Position Control
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1. 3 4 LP m la Tee Page 3 Revision 01 Where T AR is the load torque seen thru the gears And n iS the efficiency of the gearbox We now apply the 2 law of motion at the load of the motor J T Bo 3 5 Where B is the viscous damping coefficient as seen at the output Substituting 3 4 into 3 5 we are left with J GK Tn Kn m BAD 3 6 We know that Dach and T 1 K1 where mn Jee motor efficiency we can re write 3 6 as Jp ECH ett E BP Ch g mK dmn 3 7 Finally we can combine the electrical and mechanical equations by substituting 3 3 into 3 7 yielding our desired transfer function Dis Alb 3 8 V lS TRS Bohn tN gh Km Ky s eq m Where 2 Jog Jit N ing This can be interpreted as the being the equivalent moment of inertia of the motor system as seen at the output Page 4 Revision 01 3 1 Pre Lab Assignment This lab involves designing a PV controller for the servo plant We have omitted the integral gain PID as the main purpose of the integral gain is to reduce the steady state error by introducing a pole located at s 0 in the open loop Looking back at the derived equation 3 8 we can clearly see that the plant already has a pole at s 0 For this reason and for the sake of simplicity the required specifications will be met using only a proportional P and velocity derivative V controller In the classical sense a PD controller would hav2. can move on and implement your controller if you are close to meeting the requirements try fine tuning your parameters to achieve the desired response If the response is far from the specifications you should re iterate your design process and re calculate your controller gains Page 7 Revision 01 4 4 Implementation of the Controller After successfully simulating your controller and achieving your desired response you are now ready to implement your controller and observe its effect on the physical plant Open a Simulink model called o position_pv_e mdl or gq position _pv_pot ask a TA assigned to this lab if you are unsure which model is to be used in the lab The model has 2 identical closed loops one is connected similar to the simulation block of the previous section and the other loop has the actual plant in it To better familiarize yourself with the model it is suggested that you open both sub systems to get a better idea of the systems as well as take note of the I O connections In the SRVO2 plant block blue you will see a gain of 1 K_Cable to normalize the system due to our use of a gain cable to enable a greater control signal being fed into the plant Note In place of a standard derivative block in the PV controller we have place a derivative with a filter in order to eliminate any high frequencies from reaching the plant as high frequencies will in the long term damage the motor Before running the mo
3. input voltage Tn Armaturecineuiteurrent Ry Armature resistans Rm 26 Ia Armature inductance Eer Motor back emf voltage fo ooo ooo o o imao ners LL Tu Toraue generated by the motor f Torque applied at thetoad Jooo oo Back emf constant Km f 000767 Motor torque constant re f ooomer equivalent moment ofinertia at the load Jeg 2003 i ananena Boy 4003 xe man e ee Ge SRVO02 system gear ratio motor gt load Gearbox efficiency Eff CG d Proportional gain Kp Velocity gain Ky Time to peak me Page 11 Revision 01
4. SRV02 Series Q Rotary Experiment 1 QUANSER Position Control CONSULING gt e AAA eil 2 f AN e Le f ahh Li E fee Z e KR e he x R A we eS 3 H A wl EE SE 7 d z gt Se ge F d N b f sch 2 A Od gt See gt 9 By x J A d A Io nE Af 2 SR 2 VM S S a H Le ON i DN bes T e Ce KW ir SE ky at Wb Ke J fra ae i AG ANISER SANT ORO Student Handout SRV02 Series L Rotary Experiment 1 QUANSER Position Control Student Handout 1 Objectives The objective in this experiment is to introduce the student to the fundamentals of control using the PID family of compensators At the end of this session you should know the following e How to mathematically model the servo plant from first principles e An understanding of the different tuning parameters in the controller To design and simulate a PV controller to meet the required specifications To implement your controller and evaluate its performance 2 System Requirements To complete this lab the following hardware is required 1 Quanser UPM 2405 1503 Power Module or equivalent 1 Quanser MultiQ PCI MQ3 or equivalent 1 Quanser SRVO2 E servo plant 1 PC equipped with the required software as stated in the WinCon user manual e The suggested configuration for this experiment is the SRV02 E T in the High Gear configuration with a UPM 2405 powe
