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1. 0 002 c cee eee ees 51 9 Phase Lead Compensation of a Rotational Rigid Body System 2 55 10 State Feedback Compensation of a 2DOF Rectilinear System 22 225 59 11 Inverted Pendulum on a Translating Base 000 cece cece cent eees 63 12 Self Erecting Inverted Pendulum on a Rotating Base 0 2 2 00002 e eee eee ees 69 INGO ache ere E E alse chek oe eee ee ete oe tte Sat ed We easly oe As lle Bs le 74 Attribttions icisncuteer 1 1 fhe a e a a Glee Web eleda ae be etenes be foes ba eon dees BRS 75 iv Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 1 Control Systems Lab Introduction Hardware Software and Safety 1 1 Introduction 1 1 1 About this manual The purpose of this manual is to provide you the student with the laboratory procedures necessary for conducting the control system experiments in the ASE 170P course You should by no means treat this manual as the sole source of information for the design and implementation process You should rely on lecture notes reference text as well as their own knowledge of control theory to develop and implement your control algorithms This manual is only intended to provide an organized method for performing the experiments 1 1 2 Course Objectives e To learn how to investigate the properties of physical systems both through simulation and experimen
2. 9 55 10 59 11 63 12 69 aerospace 5 33 6 39 7 45 8 51 Lab Control 2 9 9 55 10 59 11 63 5 12 69 laboratory 1 1 4 25 5 33 6 39 austin 5 33 6 39 7 45 8 8 51 7 45 8 51 9 55 10 59 11 63 9 55 10 59 11 63 12 69 12 69 automatic 5 33 6 39 7 45 8 51 labview 1 1 2 9 4 25 5 33 9 55 10 59 11 63 12 69 6 39 7 45 8 51 9 55 10 59 Automatic Control 2 9 11 63 12 69 control 1 1 2 9 4 25 5 33 6 39 P plant 4 25 7 45 8 51 5 9 55 5 10 59 11 63 12 69 R rectilinear 5 4 25 Control Lab 2 9 f 2 9 S simulation 1 1 Control System 4 25 5 33 6 39 7 45 8 51 9 55 10 59 11 63 ecp 1 1 2 9 4 25 5 33 6 39 12 69 7 45 8 51 9 55 10 59 11 63 system 5 33 6 39 7 45 8 51 12 69 9 55 10 59 11 63 12 69 Educational Control Products 2 9 experiment 1 1 4 25 5 33 6 39 T texas a 3 6 39 7 45 8 51 12089 03 1 MODY 5 9551 11 63 10 59 9 55 8 51 7 45 12163 U ut 5 33 6 39 7 45 8 51 9 55 Feedback 2 9 10 59 11 63
3. 12 69 Available for free at Connexions lt http cnx org content col10302 1 5 gt ATTRIBUTIONS Attributions Collection Control Systems Laboratory Edited by Nick Lin Eduardo Gildin Robert Bishop URL http cnx org content col10302 1 5 License http creativecommons org licenses by 2 0 Module Control Systems Lab Introduction Hardware Software and Safety By Nick Lin Eduardo Gildin Robert Bishop URL http cnx org content m13025 1 3 Pages 1 8 Copyright Robert Bishop License http creativecommons org licenses by 2 0 Module Control Lab Setup Choosing Control System Hardware and Software By Erik Luther URL http cnx org content m13071 1 9 Pages 9 16 Copyright Erik Luther License http creativecommons org licenses by 2 0 Module Control Lab Setup Using LabVIEW to Control ECP Plants By Robert Bishop Nick Lin URL http cnx org content m13080 1 4 Pages 17 24 Copyright Robert Bishop License http creativecommons org licenses by 2 0 Module Introduction to Lab Hardware and LabVIEW Implementation By Nick Lin Eduardo Gildin Robert Bishop URL http cnx org content m13026 1 3 Pages 25 32 Copyright Erik Luther Robert Bishop License http creativecommons org licenses by 2 0 Module System Identification for the Rectilinear Plant By Robert Bishop URL http cnx org content m13066 1 1 Pages 33 38 Copyright Robert Bishop License ht
4. 4 1 2 Pre Lab 1 In your own words describe how the implementation VI s block diagram executes More specifically explain the execution when the system is idle and when a reference trajectory is commanded Available for free at Connexions lt http cnx org content col10302 1 5 gt 28 CHAPTER 4 INTRODUCTION TO LAB HARDWARE AND LABVIEW IMPLEMENTATION 4 1 3 Lab Procedure 4 1 3 1 Using the Model 210 Rectilinear Plant 1 2 Or Connect the drive motor and encoder feedback cables to the Model 210 plant Unclamp the first mass carriage and remove any springs that may be connected to it Be sure to position the stop bumpers to allow maximum range of motion for the carriage Load four 0 5kg brass weights onto the carriage In this configuration the carriage acts as a rigid body system Clamp the other two mass carriages by moving the stop bumpers inward so they constrain the motion of the carriage You will need to use a 1 4 inch spacer nut between the mass carriage and stop bumpers so as to not engage the limit switches Power on the PXI by pressing the rectangular button located at the bottom left corner of its front face Wait approximately 30 seconds for the system to boot up Run LabVIEW on your host PC Target the PXI real time embedded controller by selecting RT Target 146 6 105 x NOTE the IP address of your PXI system from the Execution Target drop down menu on the LabVIEW startup screen Wait for LabVIEW
5. Abort Control button on the front panel and turn off the amplifier At this time take a few minutes to connect the springs and dashpot to the mass carriages so you will be familiar with this process in future labs The springs are available in three stiffnesses that you will determine in the next lab The damping provided by the dashpot can be varied by turning the knob located at the end Turning it counterclockwise decreases the damping while turning it clockwise increases the damping For a given dashpot setting you can determine the damping coefficient experimentally as you will see in the next lab Available for free at Connexions lt http cnx org content col10302 1 5 gt 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 31 When you are finished turn off the amplifier box 4 3 2 Using the Model 205 Torsional Plant Connect the drive motor and encoder feedback cables to the Model 205 plant Mount disks to all three locations When mounting a disk at the uppermost location always be sure that you mount the disk on the underside of the center mounting hub The bottom and middle disks should be mounted on top of the mounting hub You should mount the disks so that the side with the concentric circles is facing up Load two 0 5kg brass weights onto the second disk so they both lie on the diameter line of the disk i e 1800 apart Place the center of each weight 9 0cm from the center of the disk You
6. Available for free at Connexions lt http cnx org content col10302 1 5 gt 50 CHAPTER 7 COLLOCATED NONCOLLOCATED CONTROL OF 2DOF RECTILINEAR SYSTEM Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 8 System Identification for the Torsional Plant 8 1 System Identification for the Torsional Plant 8 1 1 Objectives e Understand the dynamic equivalence between rotational and translational systems e Perform system identification using two different methods and compare the results 1This content is available online at lt http cnx org content m13065 1 1 gt Available for free at Connexions lt http cnx org content coll0302 1 5 gt 51 52 CHAPTER 8 SYSTEM IDENTIFICATION FOR THE TORSIONAL PLANT 8 1 2 Pre Lab 1 Assume that the least squares estimate has already been found for the unloaded and loaded sine sweep tests SO Tai Tq2 Ta3 Lai La2 Tag are known values Formulate the linear least squares equation to estimate the 9 individual plant parameters In other words find the y vector and H matrix that would go into the equation y where the vector of parameters to be estimated x is defined as Jai Jag Jas Cy g C2 C3 ky k2 krw 2 Outline the experimental steps you will take to identify the torsional plant using the second order model method similar to Lab 2 Your procedure should allow you to find Jaz Ja3 c1 C3 k1 k2 an
7. E Figure 5 2 Rectilinear Plant System ID Configurations Start LabVIEW on your host PC and target the RT system Open the Lab 2 Rectilinear System Identification vi file enter a loop time of 0 005 seconds and then run the VI Also turn on the amplifier now Reset the encoders if necessary and enter the parameters to execute a zero amplitude step with a dwell time of 4000ms Prepare to manually displace the first mass carriage When you are ready execute the step command and manually displace the first carriage approximately 3cm then release it Observe the natural response of the carriage and wait for the system to finish executing the trajectory and acquiring the data Recall that for underdamped systems the damped natural frequency is related to the undamped natural frequency through the following relationship wa wn V 1 C2 5 1 and it follows that wa 7 8 Available for free at Connexions lt http cnx org content col10302 1 5 gt 5 2 Wn 36 10 11 CHAPTER 5 SYSTEM IDENTIFICATION FOR THE RECTILINEAR PLANT Therefore for light damping small values of Wn Wd 5 3 For the purposes of plant identification you may assume that the damping due to friction in the system is sufficiently small to satisfy the above condition Plot the encoder 1 position data and calculate the natural frequency of this system in both Hz and rad sec Call this value wn the subscript m11 denotes mass 1 trial 1
