Rotary Experiment #03: Speed Control SRV02 Speed Control using
Contents
1. makes the response faster However as will be shown adding a gain K gt 1 makes the system less stable The phase margin of the L s system is therefore lower then the phase margin of the P s system and this translates to having a large overshoot in the response The lead compensator is used to dampen the overshoot and increase the overall stability of the system i e increase its phase margin The frequency response of the lead compensator given in 16 is o lt aToj Clead T Toj 20 Document Number 708 Revision 1 0 Page 12 SRV02 Speed Control Laboratory Student Manual and its corresponding magnitude and phase equations are Grego DI 20 and g arctana To arctan To 22 The bode of the lead compensator is illustrated in Figure 4 Bode Diagram Gm Inf Pm 180 deg at O rad sec 25 ary m ry AA AAA 20l09 y a Pd un Ds LU T 3 Cc oa G oa LY 3 v u G a 0 10 10 1 aT 10 VT 10 10 Frequency rad sec Figure 4 Bode of lead compensator Here is an overview of how gain K and the lead compensator parameters a and 7 are used to obtain the specified crossover frequency of 75 0 rad s and the phase margin of 75 0 degrees 1 Obtain a bode plot of the uncompensated P s system to find how much gain K is required to get a crossover frequency of 50 0 rad s The gain is not adjusted to yield the fully specified 75 0 rad2. POS 5 w 3 Thus when tracking the load shaft reference the transient response should have a peak time less than or equal to 0 05 seconds an overshoot less than or equal to 5 and zero steady state error In addition to the above time based specifications the following frequency domain requirements are to be met when designing the Lead compensator 75 0 deg lt PM and 4 0 g 75 0 rad 5 The phase margin mainly affects the shape of the response Having a higher phase margin implies that the system is more stable and the corresponding time response will have less overshoot The overshoot will not go beyond 5 with a phase margin of at least 75 0 degrees The crossover frequency is the frequency where the gain of the bode plot is 1 or 0 dB This parameter mainly affects the speed of the response thus having a larger decreases the peak time With a crossover frequency of 75 0 radians the resulting peak time will be less than or equal to 0 05 seconds 4 1 2 Overshoot Consider the following step setpoint rad 25 t lt t0 sS o ft 6 rad zs t0 lt t S where to is the time the step is applied i e step time Initially the SRV02 should be running at 2 5 rad s and after the step time it should jump up to 7 5 rad s Calculate the maximum overshoot of the response in radians when the step is applied Document Number 708 Revision 1 0 Page 4 SRV02 Speed Control Laboratory Student Manual 4 1 3 Ste
3. asian 24 5 1 Speed Control Simulation sii is 24 5 1 1 Setup for Speed Control SimulatiOM ooonnoccnonccnonacioncnconcnoonnncononcnnnononnnononncnnn nro nr rnan rr can nn se r a assa 24 5 12 Simulated PL Step Response ius id ds 25 5 1 3 Lead Compensator Design using Matlab ooooocnnncccnococononcnonacoonocoonncnonnnooncnnonnncon nn cnn n nono rn cnn n rn nncnannnos 28 5 1 4 Simulated Lead Step Respos ns oen Bnr n e a e a a i iie 34 5 2 Spe d Control Implementar iii 36 5 2 1 Setup for Speed Control ImplementatiON ooooonnoccnonccnoncnoncnnonenconnnonnnanonrnconnnrnonnconnnrnon nro nr rra rnnannnnnno 37 Document Number 708 Revision 1 0 Page i SRV02 Speed Control Laboratory Student Manual 5 2 2 Implementation PI Speed Control cecccecssccessecesnseeeneeeseccseecseeeeseecseeeecseeeeseeesaeeeeesesneseeeessnaaees 38 5 2 3 Implementation Lead Speed Control oooooooccnococoooccononcnononoonocoonccnononnon conan crono nn Gas nn cnn r nro EE nr nn E 41 5 3 Res lts Summary A A E id 45 6 REFERENCES TI Document Number 708 Revision 1 0 Page ii SRV02 Speed Control Laboratory Student Manual 1 Introduction The objective of this experiment is to develop a feedback system that controls the speed of the rotary servo load shaft Both a proportional integral PI controller and a lead compensator are designed to regulate the shaft speeds according to a set of specifications The following topics are covered i
4. of the following loop transfer function Lp s defined in 19 to verify that the specified crossover frequency is achieved and attach it to your report This also allows you to do any fine tuning to gain K Document Number 708 Revision 1 0 Page 29 See 3 Find the gain that the lead compensator needs to achieve the specified phase margin of 75 degrees Give the amount in decibels Also to ensure the desired specifications are reached add another 5 degrees maximum phase of the lead SRV02 Speed Control Laboratory Student Manual 4 The frequency at which the lead maximum phase occurs must be placed at the new gain crossover frequency Wz new This is the crossover frequency after the lead compensator is applied As illustrated in Figure 4 m occurs halfway between 0 dB and 20Log a i e at 1OLogio a So the new gain crossover frequency in the L s system will be the frequency where the gain is 10Log o a Find this frequency and calculate what lead compensator breakpoint frequencies are needed Document Number 708 Revision 1 0 Page 31 SRV02 Speed Control Laboratory Student Manual 5 Generate a bode of the lead compensator Cieaa s defined in 16 Document Number 708 Revision 1 0 Page 32 SRV02 Speed Control Laboratory Student Manual 6 Generate a bode of the loop transfer function L s as described in 17 Does the phase margin and gain crossover frequency meet the specifications in Sectio