5. del you must set your final values of K and K in the MATLAB workspace type it in MATLAB You can now build the system using the WinCon gt Build menu You will see the model compile and then you can use the WinCon Server to run the system click on the start button Your plant should now be responding and tracking a square wave to the commanded angle Setpoint Amplitude deg Plot the Measured Theta deg as well as the Setpoint Amplitude deg and the Simulated Theta deg This is done by clicking on the scope button in WinCon and choosing Measured Theta deg Now you must choose the Setpoint Amplitude deg and the Simulated Theta deg signals thru the Scope gt File gt Variables menu How does your actual plant response compare to the simulated response e Is there a discrepancy in the results If so why e Calculate your system T and OS Are the values what you had expected You can calculate these parameters by saving these traces as an m file and making our calculations in MATLAB You could also make your calculations directly from the WinCon scope by zooming in on the signals It is suggested to make these calculations thru MATLAB as this method will provide greater accuracy lf you are sufficiently happy with your results and your response looks similar to Figure 3 below you can move on and begin the report for this lab Remember there is no such thing as a perfect model and your calculated parameters were based on the
6. e load shaft with the following specifications 1 The Overshoot should be less than 5 gt 0 707 2 The time to first peak should be 100ms T 0 100 4 3 Simulation of the Plant In Simulink open a model called e position Dy md This model includes the modeled plant SRV 02 Plant Model as well as the PV controller K and K are both set by slider gains Before you begin you must run an M File called Setup _SRVO2_ Exp1 m This file initializes all the motor parameters and gear ratios Click on Simulation gt Start and bring up the Simulated Position scope As you monitor the response adjust K and K using the slider gains Try a variety of combinations and note the effects of varying each parameter e Make a table of system characteristics w and with respect to changes in K and K Hold one variable constant while adjusting the other e Does the system response react to how you had theorized in section 3 1 Now that you are familiar with the actions of each parameter enter in the designed K and K that you had calculated to meet the system requirements Note the values should fall within the slider limits e Does the response look like you had expected What is your percent overshoot e Calculate your T Does it match the requirements Hint To get a better resolution when calculating T decrease the time range under the parameters option of the scope If the simulated response is as expected you
7. e the form C s K K s Placing this controller into the forward path would result in introducing an unwanted zero in the closed loop transfer function As a result of the zero the closed loop transfer function no longer fits equation 3 10 and it becomes increasingly difficult to design the controller to meet time specifications With this limitation in mind we can now make the transition to use a state feedback PV approach that can meet our requirements and results in a closed loop transfer function of the form seen in equation 3 10 The PV controller that will be implemented in this lab can be seen in Figure 2 below and has the form V K 0 8 K 0 3 9 Position Setpoint Plant Model Derivative Figure 2 PV Controller for the SRVO2 Plant Page 5 Revision 01 The purpose of this lab is to design a controller using the 2 order transfer function representation of the form 2 3 10 wn 2 2 S 20 St W gt with characteristic equation sie An En 3 11 Coincidentally the characteristic equations of the PV and PD controller closed loop transfer functions are equal A PV controller in essence is a PD controller without the unwanted zero allowing the designer to meet the required specifications using only the characteristic equation 1 2 Obtain the transfer function of the closed loop model in Figure 2 Extract the characteristic equation and fit it to the form
8. es in K and K as described in section 4 3 Did these changes reflect what you had theorized in the pre lab Explain After simulating your controller with your calculated K and K did the response match what you had expected What was the percentage overshoot What was your T If you had to re iterate your design also include your iterations and why you believe your initial solution did not yield a desired response In section 4 4 you implemented your controller Did the actual system response match your simulated results If not what reasons could you conclude were responsible for the discrepancies Include your final K and K after fine tuning the controller You should also present a plot of your final system response with the actual simulated and setpoint signals this graph should look similar to Figure 3 Post Lab Questions 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 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 Most controller 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 Page 10 Revision 01 Appendix A SRV02 Nomenclature Variable SI Units Vm _ Armature circuit