8. Plant Figure 2 2 LabVIEW Real Time for RTX Options 3 This option consists of a Windows PC running Microsoft Windows and Aredence s Realtime Ex tensions RTX Will my PC work with RTX Windows and RTX run on the same computer sharing the same CPU but applications run in RTX maintain real time execution The PCI 7831R intelligent data acquisition board communicates with the PC through the standard PCI bus Control loops can be executed on both in RTX and on the intelligent data acquisition board The ECP RIO Adapter cable 5 connects the 68pin VHDCI connector from the MIO connector on the PXI 7831R to the round encoder cable connected directly to the ECP plant The banana plugs connect to the motor drive inputs on the front of the ECP Power supply The ECP Amplifier is then connected to one of ECP s mechanical plants The Real Time RTX solution provides a single PC low cost real time computing and acquisition platform that is acceptable for laboratory applications Single PC RTX Real Time Control System Software and Hardware Bundle for Academia from Na tional Instruments ttp igital ni com public nsf a Thttp digital ni publi f allkb 03BC0810E60CE93286256E7D007B61F5 Shttp cnx org content m13071 latest ECP RIO_Adapter pdf http digital ni com express nsf bycode exxu63 Available for free at Connexions lt http cnx org content col10302 1 5 gt 15 2 1 2 3 Intellegent Data Acquision I O Board PCI PXI
9. a valid reason will not receive credit If a student has a valid reason why an assignment must be submitted late he she should contact the instructor as soon as possible Grading When working in an experimental environment results are always important but so is your ability to communicate the information with others Any work you submit should be neat well organized and easy to understand Remember your work is a demonstration of your ability to understand the material you are studying as well as a reflection of your organizational skills and attention to detail The following guidelines will help ensure that you receive as much credit as possible for your work 1 Your derivation of the system s dynamic equations should be neat easy to follow and mathematically correct In addition remember to always draw a free body diagram and label any system parameters and variables that will appear in your derivation 2 The process you use to design your controller should be well outlined In other words don t just hand in your final design show the steps you took to arrive at that design 3 Any LabVIEW VI that you write should be well organized and easy to follow e g avoid crossing wires whenever possible Remember the diagram code should follow well from left to right Furthermore a neat and well organized VI will make the debugging process easier for you should problems arise 4 When performing experiments in the lab always record any
10. can determine this by looking at the concentric circles that have been cut into the disks The inner most circle is 2 0cm from the center and each successive circle occurs at 1 0cm intervals NOTE Whenever mounting weights onto the disks the threaded locking nut needs to be positioned so that it falls into the groove on the underside of the disk This helps prevent the weights from jittering around on the disk The same should be done when clamping the disks as well Now clamp the upper disk so that it cannot rotate Take a look at the VPs block diagram At the far left you will notice that the FPGA code we are referencing is that of the Model 210 the reference is being established by the pink icon that says ECP 210 on it However the FPGA codes of the Model 210 and Model 205 are slightly different so we wish to change this reference to that of the Model 205 Right click on the icon and choose Select Target VI Then locate and select the ECP Timed FPGA sync 205 vi file Once LabVIEW has established the reference you will see the text on the icon change from ECP 210 to ECP 205 As a final step right click the icon again and choose Refresh Now save the VI by using the File drop down menu or alternately by pressing Ctrl S on your keyboard Then run the VI Manually displace the first and second disks and observe the encoder measurements on the front panel Notice that the encoders make positive measurements in the counterclockwise direct
11. closed loop system is active or open loop in the case of no controller In this example a PID controller is being used to control the position of a 1DOF rigid body system The first mass cart on the ECP Model 210 plant is loaded with four 0 5kg weights and no springs or dashpots are attached Available for free at Connexions lt http cnx org content coll10302 1 5 gt 21 Figure 3 2 Partial shot of the ECP Model 210 Plant You may apply a light external force to the mass cart and feel the controller respond by attempting to attenuate the disturbance Also notice that encoder position measurements are displayed on the front panel Pressing the Reset Encoders control will set all the encoders back to 0 If any of the error conditions are detected limit switches drive motor overvoltage etc the VI will perform a safety shutdown and you will need to re run it If you wish to command a test signal to the system press the Command Trajectory control The Sub VI front panel shown below will pop open Available for free at Connexions lt http cnx org content col10302 1 5 gt CHAPTER 3 CONTROL LAB SETUP USING LABVIEW TO CONTROL ae ECP PLANTS Test Signals vi Front Panel SAX File Edit Operate Tools Browse Window Help gt 13pt Application Font tor Tar t 1 Sinusoid l Sine Sweep Impulse Step Ramp Parabolic l Cubic Preview Trajectory 1000 r ty A 800 Amplitude counts 600 0 4
12. front panel In addition to the limit switches the FPGA code has been written to prevent overspeed overvoltage of the drive motor When the code detects overspeeding overvolting of the motor it will again output zero command voltage and remain there until the error has been cleared 1 3 3 Hardware Limits on the Model 205 The FPGA code for the model 205 plant has been written to detect when the relative position between the first and second disks exceeds 3000 counts This is to prevent damage to the torsional rod if a large torque is applied to the base disk When this limit is exceeded zero command voltage is output to the drive motor until the error is cleared Just as with the model 210 plant the model 205 also has drive motor over speed overvoltage protection incorporated into the FPGA code Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 2 Control Lab Setup Choosing Control System Hardware and Software 1This content is available online at lt http cnx org content m13071 1 9 gt Available for free at Connexions lt http cnx org content coll0302 1 5 gt 9 CHAPTER 2 CONTROL LAB SETUP CHOOSING CONTROL SYSTEM 10 HARDWARE AND SOFTWARE 2 1 Choosing Lab Equipment 2 1 1 Software 2 1 1 1 National Instruments Applications and Toolkits LabVIEW 7 1 8 0 or 8 2 Full Development System LabVIEW Real Time ETS or RTX more detail under Choosing Lab Hardware LabVIEW Control Des
13. second order system in terms of the Laplace variable s is given by 5 4 2Cwns we 2 Compare the above with the equations of motion you derived in terms of mass damping coefficient and spring constant m c and k Use your knowledge of second order systems along with your recorded values of wn and wW to solve for the unloaded carriage mass m and spring constant k Repeat these calculations for the trials involving the second mass carriage and spring mc2 and k Since the same spring was used in the experiments the values for k that result from the above cal culations should be very close You may use the average of the two for all future calculations and experiments Call this value kmea to denote the medium stiffness spring Now with your recorded values for calculate c1 the damping coefficient for the first mass carriage Repeat this calculation to find the damping coefficient for the second mass carriage c2 Finally calculate the damping coefficient of the dashpot cq Available for free at Connexions lt http cnx org content col10302 1 5 gt 12 13 14 15 16 17 37 Remove the carriage extension bracket and dashpot from the second mass carriage replace the medium stiffness spring with the high stiffness spring and perform the necessary steps to obtain the resulting natural frequency wm23 Repeat this frequency measurement using the least stiff spring to obtain Wm2
