Speed Control
Contents
1. 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 bi aft Vin t Figure 1 Armature circuit in the time domain Using Kirchhoff s voltage law we obtain the following equation dI 3 1 Va RL n 7 Eom O Since L lt lt R 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 Vm Emm 3 3 We now shift over to the mechanical aspect of the motor and begin by applying Newton s 2 law of motion to the motor shaft 3 4 J nO m La Page 3 Revision 01 Where T NK 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 B 3 5 Where B is the viscous damping coefficient as seen at the output Substituting 3 4 into 3 5 we are left with JON Kalin Kn m2. Explain Page 10 Revision 01 Appendix A SRV02 Nomenclature Variable SI Units Vm _ Armature circuit input voltage Tn Armature circuit ourrent ooo ooo o Ra _ Armatureresistanee Rm 26 In Armature inductance ooo ooo o Eese Motor back emf voltage fo ooo ooo o o iaoa merses O O O Ta Tore generated by the motor f Torque applied at thetoad Jooo oo Back emfconstant Km f 000767 Motor torque constant Ke f 0 00767_ rirnan in ae u Equivalent viscous damping coefficient Beq 15e3 O Ks uan l ee x SRVO02 system gear ratio motor gt load Gearbox efficiency Eff G g Proportional gain O Kp Velocity gain Ky Time to peak Tt Page 11 Revision 01
3. WinCon menu Once it has compiled you may Start it using the WinCon server The SRV 02 should now be tracking the command input Plot the Measured Velocity as well as the Setpoint and the Simulated Velocity This is done by clicking on the scope button in WinCon and choosing Measured Plant Velocity Now you must choose the Setpoint and the Simulated Velocity signals thru the Scope gt File gt Variables menu You should now be monitoring all 3 signals on the same plot If your controller had been designed to the above specifications and procedure you should be seeing a response similar to Figure 4 below Note Try adjusting the command input gain and take note of the response DO NOT exceed a command of 60 RPM for the high gear configuration or a command of 300 RPM in the low gear configuration 200 q_tacho_lead Measured Velocity RPM 150 q_tacho_lead Setpoint RPM q_tacho_lead Simulated Velocity RPM 100 50 50 100 150 200 i 0 0 5 1 1 5 2 2 5 Time Figure 4 Step response of the actual plant velocity red and the simulated velocity blue to an input command black Page 9 Revision 01 6 Post Lab Questions amp Report After successfully designing and implementing your lead compensator you should now begin to document your report This report should include 6 1 1 2 3 System characteristic Bode plots Here you should include all Bode plots you generated wit
4. After determining your controller C s generate a Bode plot of your complete open loop system K C s G s to determine if all design specifications have been met P Magnitude dB Phase deg 135 180 S Bode Diagram Gm Int Pm 75 456 deg at 101 26 radisec 0 80 45 90 40 10 40 10 40 Frequency radfsec Figure 3 Open loop Bode plot of the complete system including the compensator As you can see the system has achieved a phase margin of 75 degrees as well as a bandwidth of 100 rad s Page Revision 01 Does your system meet the design specifications as seen in Figure 3 If you have not yet met the specifications you should go back and redesign your compensator Most control designs are iterative and will require fine tuning to achieve the best control 5 Simulation amp Implementation 5 1 Controller Simulation If you are content with the controller and have met the required design specifications you are then ready to simulate your controller You must first run an M file called Setup _SRV02_Exp2 m This file initializes all the motor parameters and gear ratios to the MATLAB workspace In Simulink open a model called s_tacho_lead mdl This model includes the plant model SRV 02 Plant Model same as Figure 2 as a block in the final closed loop form Use this model to simulate your controller You can implement your controller by making sure the following varia
5. Beg 1 3 6 We know that O nK 0 and T 1 K 1 where n isthe motor efficiency we can re write 3 6 as 2 Jw gt n gig JO a B mn g mK gK dm 3 7 Finally we can combine the electrical and mechanical equations by substituting 3 3 into 3 7 yielding our desired transfer function w s NMN KK 3 8 p 2 V mlS Jog RmS BegRm N M mm Kg eq m Where 2 Teg JN hing 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 After deriving the system transfer function using mechanical first principals it would be beneficial to understand the inherent control signals and accompanying states in the system Figure 2 below is a Simulink block diagram mapping the different stages of the system each with their corresponding gains and conversions Using only the block diagram below derive the transfer function from input armature voltage to output load shaft velocity ff_G Eff_M At Kg Armature Load shaft Inertia Voltage Current ss ea Voltage Current Torque Velocity Velocity Back EMF Figure 2 Block Diagram of the SRV0O2 Plant 1 Derive the transfer function w s l G s 7 S 2 Is the transfer function you derived using Figure 2 the same as the above transfer function of equation 3 8 Page 5 Revision 01 4 Lab Procedure 4 1 Wiring and Connections T
6. SRV02 Series Q Rotary Experiment 2 QUANSER Speed Control S cCoNSYUSN gt ae _ Student Handout SRV02 Series e Rotary Experiment 2 QUANSER Speed Control Student Handout 1 Objectives The objective in this experiment is to design a lead controller that will regulate the speed of the output shaft At the end of this session you should know the following e How to mathematically model the servo plant from first principles To acquire an open loop Bode plot of the system e To design and simulate a lead controller to meet the required specifications using phase margin design 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 SRV02 T 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 T in the Low Gear configuration with a UPM 1503 power module and a gain cable of 1 e It is assumed that the student has successfully completed Experiment 0 of the SRV02 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 SRV02 User s Manual Page
