corresponding to your configuration 4 2 Wiring To wire up the system please follow the default wiring procedure for your IPO1 or IP02 as fully described in Reference 2 When you are confident with your connections you can power up the UPM Document Number 504 Revision 02 Page 2 PV Position Control Laboratory Student Handout Figure 1 IPO1 System Figure 2 IPO2 System Document Number 504 Revision 02 Page 3 PV Position Control Laboratory Student Handout 5 Controller Design Specifications In the present laboratory i e the pre lab and in lab sessions you will design and implement a control strategy based on the Proportional Velocity PV control scheme in order for your IPO1 or IP02 closed loop sy
22. stem to satisfy the following performance requirements which are time domain specifications i The Percent Overshoot i e PO should be less than 10 i e PO 10 ii The time to first peak should be 150 ms i e t 0 15 s Document Number 504 Revision 02 Page 4 PV Position Control Laboratory Student Handout 6 Pre Lab Assignments 6 1 Assignment 1 Open Loop Transfer Function The open loop transfer function is derived in Appendix B If Appendix B has not been supplied with this handout derive the open loop transfer function of your IPO1 or IP02 from mechanical and electrical first principals To name the system s parameters you can help yourself of the nomenclature listed in Appendix A Nomenclature Hint As a reminder your IPO1 or IP02 open loop transfer function is defined by the selected plant input and plant output As illustrated in Figure 3 the plant input is the commanded voltage to the DC motor Since in this laboratory we want to control the cart s position the plant output is selected to be the cart linear position on the rack as depicted in Figure 3 Motor Voltage Cart Position IP01 or IP02 Plant x Figure 3 The IP01 or IP02 Plant Input and Output In other words the open loop transfer function for the IPO1 or IP02 system which is called G s can be written as X s V s 1 G s 6 2 Assignment 2 Open Loop Model Block Diagram 1 Following the obtai
23. th sides It should now be safe to start your real time controller To do this click on the START STOP button of the WinCon Server window Your cart position should now be tracking the desired setpoint e g square wave of 15mm Step 3 Open the sink Meas 0 and Sim 2 Resp in a WinCon Scope You should now be able to monitor on line as the cart moves the actual cart position as it tracks your pre defined reference input and compare it to the simulation result produced by the IPO1 or IP02 model To open a WinCon Scope click on the Scope button of the WinCon Server window and choose the display that you want to open e g Meas 1 and Sim 2 Resp from the selection list Step 4 Specifically discuss in your lab report the following points i How does your IPO1 or IP02 cart actual position compare to the simulated response ii Is there a discrepancy in the results If so find some of the possible reasons Document Number 504 Revision 02 Page 12 PV Position Control Laboratory Student Handout i From the plot of the actual cart position measure your system t and PO Are the values in agreement with the design specifications Hint You can accurately measure these parameters by saving the position traces of interest to a M File using the WinCon Scope feature and making the necessary calculations through Matlab As a remark you could also make these measures directly from the WinCon Scope by zooming in on the si
24. verall closed loop transfer function of your IPO1 or IP02 system by replace G s by its expression as found in Assignment 1 2 Extract from the previously obtained closed loop transfer function the system s characteristic equation 3 Fit the obtained characteristic equation to the standard form seen in Equation C 3 if available by identifying the parameters T and Thus you should obtain 2 equations expressing T and as functions of K and K as these are the only 2 variables i e controller parameters in your system 4 Using your newly obtained formulae and referring to your in class notes what changes to your IPO1 or IP02 response would you expect to see by varying the values of K and K Keep your answers simple i e will T and increase or decrease How would this translate in Document Number 504 Revision 02 Page 6 PV Position Control Laboratory Student Handout terms of changes int and Percent Overshoot PO Also relate these changes to the physical behaviour of your closed loop system Hint You can use Equations 23 and 24 presented in the next subsection Specifically i Assuming K constant what happens to T and when you increase decrease K it Assuming K constant what happens to T and when you increase decrease K 5 Using the formulae previously obtained determine the analytical expressions and numerical values for K and K in order to meet the previously specified time r
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