14. tation To learn how to perform hardware identification experiments on a physical plant To learn how to design and analyze control systems through simulation using both classical and modern control techniques To learn how to simulate control systems using both state space and transfer function representations To learn how to implement custom control algorithms in LabVIEW To further develop skills for working with others in an experimental environment 1 1 3 Course Policies Doing Your Own Work While you are encouraged to discuss theory and methods with other classmates when it comes time to analyze design and implement your system it must be done on your own As an engineer you must always fully understand the problem you are trying to solve Simply copying the work of others shows your lack of understanding of the problem Remember when you become an engineer working in industry it is no longer just your grade that is at risk your company s reputation and more importantly other people s lives are on the line Any students caught in violation of these guidelines will be dealt with according to the university s policies on scholastic dishonesty 1This content is available online at lt http cnx org content m13025 1 3 gt Available for free at Connexions lt http cnx org content coll0302 1 5 gt 1 CHAPTER 1 CONTROL SYSTEMS LAB INTRODUCTION HARDWARE SOFTWARE AND SAFETY Late Work Any work submitted late without
15. to establish a connection Now click the Open button on the LabVIEW startup screen and locate the file named Lab 1 Intro to Lab Hardware vi The VI front panel should look like the one in Fig 1 Available for free at Connexions lt http cnx org content col10302 1 5 gt 29 LabVIEW ce bs E 8 2 Figure 4 1 VI Front Panel 1 Enter a loop time of 0 005 seconds then run the VI by clicking on the arrow button at the top left corner of the front panel because of the way that the VI s block diagram is written you must enter the loop time before running the VI If you wish to change the loop time you must stop the VI enter the new loop time and then run the VI again At this time the VI code will be downloaded from the host PC to the PXI When downloading is complete the VI will automatically begin executing on the RT system At this time the control loop is being run solely on the 221 5 real time embedded controller not your host PC However a communications loop is running between the two systems to allow the user to interact with front panel activities NOTE The communications loop is part of the LabVIEW Real Time Development system You do not see its code anywhere in the VI 2 Manually displace the first mass carriage and observe the position measure ment being shown by the Encoder 1 indicator on the front panel Notice that even when the amplifier box is powered off the encoders still make measurement
16. ways 1 For the Model 205 Torsional Plant the A and B channels for encoder 3 have been switched due to the fact that the physical orientation of encoder 3 is opposite that of encoders 1 and 2 2 The Model 205 Torsional Plant does not have limit switches but to prevent damage to the torsion rods the VI will write zero voltage to the drive motor in the event that the displacement between disks 1 and 2 or disks 2 and 3 exceeds 3000 counts 67 5 degrees The voltage will remain at zero until the error is cleared e File Name of LabVIEW 8 0 Project ECP 205 Project lvproj within LabVIEW 8 0 Starting Point zip below e File Name of LabVIEW 7 1 Project ECP 205 lep within LabVIEW 7 1 Starting Point zip below 3 The Model 210 Rectilinear Plant has limit switches to prevent damage due to excessive travel of the mass carriages If a limit switch is engaged the VI returns a value of true to an error indicator and writes zero voltage to the drive motor until the error is cleared e File Name of LabVIEW 8 0 Project ECP 210 Project lvproj within LabVIEW 8 0 Starting Point zip below e File Name of LabVIEW 7 1 Project ECP 210 lep within LabVIEW 7 1 Starting Point zip below NOTE The FPGA personality can be dowloaded with example programs below under Starting Point VI s for Each Plant Section 3 1 2 1 Starting Point VI s for Each Plant The FPGA VI for both plants incorporates drive motor overvoltage protection If an overvoltage conditio
17. 00 200 0 200 400 600 800 1000 1 1 1 1 1 0 0 1 1 0o G2 04 G6 08 1 12 14 16 L8 Time Dwell Time msec 0 Amplitude Repetitions Bidirectional Inputs o 1 C gt Figure 3 3 Command tragjectory interface NOTE The Test Signals feature is only available when using LabVIEW Real Time for ETS because of the additional overhead required for the interactive user interface Take a moment to tab through the various types of test signals that are available as well as what parameters you may prescribe for each signal Selecting the bidirectional inputs option causes the commanded signal to alternate directions when more than one repetition is specified You may always press the Preview Trajectory control to see a preview of the signal When you are satisfied with your selection press the Execute Trajectory control The Sub VIs front panel will close and the signal will be sent to the system as the reference trajectory that is to be tracked When the trajectory is complete plot data will be calculated This may take a few seconds depending on the duration of your specified trajectory When the data calculation completes you may toggle on and off any trajectories that you wish to view on the graph indicator such as position velocity and acceleration Note that the velocity and acceleration amplitudes have been scaled by 0 1 and 0 01 respectively on the graph Try using the graph indicator s zoo
18. 1 1 gt Available for free at Connexions lt http cnx org content coll10302 1 5 gt 69 CHAPTER 12 SELF ERECTING INVERTED PENDULUM ON A e ROTATING BASE 12 1 2 Pre Lab 1 Derive the equations of motion for both a non inverted and inverted pendulum with a rotating base as shown in the figure below Figure 12 1 Inverted Pendulum with a Rotating Base 0 43 m Total length of the rod 0 42 m Distance from the pivot to the tip of the rod adjustable parameter 0 32 m Distance from the pivot to the center of the weight adjustable parameter 0 0166kgm2 Inertia of lower disk including pendulum base hardware 0 069kg Mass of the rod 0 089kg Mass of the attached weight 0 025 m Radius of the round weight 0 25m Distance from disk rotation axis to pivot Figure 12 2 Inverted Pendulum with a Rotating Base Parameters 2 Find the transfer function of the non inverted system 3 Design and simulate a PD controller that adds energy to the system to provide the self erecting action Available for free at Connexions lt http cnx org content col10302 1 5 gt 71 4 Find a state space realization of the inverted system 5 Design and simulate a state feedback compensator that stabilizes the system and satisfies the following performance specifications for a step input a Percent overshoot lt 5 b Settling time lt 1 0sec Available for free at Connexions lt http cnx org content col10302 1 5 gt 72 CHAPTER 12 SEL
19. 4 Now you can compute khign and kow All dynamic parameters have been identified Values for m and Mez for any configuration of masses may be found by adding the calculated mass contribution of the weights to that of the unloaded carriages Be sure that you have filled in all of the system parameters in the table provided before proceeding NOTE The following is necessary to establish the hardware gain for control modeling purposes Remove the spring connecting the first and second carriages and secure four 0 5kg brass weights onto the first carriage Using the stop blocks secure the second mass carriage clear from the first and remove any stop blocks that are constraining the first carriage Verify that the masses are secure and that the carriage slides freely Position the first mass approximately 3cm to the left negative z position of its center of travel Perform a 2 0V bidirectional step with a dwell time of 75ms recall that on the PXI 2215 counts corresponds to a voltage of 10V Plot the velocity data and observe the four segments of the profile with nominal shapes of linear increase constant acceleration nearly constant velocity zero acceleration linear decrease constant deceleration and constant Obtain the acceleration from the linear positive sloped segment of the velocity profile Repeat this for the negative sloped segment You may call these two values and Ziege respectively Be sure that you account for t