7. bles are set in the MATLAB workspace e Desired Kp This variable should be set to the gain you had calculated to attain your desired bandwidth section 4 4 e Controller_NUM This is the numerator of your compensator in decreasing orders of s Controller DEN This is the compensator denominator in decreasing orders of s Ex If your controller transfer function was C 2s7 s 1 S a s 3s 5 Controller_NUM 2 1 1 Controller_DEN 1 3 5 After setting the control parameters you are now ready to simulate your design Under the simulation menu choose start Monitor the Simulated Velocity scope and compare the signal to the Setpoint Input Looking at the system response as well as the final Bode plot in section 4 4 you should now have met all the design requirements If you are content with your controller performance and are satisfied with your simulation you are now ready to implement your controller Remember if the simulated response is not desirable you can easily re iterate your design process until you reach a satisfactory simulation Page 8 Revision 01 5 2 Implementation of the Controller Open a Simulink model called q tacho_lead mdl In this model you will see 2 matching loops This will allow you to run the simulation as well as the actual plant simultaneously enabling you to note the difference in actual plant performance as opposed to the simulated plant You must now build the model using the
8. h all plots clearly labeled and documented Design procedure Clearly indicate all the steps you took in obtaining the final controller In this section make clear reference to which Bode plots you used and clearly label the system characteristic on each plot i e phase margin Any iterations in designing the controller should also be documented If your original design did not meet the required specifications or if you wanted a better response The following plots as they are instrumental in measuring the quality of your design Make sure you include these plots and that they are labeled and documented e A final open loop Bode plot of your complete system like the one seen in Figure 3 of section 4 e A step response to your system including the actual and simulated velocities as well as the input command This should look similar to the Figure 4 of section 5 Final remarks and conclusions as well as answers to the post lab questions Post Lab Questions Were there any design limitations or problems you encountered during the lab If so how were these limitations overcome Did the actual response of the system match directly to that of the simulated model From your understanding of the system what could you theorize is the source of these discrepancies and how would you improve them If you were given the same speed control experiment again would you choose a lead compensator as a controller or would you use a different approach
9. he first task upon entering the lab is to ensure that the complete system is wired as described in the SRV02 Experiment 0 Introduction If you are unsure of the wiring please refer to the SRV0O2 Manual or ask for assistance from a T A assigned to the lab Now that all the signals are connected properly start up MATLAB and start Simulink You are now ready to start the lab 4 2 Controller Specifications This lab requires you to design a Lead Compensator to control the Servo plant with the following specifications e The system should have zero steady state error for a step input e The system Bandwidth should be 100 rd s approximately 16 Hz e The open loop system should have a phase margin of approximately 75 degrees e The system should have no over shoot very minimal at the most 4 3 Open Loop Characteristics When designing a controller of a system in the frequency domain it is necessary to first study the open loop response of the system In cases where the system cannot be modeled from first principles or the system is too complicated an open loop Bode plot is acquired by inputting a sinusoid of varying frequency and recording the magnitude and phase of the corresponding output In this case our model is of first order and our model is sufficiently accurate The open loop Bode plot to be used in the design will therefore be generated by MATLAB using our plant model In order to achieve a zero steady state error to a ste
10. p input our system must be of type 1 By definition a system is type 1 when it has a single pole located at the origin We must therefore introduce an integrator in the loop to track a step input with no steady state error We now have the transfer function G s with an integrator yielding an open loop transfer function of G s S 4 4 Controller Parameters After achieved the first criteria of zero steady state error with the integrator the next task should be to set the bandwidth of the system Note All relevant motor parameters can be found in Appendix A at the back of this handout or in the SRV0O2 User Manual Page 6 Revision 01 1 Generate a Bode plot of your open loop system and determine how much gain Kp must be introduced to achieve your desired system bandwidth Hint Your bandwidth will be the zero crossing of the open loop Bode plot Also you should remember to use G s when generating your Bode plot S After you select a desired Kp your new open loop system is K G s Using your new open loop system generate another Bode plot to determine your S phase margin Calculate the amount of phase your compensator would require to add such that the design specification is met 2 Once you have decided on your parameters Design a Lead compensator that adds the required phase atthe required frequency Refer to your in class material on how to go about designing such a compensator
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