9. plant model A control design will usually involve some form of fine tuning and will more than likely be an iterative process At this point you should be fine tuning your K and K based on your findings from above use the table created in section 4 3 of this lab as a guide to ensure your response matches the system requirements as seen in Figure 3 Page 8 Revision 01 Step Response of the SRV0Z q_position_pv_e Measured Theta deg q_position_pv_e Setpoint Amplitude deg q_position_pv_e Simulated Theta deg Position deg ech e 1 05 1A Tas ke 1 25 eal Time s Figure 3 Step Response to a Command of 30 degrees We can see by looking at Figure 3 that the position response has a 100ms time to peak and an overshoot of less than 5 The system requirements have been met and implemented using a PV controller Page 9 Revision 01 5 Post Lab Questions and Report After successfully designing and implementing your controller you should now begin to document your report This report should include VI 5 1 1 2 3 Your solutions to the pre lab assignment of section 3 1 Included should be the characteristic equation of the system formulas relating w and to K and K and your expected changes in response to variations of K and K Your designed K and K to meet the system specifications and your steps at calculating the results A table relating changes in w and to chang
10. r module and a gain cable of 5 e It is assumed that the student has successfully completed Experiment 0 of the SRVOZ2 and is familiar in using WinCon to control the plant through Simulink It is also assumed that all the sensors and actuators are connected as per dictated in the Experiment 0 as well as the SRVO2 User s Manual Page 2 Revision 01 3 Mathematical Model This section of the lab should be read over and completely understood before attending the lab It is encouraged for the student to work through the derivations as well as to get a thorough understanding of the underlying mechanics For a complete listing of the symbols used in this derivation as well as the model refer to Appendix A SRVO2 Nomenclature at the back of this handout We shall begin by examining the electrical component of the motor first In Figure 1 you see the electrical schematic of the armature circuit Ry La aft Vatt Figure 1 Armature circuit in the time domain Using Kirchhoff s voltage law we obtain the following equation di 3 1 Va RL SET A Since Ln lt lt Ra we can disregard the motor inductance leaving us with a 22 i R m We know that the back emf created by the motor is proportional to the motor shaft velocity w such that SS V K w 3 3 mR m We now shift over to the mechanical aspect of the motor and begin by applying Newton 2 law of motion to the motor shaft T
11. seen in equation 3 11 Obtain 2 equations expressing w and as functions of K and K as these are the only 2 variables in your system Using your newly obtained formulas and referring to your in class notes what changes to your response would you expect to see by varying the values of K and K What happens to oo when you increase decrease K What happens to when you increase decrease K and or K Keep your answers simple i e will oo and increase or decrease For the in lab portion of this experiment you are required to design a PV controller that will yield the following time requirements The Overshoot should be less than 5 gt 0 707 e The time to first peak should be 100ms T 0 100 Using the formulas from Question 1 choose values for K and K to meet the requirements Hint T 1 Cn 3 12 eet OS e VIO Page 6 Revision 01 4 Lab Procedure 4 1 Wiring and Connections The first task upon entering the lab is to ensure that the complete system is wired as described in the SRV0O2 Experiment 0 Introduction If you are unsure of the wiring please refer to the SRV0O2 User Manual or ask for assistance from a TA assigned to the lab Now that all the signals are connected properly start up MATLAB and start Simulink You are now ready to begin the lab 4 2 Controller Specifications This lab requires you to design a Proportional Velocity PV controller to control the position of th
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