20. 7831R Reconfigurable Multifunction 1 0 Using the LabVIEW FPGA Module Each solution uses the National Instruments PCI 7831R Reconfigurable FPGA The FPGA is most useful because it offers 8 analog inputs 8 analog outputs and 96 digital I O lines making it scalable for both teaching applications and research The on board FPGA can be given a fixed personality for student use or can be reprogrammed with the LabVIEW FPGA Module specifically for your needs PID control loop rates up to 200 000 Hz The 7831R also allows custom safety features to be implemented in the FPGA to protect students and equipment Because these safety features are implemented in hardware they are not dependent on the stability of the code running on the PC or real time OS User s Manual for the PCI 7831R and PXI 7831R The following instructions and pin outs detail the wiring between the NI 7831R FPGA board to the ECP amplifier box This cable is built and sold by National Instruments You can download the cable detail and pin outs here ECP Plant to NI RIO FPGA board Download 2 1 2 4 ECP Hardware Please see ECP s website for more information on ECP hardware options ECP Systems Website lhttp www ni com pdf manuals 370489b pdf http cnx org content m13071 latest ECP RIO_Adapter pdf 2http www ecpsystems com controls_family htm Available for free at Connexions lt http cnx org content col10302 1 5 gt CHAPTER 2 CONTROL LAB SETUP CHOOSING CONTR
21. Control Systems Laboratory Collection Editors Nick Lin Eduardo Gildin Robert Bishop Control Systems Laboratory Collection Editors Nick Lin Eduardo Gildin Robert Bishop Authors Robert Bishop Eduardo Gildin Nick Lin Erik Luther Online lt http cnx org content col10302 1 5 gt CONNEXIONS Rice University Houston Texas This selection and arrangement of content as a collection is copyrighted by Robert Bishop It is licensed under the Creative Commons Attribution 2 0 license http creativecommons org licenses by 2 0 Collection structure revised October 20 2005 PDF generated October 25 2012 For copyright and attribution information for the modules contained in this collection see p 75 Table of Contents 1 Control Systems Lab Introduction Hardware Software and Safety 1 2 Control Lab Setup Choosing Control System Hardware and Software 9 3 Control Lab Setup Using LabVIEW to Control ECP Plants 2 22 17 4 Introduction to Lab Hardware and LabVIEW Implementation 2 25 5 System Identification for the Rectilinear Plant 0 0 0 0 e eee 33 6 Rigid Body PD and PID Control 0 0 c cece teen e eet eeeees 39 7 Collocated Noncollocated Control of 2DOF Rectilinear System 2 2254 45 8 System Identification for the Torsional Plant
22. D CONTROL OF 2DOF 4 i RECTILINEAR SYSTEM 7 1 2 Pre Lab 1 Consider the system shown below Both mass carriages are loaded with four 0 5kg brass weights and the medium stiffness spring is connecting them Figure 7 1 2DOF Plant Configuration Derive the equations of motion for this system and rewrite them so that the control effort is u t DAC counts and the respective positions velocities and accelerations are Zie ie Tic Lre T2e Le 2 From your EOM derive the appropriate transfer function numerator and denominator polynomials Ni s No s and D s in the block diagram below Gs R s oa iae Figure 7 2 PD Notch Filter Control 3 Using root locus techniques find the rate feedback gain k that provides satisfactory damping of the complex roots of the inner loop z s R s 4 With k determined you can now design for the system given by G s in the block diagram Design a notch filter Gn s Nn s Dn s with two poles at 5 0Hz and two additional higher frequency poles at 8 022 using 2 2 for both poles Place the zeros of G s such that they cancel the oscillatory poles of G s Finally normalize the notch filter transfer function to have unity DC gain 5 Write a LabVIEW VI that simulates this plant configuration with two differentcontrollers Write your VI so it displays the response of both mass carriages a Collocated Simulate your critically damped PD control
23. DOF spring mass damper system Does the response look familiar Save the plot of the disk 1 and 2 frequency responses and hand it in with the rest of your work You are now finished with you introduction to the Model 205 plant Stop the VI by hitting the Abort Control button and turn off the amplifier box Close all VI windows and exit LabVIEW Then turn off the PXI Return all plant materials to the instructor Available for free at Connexions lt http cnx org content col10302 1 5 gt CHAPTER 4 INTRODUCTION TO LAB HARDWARE AND LABVIEW 2 8 IMPLEMENTATION 4 1 4 Post Lab 1 Consider a controller Gc s in series with a plant G s with unity negative feedback Denote the reference input tracking error control effort and output by R s E s U s and Y s respectively Draw the block diagram for this system making sure to label all the signals 2 Now consider the hardware we have in the lab Instead of having just Gc s G s etc draw a diagram that shows each piece of lab hardware and which signal s it sends and or receives Your diagram should include at least the following mass carriages or torsion disks choose either one amplifier box PXI Reconfigurable I O module Encoders drive motor PXI embedded controller 3 Be sure to label all forces torques displacements and signals that occur in the system Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 5 System Iden
24. F ERECTING INVERTED PENDULUM ON A ROTATING BASE 12 1 3 Lab Procedure N Configure the plant for this experiment Code your self erecting controller into the control loop VI Before proceeding to the inverted system controller test your self erecting algorithm to make sure that it executes correctly Once you have achieved the self erecting action code your controller for the inverted system into the VI Your VI should be written such that the controller for the inverted system automatically takes over once the pendulum is near the inverted position Run the VI and after carefully checking for stability execute a 1000 count step input and save the plot Available for free at Connexions lt http cnx org content col10302 1 5 gt 73 12 1 4 Post Lab 1 Look at your step response plot What do you notice about the initial direction of the base disk s displacement Can you explain why this happens in terms of the closed loop system s zero s Available for free at Connexions lt http cnx org content col10302 1 5 gt 74 INDEX Index of Keywords and Terms Keywords are listed by the section with that keyword page numbers are in parentheses Keywords do not necessarily appear in the text of the page They are merely associated with that section Ex apples 1 1 1 Terms are referenced by the page they appear on Ex apples 1 210 4 25 L lab 1 1 4 25 5 5 33 6 39 7 45 8 51
25. I Perform a 3000 count step input and save the plot Perform a ramp input with a velocity of 1000 counts second and a dwell time of 3 seconds Save the plot fe ee Available for free at Connexions lt http cnx org content col10302 1 5 gt CHAPTER 9 PHASE LEAD COMPENSATION OF A ROTATIONAL me RIGID BODY SYSTEM 9 1 4 Post Lab 1 What was the system s steady state error to the ramp input What would you expect it to be for a parabolic input 2 Explain how gain margin and phase margin relate to a system s stability Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 10 State Feedback Compensation of a 2DOF Rectilinear System 10 1 State Feedback Compensation of a2DOF Rectilinear System 10 1 1 Objectives 1 Design simulate and implement a state feedback compensator for a 2DOF mass spring system 1This content is available online at lt http cnx org content m13067 1 1 gt Available for free at Connexions lt http cnx org content coll0302 1 5 gt 59 CHAPTER 10 STATE FEEDBACK COMPENSATION OF A 2DOF i RECTILINEAR SYSTEM 10 1 2 Pre Lab 1 Derive the equations of motion for the 2DOF rectilinear mass spring The plant configuration is shown below The first and second mass carriages are free and the third is clamped The medium stiffness spring is connecting the first and second carriages and the low stiffness spring is connecting the second and third Figu