5. s because the lead compensator also adds gain to the system as depicted in the magnitude bode plot of Figure 4 which raises the crossover frequency 2 Generate a bode plot of the K P s system to find its phase margin and find out how much more phase is needed to get the required phase margin of 75 0 degrees This determines what the Document Number 708 Revision 1 0 Page 13 SRV02 Speed Control Laboratory Student Manual T maximum phase of the lead compensator parameter m should be Design a to get the necessary additional phase margin The a parameter determines the maximum phase of the lead compensator Om which is illustrated in Figure 4 Determine the frequency where the maximum phase of the lead compensator should occur shown in Figure 4 by the variable On Calculate parameter T based on the values of a and On Obtain a bode of the open loop compensated system L s C s P s and ensure the crossover frequency and phase margin specifications are met Simulate the step response and ensure the time domain requirements are met The lead compensator has two parameters a and 7 To attain the maximum phase shown in Figure 4 Om the Lead compensator has to add 20log a of gain This is determined using the equation 1 su y 23 As illustrated in Figure 4 the maximum phase occurs at the maximum phase frequency m Using the equation T hae 24 parameter T is used to attain a certain maximum phase
6. steps to design the lead compensator for the SRV02 speed response 1 The bode plot of the open loop uncompensated system P s must first be found This was already done manually in Section 4 3 but Matlab will now be used To generate the Bode of P s enter the following commands in Matlab Plant transfer function P tf K tau 1 Integrator transfer function I tf 1 1 01 Plant with Integrator transfer function Pi series P Bode of Pi s figure 1 margin Pi set 1 name Pi s Recall that the model parameter K and tau are already stored in the Matlab workspace after running the setup_srv02_exp03_spd m script These parameters are used with the commands tf and series to create the P s transfer function The margin command generates a bode of the Document Number 708 Revision 1 0 Page 28 008 SRV02 Speed Control Laboratory Student Manual system and it lists the gain and phase stability margins as well as the phase and gain crossover frequencies Attach the bode to your report and compare it with the bode done manually in Section 4 3 ola 2 2 Find how more gain is required such that the gain crossover frequency is 50 0 rad s use the ginput Matlab command As already mentioned the lead compensator adds gain to the system and will increases the phase as well Therefore gain K is not to be designed to meet the fully specified 75 0 rad s Generate a bode
7. system The PJ Compensator subsystem contains the PI control detailed in Section 4 2 and the Lead Compensator block has the compensator described in Section 4 3 A s_srv02_spd File Edit View Simulation Format Tools Quarc Help Doh amp mics ka 5 Normal J Se hh amp BEE amp SRVO02 Experiment 3 Simulated Speed Control SRVO2 Signal Amplitude Generator rad s Constant Constant Setpoint rad s rad s PI Compensator Manual Switch Lead Compensator SRV02 Model 100 Figure 5 Simulink diagram used to simulate the closed loop SRV02 speed response First ensure the lab files and the Matlab workspace have been setup for the Speed Control simulation as described in Section 5 1 1 Then proceed to Section 5 1 2 to perform the PI speed control simulation In Section 5 1 3 the lead compensator is designed using Matlab and then the closed loop speed response when using the lead control is simulated in Section 5 1 4 Document Number 708 Revision 1 0 Page 24 SRV02 Speed Control Laboratory Student Manual 5 1 1 Setup for Speed Control Simulation Follow these steps to configure the Matlab setup script and the Simulink diagram for the Speed Control simulation laboratory 1 Load the Matlab software 2 Browse through the Current Directory window in Matlab and find the folder that contains the SRV02 speed controller files e g s_srv02_spd mal 3 Double click on the s_srv02_spd mdl file to open the SRV02 Speed Co