26. Inverted Pendulum on a Translating Base 11 1 Inverted Pendulum on a Translating Base 11 1 1 Objectives e Understand the dynamics of an inverted pendulum with a translating base e Use state feedback to control an unstable system 1This content is available online at lt http cnx org content m13064 1 1 gt Available for free at Connexions lt http cnx org content coll10302 1 5 gt 63 64 CHAPTER 11 INVERTED PENDULUM ON A TRANSLATING BASE 11 1 2 Pre Lab 1 Derive the equations of motion for an inverted pendulum with a translating base shown in the figure below Figure 11 1 Inverted Pendulum with a Translating Base Available for free at Connexions lt http cnx org content col10302 1 5 gt 65 Parameter Value Description 0 43m Total length of the rod 0 42m Distance from the pivot to the tip of the rod adjustable parameter 0 32m Distance from the pivot to the center of the weight adjustable parameter 1 22kg Mass of the base including carriage equivalent motor drive inertia and pendulum base hardware 0 069 g Mass of the rod 0 089kg Mass of the attached weight 0 025 m Radius of the round weight Figure 11 2 Pendulum Parameters 2 Find a state space realization of the system 3 Design and simulate a full state feedback compensator that stabilizes the system and satisfies the following performance specifications a Percent overshoot lt 10 b Setting time lt 2sec Av
27. OL SYSTEM IS HARDWARE AND SOFTWARE 2 2 Lab Setup 2 2 1 Software Installation Step by step control system software installation instructions Download 13http cnx org content m13071 latest Software Installation Notes doc Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 3 Control Lab Setup Using LabVIEW to Control ECP Plants 1This content is available online at lt http cnx org content m13080 1 4 gt Available for free at Connexions lt http cnx org content coll0302 1 5 gt 17 CHAPTER 3 CONTROL LAB SETUP USING LABVIEW TO CONTROL 5 ECP PLANTS 3 1 Using LabVIEW to Control ECP Plants This document provides a brief overview of how to use the National Instruments LabVIEW Virtual Instru ment VI developed by The University of Texas at Austin Aerospace Engineering Controls Laboratory to perform control system experiments with the Educational Control Products ECP Model 210 Rectilinear and Model 205 Torsional plants 3 1 1 FPGA Personality VIs 3 1 1 1 FPGA VI Specifics for each Plant The provided FPGA VIs contain the code for the reconfigurable I O board which sends and receives signals such as motor drive voltage and quadrature encoder channels from the plants Furthermore the FPGA code incorporates safety features such as motor overvoltage protection to help prevent damage to the plants The FPGA VIs for the two plants are similar but differ in the following
28. SETUP USING LABVIEW TO CONTROL 2 ECP PLANTS open loop case a command signal amplitude of 32768 to 32767 corresponds to 10V to 10V sent to the drive motor Please refer to the following resources for more detailed plant dynamics and hardware descriptions ECP Plant Manuals and National Instruments Resources Manual for Model 210 210a Rectilinear Control System Instructor s Edition Manual for Model 205 205a Torsional Control System Instructor s Edition National Instruments PCI PXI 7831R Hardware http www ni com pdf manuals 370489b pdf Additional NI hardware and LabVIEW programming resources can be found on http www ni com http www ni com pdf manuals 370489b pdf http www ni com Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 4 Introduction to Lab Hardware and LabVIEW Implementation 1This content is available online at lt http cnx org content m13026 1 3 gt Available for free at Connexions lt http cnx org content coll10302 1 5 gt 25 CHAPTER 4 INTRODUCTION TO LAB HARDWARE AND LABVIEW IMPLEMENTATION 4 1 Introduction to Lab Hardware and LabVIEW Implementation 26 4 1 1 Objectives e Become familiar with how the lab hardware works e Understand how the LabVIEW control loop block diagram executes e Gain experience in interacting with the VI front panel Available for free at Connexions lt http cnx org content col10302 1 5 gt 27
29. Use only oscillations with amplitude greater than 1000 counts in your calculation This is because smaller amplitudes start to become dominated by nonlinear friction effects Remove the four brass weights and repeat steps 5 and 6 to obtain w for the unloaded carriage Decrease the execution time if necessary Measure the initial cycle amplitude Xo and the last cycle amplitude Xn for the n cycles measured in Step 6 Using relationships associated with the logarithmic decrement find the damping ratio call it Cm12 as 1 Xo 1 Xo ee i a pie Ke Configure the plant as shown in Fig 2b where the first mass carriage is now clamped and the second is free Repeat steps 5 through 8 for the second mass carriage to obtain Wn 5 Wnm22 and Cm22 How does this damping ratio compare with that for the first mass Be sure to save this plotted data as it will be used in the next experiment Connect the mass carriage extension bracket and dashpot to the second mass as shown in Fig 2c and load four brass weights onto the second mass carriage Open the damping air flow adjustment knob 2 0 turns from the fully closed position Perform the necessary steps to obtain where the qd subscript denotes the dashpot For this calculation use amplitudes gt 500 counts Each brass weight has a mass of 0 5 0 0169 You may weigh the pieces if a more precise value is desired Call the mass of the four weights combined mu Recall that the dynamics for a
30. ailable for free at Connexions lt http cnx org content col10302 1 5 gt 66 CHAPTER 11 INVERTED PENDULUM ON A TRANSLATING BASE 11 1 3 Lab Procedure 1 Configure the plant as shown above in Fig 1 2 Code your state feedback compensator into the control loop VI 3 Perform a 2500 count step input and save the plot 4 Implement dither into your system and perform the step input again Save the plot when you are finished Available for free at Connexions lt http cnx org content col10302 1 5 gt 67 11 1 4 Post Lab 1 How did the response of the system with no dither compare to your simulation Can you explain the discrepancy 2 What effect did dither have on the response of the system Was this response trajectory closer to what you had simulated Available for free at Connexions lt http cnx org content col10302 1 5 gt 68 CHAPTER 11 INVERTED PENDULUM ON A TRANSLATING BASE Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 12 Self Erecting Inverted Pendulum on a Rotating Base 12 1 Self Erecting Inverted Pendulum on a Rotating Base 12 1 1 Objectives 1 Understand the dynamics of an inverted pendulum with a rotating base 2 Use state feedback to control on unstable system 3 Code a self erecting control algorithm into LabVIEW which automatically switches to inverted pen dulum control 1This content is available online at lt http cnx org content m13068
31. ass carriage Gently displace the carriages and note the relative stiffness of the servo system at the first mass Now implement the low gain controller from step 5 1 and perform a 3000 count step and save the plot Manually displace the first and second masses and note their relative stiffness Are they generally more or less stiff than for the controller from the step above How does the speed compare to the high gain controller How about the steady state error Now implement your noncollocated PD notch filter controller from step 5b of the pre lab and perform a 3000 count step save the plot From the response plot determine the rise time and overshoot of the second mass carriage Available for free at Connexions lt http cnx org content col10302 1 5 gt 49 7 1 4 7 4 Post Lab 1 What was the predominant behavior of the second mass carriage with the highgain collocated PD controller Can you give an explanation for the difference in the responses of the two masses in terms of their closed loop transfer functions 2 What differences did you observe in the responses between the low gain and high gain collocated PD controllers 3 What was the rise time and overshoot for your noncollocated PD notch filter controller Was this better or worse than you were able to achieve with the collocated controllers How did the steady state error of the system for this controller compare to that of the low gain collocated PD controller
32. become useful for performing calculations in later labs Take a look at the response of the first mass carriage which you just commanded Since no control algorithm was implemented you are looking at the open loop response of the system If you wish to save the data to a spreadsheet file enter a filename in the file path box and press the Save Raw Data control Note that this only saves the time reference trajectory control effort and encoder data not the velocity or acceleration The file will be saved to the hard drive on the PXI You can use an FTP client to download the file to your host PC The file can be imported by any application that can handle spreadsheets such as Excel or Matlab Also you can save the response plot for later viewing or inserting into a report The easiest way to do this is to simply right click on the plot and choose the Copy Data option this option will be under the Data Operations menu if the VI is not running Then just paste the figure into an image editing program such as Paint or a word processing application that can handle embedded images Unchecking the Autoscale Y Axis option will help ensure that the pasted image will look the same as it does on the VI front panel Save the plot of the reference trajectory and response of the first mass carriage that you just commanded and hand it in with the rest of your work You are now finished with the introduction to using LabVIEW with the Model 210 plant Press the
33. connect to the motor drive inputs on the front of the ECP Power supply The ECP Amplifier is then connected to one of ECP s mechanical plants http cnx org content m13071 latest ECP RIO_Adapter pdf 3http ohm ni com advisors pxi 4http digital ni com public nsf websearch CB3434DA 94466DD286256E9E006BB775 http cnx org content m13071 latest ECP RIO_Adapter pdf Available for free at Connexions lt http cnx org content col10302 1 5 gt 13 The Real Time PC solution provides a lower cost real time computing and acquisition platform that is ideal for laboratory and research applications while still maintaining determinism and reliability Real Time PC ETS Real Time Control System Bundle for Academia from National Instrumets Shttp digital ni com express nsf bycode exxu63 Available for free at Connexions lt http cnx org content col10302 1 5 gt CHAPTER 2 CONTROL LAB SETUP CHOOSING CONTROL SYSTEM 4 HARDWARE AND SOFTWARE 2 1 2 2 The LabVIEW Real Time Module for RTX The LabVIEW Real Time Module for RTX targets is used with desktop PCs running RTX a real time extension for Windows This real time operating system runs in parallel with Windows on the same processor providing a single box solution for both user interface and deterministic operations The OS can be purchased from National Instruments or from Venturecom directly LabVIEW for RTX is a single PC solution for Real Time processing PCI 7831R ECP
34. d 4 on the terminal block ECP may instruct you to connect the 5V and ground wires for encoder 4 to pins 1 and 3 on the terminal block however doing so will result in the encoder not receiving power e Encoder Counts Per Revolution Encoder 1 16000 counts 360 degrees Encoder 2 16000 counts 360 degrees Encoder 3 16000 counts 360 degrees Encoder 4 16384 counts 360 degrees pendulum encoder NOTE See special hook up instructions p 18 for the pendulum encoder on note above This only applies to the ECP pendulum attachment that requires bare wires to be hooked up inside the ECP Amplifier box 3 1 1 2 Autorunning FPGA VIs to Zero Analog Outputs NOTE This must only be done once for the life of the FPGA Board To ensure that the system has the correct power on states when the real time target is booted but before the control loop VI is run you should configure the target to autorun the FPGA VI at power on To enable this feature the Autorun VI option should be selected when building the FPGA project code Then in the LabVIEW Embedded Project Manager select Tools gt Download VI or Attributes to Flash Memory In this window you can download the FPGA VI from the host machine to the flash memory on the target and configure autoload options See Chapter 4 of the LabVIEW FPGA Module User s Manual for more information 3 1 2 Using the Real Time VI for Control System Experiments 3 1 2 1 Starting Point VI s for Each Pla
35. d knw You may exclude the procedure for identifying the inertia and damping for disk 2 When formulating your procedures remember that disks 2 and 3 can be clamped disk 1 cannot Available for free at Connexions lt http cnx org content col10302 1 5 gt 53 8 1 3 Lab Procedure 8 1 3 1 System Identification Using Least Squares 1 2 Configure the plant with all three disks rotating freely and no brass weights attached Perform a 1638 count 0 5V linear sine sweep from 0 to 8Hz with a sweep time of 20 seconds When the execution is complete enter a file name such as 3DiskSweep Unloaded and save the raw data from the front panel Now load two 0 5kg brass weights onto each of the three disks so their centers are 9 0cm from the axis of rotation Perform the sine sweep again Enter a file name such as 3DiskSweepLoaded and save the raw data You are now ready to identify the system parameters using least squares estimation 8 1 3 2 System Identification Using Second Order Model 1 Follow the steps you outlined in the pre lab to identify the system parameters using the second order model method Available for free at Connexions lt http cnx org content col10302 1 5 gt 54 CHAPTER 8 SYSTEM IDENTIFICATION FOR THE TORSIONAL PLANT 8 1 4 Post Lab 1 Complete the table below remember to include units Least Squares Values Second Order Model Values J Figure 8 1 Post Lab Table 2 How close are your least squa
36. ght attached to a slender rod The position of the weight can be varied therefore changing the center of gravity of the assembly The rod attaches to a low friction pivot joint whose angular position is measured by a quadrature encoder The base plate allows for the accessory to be mounted on both the Model 210 and Model 205 plants ECP A 51 External Image Please see http www ecpsystems com subPageImages penasscMain gif Figure 1 3 ECP A 51 Inverted Pendulum Accessory 1 2 4 PXI 1042 Chassis The National Instruments PXI 1031 chassis 8 provides a foundation to which a variety of PXI expansion modules can be added This makes it a highly customizable measurement and testing platform Shttp www ecpsystems com controls_pendassc htm http www ecpsystems com controls_pendassc htm Shttp sine ni com nips cds view p lang en nid 13906 Available for free at Connexions lt http cnx org content col10302 1 5 gt NI PXI 1031 a we yug seo aoe S Ba Tia 3 i Banna bea a i i s CI 0 i 0 1 d l E de thes i 2 ey a o ih ba i T ai i E 1 e a LEET OUr l pi tonen an 00 ah Ty i S i 2 0 ts 3 A i A Figure 1 4 National Instruments PXI 1031 Chassis 1 2 5 PXI 8186 Real Time Embedded Controller The National Instruments PXI 8186 is a Pentium4 based real time embedded controller In addition to havi
37. he scaling of velocity data that is shown on the front panel graph indicator and remember to include units in your calculation Calculate the average of the magnitudes of the positive and negative accelerations call this value zie to be used in obtaining knw below Recall that the hardware gain for this system is given by krw keka ke kmpKep ke where kce the DAC gain 10V 32 768 DAC counts ka the servo amp gain to be determined Amps V k the servo motor torque constant to be determined Nm Amp kmp the motor pinion pitch radius inverse 26 25m7 k ep the encoder pinion pitch radius inverse 89 1 ke the encoder gain 16 000 pulses 2 zradians Using what you have learned about hardware gain calculate a value for the product kakt Use this value to compute the hardware gain knw Save any files or plots of interest Stop and exit the VI power off the amplifier and PXI and return all plant materials to the instructor Available for free at Connexions lt http cnx org content col10302 1 5 gt 38 CHAPTER 5 SYSTEM IDENTIFICATION FOR THE RECTILINEAR PLANT 5 1 4 Post Lab 1 Complete the table below making sure to include units Second Order Model Values Ito Aimed Khigh Khaw Figure 5 3 Post Lab Table 2 How do your values of me and c compare with mez and cg Can you explain why they may be different 3 What were your values for Gmi2 and Are these values sufficiently sma
38. ign Toolkit LabVIEW Simulation Module LabVIEW FPGA 2 1 1 2 National Instruments Drivers e LabVIEW Device Driver CDs e NI RIO Driver CD 2 1 1 3 Venturecom Applications e Real Time eXtention for Windows RTX Optional Available for free at Connexions lt http cnx org content col10302 1 5 gt 11 2 1 2 Choosing Lab Hardware The lab currently uses the hardware laid out as option one 1 below LabVIEW Real Time Module for ETS with PXI hardware However there are several hardware combinations that can be used for implementation of a Real Time system to control ETS plants using LabVIEW These options each have their own benefits The options have been broken down by Real Time OS software support Available for free at Connexions lt http cnx org content col10302 1 5 gt CHAPTER 2 CONTROL LAB SETUP CHOOSING CONTROL SYSTEM 5 HARDWARE AND SOFTWARE 2 1 2 1 LabVIEW Real Time Module for ETS The LabVIEW Real Time Module for ETS targets is for real time devices that use a single dedicated kernel running embedded code This option can be purchased from National Instruments for real time PXI targets It is also used for desktop PCs running as a dedicated real time target i l ad ethemet J pe m PXI Chassis RT Controller amp PXI 7831R ECP Plant ethemet PCI 7831R ECP Plant Figure 2 1 LabVIEW Real Time for ETS Options 1 This option consists of a Windows PC communicating with a PXI real time controlle