8. to the downward position Open the load shaft position scope w_ rad and the motor input voltage scope Vm V Start the simulation By default the simulation runs for 5 seconds The scopes should be displaying responses similar to figures 6 and 7 Verify if the time domain specifications in Section 4 1 1 are satisfied and if the motor is being saturated To calculate the steady state error peak time and percentage overshoot use the simulated response data stored in the data_spd variable If the specifications are not satisfied go back in the lead compensator design You may have to for example need to add more maximum phase in order to increase the phase margin If the specifications are met move on to the next step Generate a Matlab figure showing the Simulated Lead speed response and its input voltage and attach it to your report Document Number 708 Revision 1 0 Page 35 008 SRV02 Speed Control Laboratory Student Manual 5 2 Speed Control Implementation The g_srv02_spd Simulink diagram shown in Figure 8 is used to perform the speed control exercises in this laboratory The SRV02 ET Speed subsystem contains QuaRC blocks that interface with the DC motor and sensors of the SRV02 system as discussed in Reference 6 The PI Control subsystem implements the PI control detailed in Section 4 2 and the Lead Compensator block implements the lead control described in Section 4 3 Document Number 7
9. 08 Revision 1 0 Page 36 SRV02 Speed Control Laboratory Student Manual q_srv02_spd File Edit View Simulation Format Tools WinCon QuaRC Help o HS Ba Gs controls development made easy SRVO2 Signal Amplitude Generator rad s Constant Constant Setpoint rad s rad s PI Compensator Manual Switch Lead Compensator SRVO2 ET Speed Figure 8 Simulink model used with QuaRC to run the PI and lead speed controllers on the SRV02 5 2 1 Setup for Speed Control Implementation Before beginning the in lab exercises on the SRV02 device the q_srv02 spd Simulink diagram and the setup _srv02 exp03 spd m script must be configured Follow these steps to get the system ready for this lab l 2 3 Setup the SRV02 in the high gear configuration and with the disc load as described in Reference 5 Load the Matlab software Browse through the Current Directory window in Matlab and find the folder that contains the SRV02 speed control files e g q_srv02_spd mdl Double click on the q_srv02_spd madl file to open the Speed Control Simulink diagram shown in Figure 8 Configure DAQ Double click on the HIL Initialize block in the SRV02 ET subsystem which is located inside the SRV02 ET Speed subsystem and ensure it is configured for the DAQ Document Number 708 Revision 1 0 Page 37 SRV02 Speed Control Laboratory Student Manual device that is installed in your system See Reference 6 for more
10. Quanser QuaRC Installation Manual 4 Quanser UPM User Manual 5 Quanser SRVO2 User Manual 6 Quanser SRV02 QuaRC Integration Student Manual 7 Quanser Rotary Experiment 1 SRV02 Modeling Student Manual 8 Quanser Rotary Experiment 2 SRV02 Position Control Student Manual Document Number 708 Revision 1 0 Page 46
11. Rotary Motion Servo Plant SRV02 e Rotary Experiment 03 Speed Control aU NS EE SRV02 Speed Control using QuaRC Student Manual SRV02 Speed Control Laboratory Student Manual Table of Contents VEST RODUCTION ii 1 A d sasan s sis dasasa sG Gas h s asassisa Ga h ise Gsaasisss sa s isas 1 3 OVERVIEW A E IT 2 A A NO 3 4 1 Desired Speed Control RESPONSE A a a 3 4 1 1 SRV02 Speed Control Specifications cccccccccescccsssecenscesseeeeneceseceseeeseeeeeseecessecesseeseeeeseeeeseeseneeaeees 3 aA OIEI O A S E E AE 4 Aa Steady state PO Ad id da 5 42 PEControl D signe s an ag ea hea cad 7 4 2 1 Closed loop Transfer FUNCtION ccccccccccesscessseeeseeceeeeesceeseseceseeessaeeseseeenseeeeseecesaecnceseseeesseeeeseessesaaes J 4 2 2 Finding PI Gains to Satisfy Specifications ccccccssseeesscceseeceseeeseneceseeceseceeseeceseeeseeeneeessaeeeeesseaeees 8 4 3 Lead Control DA A A A R E r ea aan 11 4 3 1 Finding Lead Compensator Parameters cccccssssesssseeeseeeesseeeneeceseeeseeessneeesteeeeaeeceeesnseeesueeeeseeeeeees 12 4 3 2 Magnitude Bode Plot of Uncompensated System cccsccccscecesseestseeeseeceseecsseeessaeeeeesnteeeeeesenneeeesenes 17 4 3 3 Phase Bode Plot of Uncompensated System cccccecsscessseessneessseeeseeeeeeeceeceeeeceseeesentaeeesenseteeeeeeees 20 PALO ASE INQIS ata eg cacy a e dd 22 S IN LAB PROCEDURES ss isciasiseicsccnicsdsssexduiies carta Reid
12. Section 4 4 Then find the steady state error by comparing the average of the measured signal with the desired speed Is the steady state error specification satisfied Document Number 708 Revision 1 0 Page 40 SRV02 Speed Control Laboratory Student Manual ola gt 12 Measure the percentage overshoot and the peak time of the SRV02 load gear step response Taking into account the noise in the signal does the response satisfy the specifications given in Section 4 1 1 13 Make sure QuaRC is stopped 14 Shut off the power of the UPM if no more experiments will be performed on the SRV02 in this session Document Number 708 Revision 1 0 Page 41 SRV02 Speed Control Laboratory Student Manual 5 2 3 Implementation Lead Speed Control In this section the speed of the SRV02 is controlled using the lead compensator Measurements will then be taken to see if the specifications are satisfied Follow the steps below 1 du 3 4 Run the setup srv02 exp03 spd m script Enter the K a and 7 lead parameters found in Section 5 1 3 n the SRV02 Signal Generator block set the Signal Type to square and the Frequency to 0 4 Hz In the Speed Control Simulink model set the Amplitude rad s gain block to 2 5 rad s and the Offset rad s constant block to 5 0 rad s To engage the lead compensator set the Manual Switch in the Speed Control Simulink diagram to the downward position Open the load shaft speed sco