39. important data that is acquired from the system they may be necessary for calculations that you will need to perform later 5 Your answers to the post lab questions should demonstrate that you fully understand all aspects of the experiment s you just performed Also remember that with experimentation there is often no right answer You should answer the question based on your observations and the results obtained from your particular system which may be very different than somebody else s Program Debugging Some students tend to think of the instructor as a program debugging aid You should try diligently to find your own errors before seeking assistance Part of the objective of the computer assignments is to help you develop the ability to use the computer INDEPENDENTLY You are not using the computer independently if someone else debugs your programs You should only seek debugging assistance from the instructor if you have made a diligent effort to find your mistakes Available for free at Connexions lt http cnx org content col10302 1 5 gt 1 2 Lab Hardware The experiments for this course will be performed on plants from ECP Educational Control Products which will be controlled by a National Instruments PXI chassis equipped with an embedded real time controller and a reconfigurable multifunction I O module 1 2 1 Model 210 Rectilinear Plant The ECP Model 210 Rectilinear Plant holds three mass carriages which can be loaded w
40. ion with respect to a top view reference position You will need to remember this for the future when you derive the torsional plant s equations of motion When you are finished reset the encoders Now turn on the amplifier box Suppose we wish to acquire and view the natural response of the system for a particular set of initial conditions You can accomplish this by executing a step with zero amplitude hence zero control effort is being input to the plant Select a dwell time of 4000ms This will cause the system to acquire 8 seconds of data To see why this is true preview a step input with a nonzero amplitude and observe how the dwell time is defined for this type of input Now execute the zero amplitude step and manually displace the first disk by approximately 450 then release it Wait for the VI to finish acquiring the data and then plot the measurements from encoder 1 and 2 Try a different set of initial conditions e g displace the two disks in opposing directions and observe the response Reset the encoders and execute a sine sweep with a 500 count amplitude again you will learn how to compute the drive motor voltage and torque corresponding to this amplitude in the next lab Enter 0 1Hz and 10Hz as your start and end frequencies respectively Input a sweep time of 30 seconds and set the sweep method to logarithmic When the sweep is complete select to view the frequency response from the control on the front panel This is a 2
41. is is with a case structure Place the controller gains and case selector as controls on the front panel Set k ka 0 and enter the value of kp you found in step 5 After carefully checking for stability acquire and plot the natural response of the system Find the frequency of the oscillation Is it what you expected Now set kp ki 0 and enter the value of kg you found in step 5 Manually displace the mass carriage what do you feel Do not excessively coerce the carriage as this may cause the motor drive protection to open the control loop Now enter a value of kd five times as large and manually displace the carriage again What do you notice now Now implement the values of kp and kg you found for the four cases in step 6 Perform a 3000 count step for each case choose a dwell time long enough for the system to reach steady state Does the system s response agree with your simulations Save these plots and turn them in when you complete the lab With your critically damped kp and parameters from above add integral action by entering the value of k you found in step 7 Perform a 3000 count step and save the response plot Change the control algorithm to the second case with the differentiator in an inner feedback loop and plot and save the step response What differences do you notice between this response and the case with the differentiator in the forward loop Stop and exit the VI power off the amplifier and PXI a
42. ith brass weights and connected in a variety of configurations using springs of varying stiffness The adjustable dashpot can be used to provide damping for the system A single drive motor provides actuation to the system via the first mass carriage and position measurements are taken by quadrature encoders ECP Model 210 External Image Please see http www ecpsystems com subPageImages lin gif Figure 1 1 ECP Model 210 Rectilinear Plant 1 2 2 Model 205 Torsional Plant The ECP Model 205 Torsional Plant holds three disks each of which can be loaded with brass weights at varying positions The disks are connected through their centers by thin rods giving the system rotational stiffness A single driver motor actuates the system via the bottom disk and quadrature encoders provide angular position measurements ECP Model 205 External Image Please see http www ecpsystems com subPageImages tors gif Figure 1 2 ECP Model 205 Torsional Plant http www ecpsystems com controls_torplant htm 3http www ecpsystems com controls _torplant htm http www ecpsystems com controls_recplant htm http www ecpsystems com controls_recplant htm Available for free at Connexions lt http cnx org content col10302 1 5 gt CHAPTER 1 CONTROL SYSTEMS LAB INTRODUCTION HARDWARE SOFTWARE AND SAFETY 1 2 3 A 51 Inverted Pendulum Accessory The ECP A 51 Inverted Pendulum Accessory consists of a cylindrical wei
43. ler from Lab 3 where you are feeding back the position of the first carriage Use the PD controller with the differentiator in the inner feedback loop With these gains what do you notice about the behavior of the second mass carriage Remember to record these gains so you can implement them in the lab Now iteratively Available for free at Connexions lt http cnx org content col10302 1 5 gt 47 reduce the controller gains until you are able to achieve minimal overshoot for both carriages try for less than 10 with as fast a response as possible Again don t forget to record the gains b Noncollocated Simulate the controller you designed in steps 3 and 4 above Find kp and kg to meet rise time and overshoot less than 0 5sec and 10 respectively Available for free at Connexions lt http cnx org content col10302 1 5 gt 48 CHAPTER 7 COLLOCATED NONCOLLOCATED CONTROL OF 2DOF RECTILINEAR SYSTEM 7 1 3 Lab Procedure 1 Configure the Model 210 plant for this experiment Be sure to check that you are using the medium stiffness spring between the first and second carriages Code the two controller structures collocated PD and noncollocated PD notch filter into the LabVIEW control loop Again you can use a case selector to easily switch between the two algorithms Implement the high gain controller from step 5 1 of the pre lab and perform a 3000 count step and save the plot Notice the behavior of the second m
44. ll for the approximations made in steps 6 and 8 to be valid 4 Explain the importance of accurately identifying the plant parameters and hardware gain in terms of how they will affect controller design Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 6 Rigid Body PD and PID Control 6 1 Rigid Body PD and PID Control 6 1 1 Objectives 1 Understand the individual effects of proportional derivative and integral action 2 Design PD and PID controllers for the 1DOF rigid body system 3 Implement your first controller in LabVIEW 1This content is available online at lt http cnx org content m13069 1 1 gt Available for free at Connexions lt http cnx org content coll0302 1 5 gt 39 40 CHAPTER 6 RIGID BODY PD AND PID CONTROL 6 1 2 Pre Lab 1 Derive the equations of motion for the IDOF mass carriage loaded with four 0 5kg brass weights rigid body system that you will control in this lab The plant configuration is shown below Et Figure 6 1 Rigid Body Plant Configuration N Starting with the EOM from the previous question rewrite it so that the control effort into the system is u t in units of DAC counts and the position velocity and acceleration are e te te where the subscript e denotes the encoder 3 Find the plant s transfer function G s 4 Consider a PID controller ki Ge s kp y T has Find the closed loop transfer function of