13. ady state Error The steady state error when controlling the speed of the SRV02 is calculated in this section Consider controlling the speed with a unity feedback system This is illustrated in Figure 1 when the compensator is defined C s 1 7 Compensator Plant E s Figure 1 Unity feedback loop 1 As given in Reference 7 the SRV02 voltage to speed transfer function is P s tst lo 8 Given the reference step Ro R s 9 s find the steady state error of the system using the final value theorem Document Number 708 Revision 1 0 Page 5 SRV02 Speed Control Laboratory Student Manual Cog lm s E s s gt 0 10 Make sure the error transfer function E s derivation is shown 2 Evaluate the steady state error numerically based on the model parameters obtained in Reference 7 and the step amplitude Ro 5 0 rad s Based on the steady state error result from a step response with a unity proportional gain what Type of system is the SRV02 when performing speed control 0 1 2 or 3 Document Number 708 Revision 1 0 Page 6 SRV02 Speed Control Laboratory Student Manual 4 2 PI Control Design 4 2 1 Closed loop Transfer Function The proportional integral PI compensator used to control the velocity of the SRV02 has the structure Vnt ko By 0 ft 0 t t o 40 0 t dt 11 where k is the proportional control gain k is the integral control gain
14. control specifications with the PV gains found in Reference 8 to meet the position control requirements Document Number 708 Revision 1 0 Page 9 SRV02 Speed Control Laboratory Student Manual oa 3 Calculate the minimum damping ratio and natural frequency required to meet the specifications given in Section 4 1 1 oluje 4 Based on the nominal SRV02 model parameters K and 7 found in Experiment 1 SRV02 Modeling Reference 7 calculate the PI control gains needed to satisfy the time domain response requirements Document Number 708 Revision 1 0 Page 10 SRV02 Speed Control Laboratory Student Manual 4 3 Lead Control Design Alternatively a lead or lag compensator can be designed to control the speed of the servo The lag compensator is actually an approximation of a PI control and this at first may seem like the more viable option However due to the saturation limits of the actuator the lag compensator cannot achieve the desired zero steady state error specification which is given in 1 of Section 4 1 1 Instead a lead compensator with an integrator as shown in Figure 3 will be designed Compensator C s I i Plant I I I Figure 3 Closed loop SRV02 speed control with lead compensator Document Number 708 Revision 1 0 Page 11 SRV02 Speed Control Laboratory Student Manual To obtain zero steady state error an integrator is placed in series with the plant This syste
15. frequency This changes where the Lead compensator breakpoint frequencies 1 a T and 1 T shown in Figure 4 occur The slope of the lead compensator gain changes at these frequencies l Calculate how much gain in dB the lead compensator has to contribute in order for a system to get an additional phase margin of 45 degrees 2 Find the breakpoint frequencies 1 a T and 1 T needed for the maximum phase of the lead Document Number 708 Revision 1 0 Page 14 compensator to occur at a frequency of 65 0 rad s 3 Show the derivation of Equation 24 Thus show how to derive the frequency at which the maximum phase of the lead compensator occurs n 1 0 Page 15 SRV02 Speed Control Laboratory Student Manual 4 The maximum phase is defined by the expression m arctana To arctan T0 25 Using the derived maximum phase frequency and the trigonometric identity tan x tan y A a 26 show that the maximum phase equals a 1 tad m la 27 oja gt 5 Next show how to derive the lead gain equation given in 23 from the exercises just completed and using the trigonometric identity sin x a a 08 1 BHUA ii Document Number 708 Revision 1 0 Page 16 SRV02 Speed Control Laboratory Student Manual 4 3 2 Magnitude Bode Plot of Uncompensated System In this section the bode plot of the P s system i e the plant in series with an integrator will be fou
16. fter running setup_srv02_exp03_spd m 5 1 2 Simulated Pl Step Response The closed loop step speed response of the SRV02 will be simulated to confirm that the designed PI control satisfies the specifications without saturating the motor In addition the affect of the set point Document Number 708 Revision 1 0 Page 25 SRV02 Speed Control Laboratory Student Manual weight will be examined Follow these steps to simulate the SRV02 PI speed response 1 Enter the proportional and integral control gains found in Section 4 2 2 The speed reference signal is to be a 0 4 Hz square wave that goes between 2 5 rad s and 7 5 rad s i e between 23 9 rpm and 71 6 rpm In the SRV02 Signal Generator block set the Signal Type to square and the Frequency to 0 4 Hz Inthe Speed Control Simulink model set the Amplitude rad s gain block to 2 5 rad s and the Offset rad s block to 5 0 rad s Set the Manual Switch to the upward position to activate the PI control Open the load shaft position scope w_ rad and the motor input voltage scope Vm V Start the simulation By default the simulation runs for 5 seconds The scopes should be displaying responses similar to figures 6 and 7 Note that in the w_ rad scope the yellow trace is the setpoint position while the purple trace is the simulated speed generated by the SRV02 Model block w_l rad s Ea DEK Time offset 0 Time offset 0 Figure 6 Simula
17. information on configuring the HIL Initialize block 6 Configure Sensor To perform the speed control experiment the angular rate of the load shaft should be measured using the tachometer This has already been set in the Spd Src Source block inside the SRV02 ET Speed subsystem 7 Configure setup script Set the parameters in the setup _srv02_exp03_spd m script according to your system setup See Section 5 1 1 for more details 5 2 2 Implementation Pl Speed Control In this lab the angular rate of the SRV02 load shaft i e the disc load will be controlled using the developed PI control Measurements will then be taken to ensure that the specifications are satisfied Follow the steps below 1 Run the setup _srv02 exp03_spd m script 2 Enter the proportional and integral control gains found in Section 4 2 2 3 Inthe SRV02 Signal Generator block set the Signal Type to square and the Frequency to 0 4 Hz 4 Inthe Speed Control Simulink model set the Amplitude rad s gain block to 2 5 rad s and the Offset rad s constant block to 5 0 rad s 5 Open the load shaft speed scope w_ rad s and the motor input voltage scope Vm V 6 Set the Manual Switch to the upward position to activate the PI control 7 8 Click on QuaRC Build to compile the Simulink diagram Select QuaRC Start to begin running the controller The scopes should be displaying responses similar to figures 9 and 10 Note that in the w_ rad s scope the yel
18. low trace is the setpoint position while the purple trace is the measured position DER w_l rad Time offset 0 01 Time offset 0 01 Figure 9 Measured PI speed step response Figure 10 PI motor input voltage 9 When a suitable response is obtained click on the Stop button in the Simulink diagram tool bar Document Number 708 Revision 1 0 Page 38 SRV02 Speed Control Laboratory Student Manual or select QuaRC Stop from the menu to stop running the code Generate a Matlab figure showing the PI speed response and its input voltage Attach it to your report As in the s_srv02_spd Simulink diagram when the controller is stopped each scope automatically saves their response to a variable in the Matlab workspace Thus the theta_l rad scope saves its response to the data_spd variable and the Vm V scope saves its data to the data_vm variable 10 Due to the noise in measured speed signal it is difficult to obtain an accurate measurement of the specifications In the Speed Control Simulink mode set the Amplitude rad block to 0 rad s and the Offset rad block to 7 5 rad s in order to generate a constant speed reference of 7 5 rad s Generate a Matlab figure showing that illustrate the noise in the signal Document Number 708 Revision 1 0 Page 39 SRV02 Speed Control Laboratory Student Manual 11 Measure the peak to peak ripple found in the speed signal eo meas and compare it with the estimate in
19. m is denoted by the transfer function P pae 15 S where P s is the plant transfer function shown in 8 The phase margin and crossover frequency specifications listed in 4 and 5 of Section 4 1 1 can then be satisfied using a proportional gain K and the lead transfer function liaTs Clead TL Ts 16 The a and 7 parameters change the location of the pole and the zero of the lead compensator which changes the gain and phase margins system The stability margins of the compensated open loop system L s C s P s 17 is examined This is called the loop transfer function and the complete compensator which is used to control the angular rate of the SRV02 load gear is defined K 1 aTs re 1 7s s ii 4 3 1 Finding Lead Compensator Parameters The Lead compensator is an approximation of a proportional derivative or PD control Similarly when controlling the position of the SRV02 using a PV control as examined in Reference 8 a PD control can be used to dampen the overshoot in the transient of a step response and effectively make the system more stable i e increase its phase margin In this particular case the lead compensator is designed for the following system Ko P s Los a 19 The proportional gain K is designed to attain a certain crossover frequency Increasing the gain crossover frequency essentially increases the bandwidth of the system which decreases the peak time in the transient response i e
20. n 4 1 1 Document Number 708 Revision 1 0 Page 33 SRV02 Speed Control Laboratory Student Manual 7 Go on to Section 5 1 4 to simulate the step response and check whether the time domain specifications are met Keep it mind that the goal of the lead design is the same as the PI control the response should meet the desired steady state error peak time and percentage overshoot specifications given in Section 4 1 1 Thus if the crossover frequency and or phase margin specifications are not quite satisfied the response should be simulated to verify if the time domain requirements are satisfied If so then the design is complete If not then the lead design needs to be re visited 5 1 4 Simulated Lead Step Response The closed loop step speed response of the SRV02 is simulated in order to verify that the time based specifications in Section 4 1 1 are met without saturating the motor Document Number 708 Revision 1 0 Page 34 SRV02 Speed Control Laboratory Student Manual Follow these steps to simulate the SRV02 lead speed response Enter the K a and T lead control parameters found in Section 5 1 3 above In the SRV02 Signal Generator block set the Signal Type to square and the Frequency to 0 4 1 2 3 ox 8 Hz In the Speed Control Simulink model set the Amplitude rad s gain block to 2 5 rad s and the Offset rad s constant block to 5 0 rad s To engage the lead control set the Manual Switch
21. n this laboratory Design a proportional integral PI controller that regulates the angular rate of the servo load shaft according to certain time domain requirements Set point weight Design a lead compensator according to some time domain and frequency domain specifications Simulate the PI and lead controllers using the developed model of the plant and ensure the specifications are met without any actuator saturation Implement the controllers on the Quanser SRV02 device and evaluate its performance 2 Prerequisites In order to successfully carry out this laboratory the user should be familiar with the following Data acquisition card e g Q8 the power amplifier e g UPM and the main components of the SRV02 e g actuator sensors as described in References 1 4 and 5 respectively Wiring and operating procedure of the SRV02 plant with the UPM and DAC device as discussed in Reference 5 Transfer function fundamentals e g obtaining a transfer function from a differential equation Laboratory described in Reference 6 in order to be familiar using QuaRC with the SRV02 Document Number 708 Revision 1 0 Page 1 Table 1 below lists and describes the various files supplied with the SRV02 Speed Control laboratory File Name 03 SRV02 Speed Control Student Manual pdf setup _srv02 exp03 spd m config srv02 m d_model_param m cale_conversion_constants m s srv02 spd mdl q sr
22. nd 1 Find the frequency response magnitude P of the transfer function P s given in 15 2 The DC gain is the gain when the frequency is zero i e 0 rad s However because of its integrator Pi s has a singularity at zero frequency and the DC gain is therefore not technically defined for this system Instead approximate the DC gain by using 1 rad s Make sure the DC gain estimate is evaluated numerically in dB using the nominal model parameters K and t found in Reference 7 Document Number 708 Revision 1 0 Page 17 SRV02 Speed Control Laboratory Student Manual o 12 3 The gain crossover frequency 0 is the frequency at which the gain of the system is 1 or 0 dB Express the crossover frequency symbolically in terms of the SRV02 model parameters and then evaluate the expression using the nominal SRV02 model parameters oja gt 4 Determine the breakpoints of P Breakpoints are the asymptotes of the system which affect the slope of the magnitude plot In this system there are two pole breakpoints that change the rate at which the gain is attenuated Denote the higher frequency breakpoint by the variable Document Number 708 Revision 1 0 Page 18 SRV02 Speed Control Laboratory Student Manual oja gt 5 Before drawing the bode magnitude plot approximate the low frequency gain of the system when lt and the high frequency gain when gt Breaking
23. nsor Noise When using analog sensors such as a tachometer there is often some inherent noise in the measured signal In this section the noise from the tachometer will be estimated 1 The peak to peak noise of the measured SRV02 load gear signal can be calculated using 1 190721 29 where K is the peak to peak ripple rating of the sensor and is the speed of SRV02 load gear Based on the ripple peak to peak specification of the tachometer given in Reference 5 calculate the amount of noise that is to be expected when the signal is running at 7 5 rad s Document Number 708 Revision 1 0 Page 22 SRV02 Speed 2 Taking the noise into account what is the maximum peak in the speed response that is to be expected Show the equation used and evaluate the peak value as well as the corresponding maximum percentage overshoot SRV02 Speed Control Laboratory Student Manual 5 In Lab Procedures Students are asked to simulate the closed loop PI and Lead responses Then the PI and Lead controllers are implemented on the actual SRV02 Before going through these experiments go through Section 5 1 1 to configure the lab files according to your SRV02 setup 5 1 Speed Control Simulation The s_srv02_pos Simulink diagram shown in Figure 5 is used to simulate the closed loop speed response of the SRV02 when using either the PI or Lead controls The SRV02 Model uses a Transfer Fen block from the Simulink library to simulate the SRV02
24. ntrol Simulation Simulink diagram shown in Figure 5 4 Double click on the setup _srv02_exp03_spd m file to open the setup script for the position control Simulink models 5 Configure setup script The controllers will be ran on an SRV02 in the high gear configuration with the disc load as in Reference 7 In order to simulate the SRV02 properly make sure the script is setup to match this configuration e g the EXT GEAR CONFIG should be set to HIGH and the LOAD_TYPE should be set to DISC Also ensure the ENCODER TYPE TACH_OPTION K_ CABLE UPM_TYPE and VMAX DAC parameters are set according to the SRV02 system that is to be used in the laboratory Next set CONTROL _ TYPE to MANUAL 6 Run the script by selecting the Debug Run item from the menu bar or clicking on the Run button in the tool bar The messages shown in Text 1 below should be generated in the Matlab Command Window The correct model parameters are loaded but the control gains and related parameters loaded are default values that need to be changed That is the PI control gains are all set to zero the lead compensator parameters a and T are both set to 1 and the compensator proportional gain K is set to zero SRVO2 model parameters K 1 53 rad s V tau 0 0254 s PI control gains kp 0 V rad ki 0 V rad s Lead compensator parameters Ke 0 V rad s 1 a T 1 rad s 1 T 1 rad s Text 1 Display message shown in Matlab Command Window a
25. pe w_ rad s and the motor input voltage scope Vm V Click on QuaRC Build to compile the Simulink diagram Select QuaRC Start to begin running the controller The scopes should be displaying responses similar to figures 9 and 10 When a suitable response is obtained click on the Stop button in the Simulink diagram tool bar or select QuaRC Stop from the menu to stop running the code Generate a Matlab figure showing the lead speed response and its input voltage Attach it to your report Document Number 708 Revision 1 0 Page 42 10 Measure the steady state error the percentage overshoot and the peak time of the SRV02 load gear For the steady state error it may be beneficial to give a constant reference and take its average as done in Section 5 2 2 Does the response satisfy the specifications given in Section 4 1 1 Document SRV02 Speed Control Laboratory Student Manual o u 2 11 Using both your simulation and implementation results comment on any differences between the PI and lead controls 008 12 Make sure QuaRC is stopped 13 Shut off the power of the UPM if no more experiments will be performed on the SRV02 in this session Document Number 708 Revision 1 0 Page 44 Fill out Table 2 below with the pre laboratory and in laboratory results obtained such as the designed PI gains the designed lead parameters the measured peak time percentage overshoot steady state erro
26. r from the simulated and measured step responses and so on Section Description Symbol Value 4 2 2 Pre Lab Finding PI Gains to Satisfy Specifications Open Loop Steady State Gain Open Loop Time Constant Proportional gain Integral gain Pre Lab Magnitude Bode Plot of Uncompensated System DC Gain Estimate of P s Gain crossover frequency Breakpoint frequencies 4 3 3 Pre Lab Phase Bode Plot of Uncompensated System Phase margin Pre Lab Sensor Noise Peak to peak ripple Percentage overshoot with noise consideration In Lab Simulated PI Step Response Peak time Percentage overshoot Steady state error In Lab Lead Compensator Design using Matlab 1 Gain crossover frequency Og 1 Phase margin PM 2 Compensator proportional gain K Lead gain parameter 20Log a rad V s S V rad V s rad rad s deg V rad dB SRV02 Speed Control Laboratory Student Manual 4 Lead frequencies 1 a T rad s 1 T rad s In Lab Simulated Lead Step Response Peak time Percentage overshoot Steady state error In Lab Implementation PI Speed Control Measured peak to peak ripple Steady state error Peak time Percentage overshoot In Lab Implementation Lead Speed Control Peak time Percentage overshoot Steady state error Table 2 SRV02 Experiment 3 Speed control results summary 6 References 1 Quanser DAO User Manual 2 Quanser QuaRC User Manual type doc quarc in Matlab to access 3
27. t is the setpoint or reference load angular rate t is the measured load shaft angular rate bsp is the set point weight and V t is the voltage applied to the SRV02 motor The block diagram of the PI control is illustrated in Figure 2 Set point Proportional Weight Control Gain Integral Control Gain Integrator Figure 2 Block diagram of SRV02 PI speed control 1 Find the closed loop SRV02 speed transfer function Q s Q s using the time based PI control defined in Equation 11 the block diagram in Figure 2 and the process model in 8 Document Number 708 Revision 1 0 Page 7 oluje SRV02 Speed Control Laboratory Student Manual Assume the zero initial conditions thus Q 0 0 4 2 2 Finding Pl Gains to Satisfy Specifications Recall from Reference 8 that the percentage overshoot and peak time equations are r 2 12 PO 100e and P 2 13 1 When the set point weight is zero i e bsp 0 the closed loop SRV02 speed transfer function has the structure of a standard second order system Similarly as done in Reference 8 for the PV gains find expressions for the control gains k and k that equate the characteristic equation of the SRV02 closed loop system to the standard characteristic equation ae 2Co s 0 2 14 Document Number 708 Revision 1 0 Page 8 o u j2 SRV02 Speed Control Laboratory Student Manual 2 Compare the PI control gains needed to satisfy the speed
28. ted PI speed response Figure 7 Simulated PI motor input voltage Generate a Matlab figure showing the Simulated PI speed response and its input voltage and attach it to your report After each simulation run each scope automatically saves their response to a variable in the Matlab workspace The w_ rad scope saves its response to the variable called data_spd and the Vm V scope saves its data to the data_vm variable The data_spd variable has the following structure data_spd 1 is the time vector data_spd 2 is the setpoint and data_spd 3 is the simulated angular speed For the data_vm variable data vm 1 is the time and data vm 2 is the simulated input voltage Document Number 708 Revision 1 0 Page 26 SRV02 Speed Control Laboratory Student Manual 7 Measure the steady state error the percentage overshoot and the peak time of the simulated response Does the response satisfy the specifications given in Section 4 1 1 Document Number 708 Revision 1 0 Page 27 SRV02 Speed Control Laboratory Student Manual 8 Ifthe specifications are satisfied without overloading the servo motor proceed to the next section to simulate the lead response 5 1 3 Lead Compensator Design using Matlab In this section Matlab is used to design a lead compensator that will satisfy the frequency based specifications given in Section 4 1 1 Review the summarized design steps listed in Section 4 3 Follow these
29. up the system into different frequency bands is especially useful when plotting the bode of more complex systems Make sure the resulting equations are expressed in terms of the SRV02 model parameters and are also given in decibels opi gt 6 Using the DC gain estimate the gain crossover frequency as well as the low and high frequency gain approximations draw the magnitude bode plot of the P s system Label the bode plot with the DC gain along with the crossover and breakpoint frequencies Document Number 708 Revision 1 0 Page 19 SRV02 Speed Control Laboratory Student Manual 4 3 3 Phase Bode Plot of Uncompensated System In this section the phase bode plot of the uncompensated system will be plotted 1 Find the phase of the Pi s system Document Number 708 Revision 1 0 Page 20 SRV02 Speed Control Laboratory Student Manual opi gt 2 The phase margin is the amount of phase that is over 180 degrees when the gain is at 0 dB i e at the gain crossover frequency It is a way of determining relatively stability The more phase margin the more stable a system is and this translates to having less overshoot in the time response of the system Calculate the phase margin PM of the system 3 Plot the phase bode of system P s and label where the gain crossover frequency occurs Document Number 708 Revision 1 0 Page 21 SRV02 Speed Control Laboratory Student Manual 4 4 Se
30. v02 spd mdl Description This laboratory guide contains pre lab and in lab exercises demonstrating how to design and implement a speed controller on the Quanser SRV02 rotary plant using QuaRC The main Matlab script that sets the SRV02 motor and sensor parameters as well as its configuration dependent model parameters Run this file only to setup the laboratory Returns the configuration based SRV02 model specifications Rm kt km Kg eta_g Beq Jeq and eta_m the sensor calibration constants K POT K_ ENC and K_TACH and the UPM limits VMAX UPM and IMAX UPM Calculates the SRV02 model parameters K and tau based on the device specifications Rm kt km Kg eta_g Beq Jeq and eta_m Returns various conversions factors Simulink file that simulates the closed loop SRV02 speed control using either the PI control or the lead compensator Simulink file that runs the PI or Lead speed control on the actual SRV02 system using QuaRC File Name Description Table 1 Files supplied with the SRV02 Speed Control experiment Section 4 1 1 outlines the specifications of the closed loop system Given a step input with a certain amplitude the expected overshoot and steady state error of the system are calculated in Section 4 1 2 and Section 4 1 3 respectively The time domain requirements for controlling the speed of the SRV02 load shaft are ai 1 gt SRV02 Speed Control Laboratory Student Manual ts 0 05 s l nd 2
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