45. m options if you wish to zoom in on a portion of the graph Toggling the cursor on brings up the cursor on the graph You may lock the cursor to any of the 14 plot histories and click and drag on it to obtain point by point numeric data The first number shown in the cursor legend is the time and the second is the amplitude for the plot to which you are currently locked If you wish to save the data enter a file name in the path control on the front panel and press the Save Raw Data control This will save the time reference signal control effort and four encoder position histories for the commanded trajectory velocity and acceleration data are not saved The file is saved as spreadsheet data on the PXI s hard drive You may use an FTP client of your choice to access the PXI and copy the file Available for free at Connexions lt http cnx org content col10302 1 5 gt 23 to your host machine When you are finished with your experiment press the Abort Control control on the front panel and the VI will shut down the control loop Programming a Control Algorithm in the VI s Block Diagram The Real Time control loop VI has been written such that a variety of control algorithms can be imple mented with little change to the VI s block diagram code The only change that needs to be made is the code that exists between the reference signal desired position and the control effort analog output Open the block diagram for the VI shown belo
46. n is detected zero voltage will be written to the motor until the error is cleared The portion of the code which interprets encoder signals has been written such that for the 210 plant a displacement to the right results in a positive measurement For the 205 plant a positive measurement results from a counterclockwise disk displacement When using the ECP pendulum accessory a counterclockwise rotation will result in a positive encoder measurement encoder 4 The portion of the code which sends signals to the drive motor has been written such that a positive control effort results in a counterclockwise when viewed from the shaft rotation of the drive motor Therefore for the 210 plant this will result in an input force to the right For the 205 plant this will result in a clockwise input torque at the base disk If you decide to write new FPGA code using the LabVIEW Embedded Project Manager use the following tables as a reference for assigning FPGA channels e Note that if you use the ECP pendulum accessory and are required to connect the pendulum encoder cable manually to the terminal block inside the amplifier box then you should connect the 5V and ground wire to pins 2 and 4 respectively on the terminal block This is due to the fact that the National Instruments ECP to RIO cable maps the 5V and ground channels for all the encoders to Available for free at Connexions lt http cnx org content col10302 1 5 gt 19 only pins 2 an
47. nd return all plant materials to the instructor Available for free at Connexions lt http cnx org content col10302 1 5 gt 43 6 1 4 Post Lab 1 ply What was the effect of k in step 3 above If you doubled your value of k in this step what would you expect the natural frequency of the system to be You should show this mathematically What was the effect of kg in step 4 above What differences did you notice between the PD controller and the PID controller What differences did you notice when the differentiator was in an inner feedback loop as opposed to the forward loop Available for free at Connexions lt http cnx org content col10302 1 5 gt 44 CHAPTER 6 RIGID BODY PD AND PID CONTROL Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 7 Collocated Noncollocated Control of 2DOF Rectilinear System 7 1 Collocated Noncollocated Control of 2DOF Rectilinear System 7 1 1 Objectives e Implement a PD controller for a 2DOF system with a oscillatory mode e Understand the limitations of PD PID control for higher order systems e Design simulate and implement a noncollocated controller with multiple feedback loops to acquire an acceptable response for the system 1This content is available online at lt http cnx org content m13063 1 1 gt Available for free at Connexions lt http cnx org content coll0302 1 5 gt 45 CHAPTER 7 COLLOCATED NONCOLLOCATE
48. nexions is part of an exciting new information distribution system that allows for Print on Demand Books Connexions has partnered with innovative on demand publisher QOOP to accelerate the delivery of printed course materials and textbooks into classrooms worldwide at lower prices than traditional academic publishers
49. ng the ability to act as a Windows PC the 221 8186 can also run an NI developed real time operating system which allows it to work as a deployment platform for LabVIEW Real Time applications http sine ni com nips cds view p lang en nid 13906 l0http sine ni com nips cds view p lang en nid 13447 Available for free at Connexions lt http cnx org content col10302 1 5 gt CHAPTER 1 CONTROL SYSTEMS LAB INTRODUCTION HARDWARE SOFTWARE AND SAFETY NI PXI 8186 Figure 1 5 National Instruments PXI 8186 Embedded Controller 1 2 6 PXI 7831R Reconfigurable Multifunction I O The National Instruments PXI 7831R Reconfigurable Multifunction I O is a module that can input and output both analog and digital signals It is equipped with an FPGA field processor gate array which is configurable with the LabVIEW FPGA Module lhttp sine ni com nips cds view p lang en nid 13447 2http sine ni com nips cds view p lang en nid 14757 Available for free at Connexions lt http cnx org content col10302 1 5 gt NI PXI 7831R Figure 1 6 National Instruments PXI 7831R Reconfigurable Multifunction 1 01 1 3 Safety Procedures The following procedures are to help prevent damage to the lab equipment and also to ensure your safety Be sure to read and understand all of the information in this section before performing any experiments Should you ever have any questions regarding the operation of the lab hardware d
50. nt e LabVIEW Real Time for ETS Example VIs ECP 205 and 210 LabVIEW 8 0 Project ECP_LabVIEW_ 8 0_ Starting Point zip download FPGA personality included ECP 205 and 210 LabVIEW 7 1 Project ECP_LabVIEW_7 1_ Starting Point zip download FPGA personality included e LabVIEW Real Time for RTX Example VIs ECP 210 Rectilinear Plant not yet posted ECP 205 Torsional Plant not yet posted 3 1 2 2 Usage Instructions Extract all folders and VIs to a directory on your host PC Be sure to keep the file and folder paths intact to avoid having to relocate VIs The files in the FPGA VIs and Sub VIs folders do not need to be changed Target your real time device from the LabVIEW start up screen and then open the example ECP 210 110001 PID vi You will see the front panel shown below http cnx org content m13080 latest ECP_LabVIEW_ 8 0 Starting Point zip 3http cnx org content m13080 latest ECP_ LabVIEW_7 1_ Starting Point zip Available for free at Connexions lt http cnx org content col10302 1 5 gt 20 CHAPTER 3 CONTROL LAB SETUP USING LABVIEW TO CONTROL ECP PLANTS Figure 3 1 LabVIEW front panel of example ECP 210 1DOF PID vi Section 3 1 2 1 Starting Point 171 5 for Each Plant Take a few moments to familiarize yourself with the various controls and indicators that are available on the front panel When you are ready power on the ECP amplifier box and run the VI Once the VI completes downloading to the PXI the
51. o not hesitate to ask the instructor 1 3 1 General Safety Precautions e Always check to make sure that all of the system components brass weights disks spring etc are securely fastened before powering on the ECP amplifier box and implementing your VI e Whenever you are reconfiguring the plant setup always be sure to check that your VI is not running and that the amplifier box is turned off e When implementing an untested control algorithm check for stability by using a long slender object such as a ruler or unsharpened pencil to apply gentle force to the mass disk nearest to the drive 3http sine ni com nips cds view p lang en nid 14757 Available for free at Connexions lt http cnx org content col10302 1 5 gt CHAPTER 1 CONTROL SYSTEMS LAB INTRODUCTION HARDWARE SOFTWARE AND SAFETY motor e Do not disturb the system while it is executing a commanded trajectory e Inthe event of an emergency shut off power to the system by pressing the red button on the amplifier box 1 3 2 Hardware Limits on the Model 210 Located near each mass carriage are two stop bumpers that prevent the carriage from exceeding their maximum allowable displacement On each stop bumper is an electrical switch which sends out a signal when it is engaged When the LabVIEW FPGA code receives this signal it immediately outputs zero command voltage to the drive motor This voltage remains zero until the error is cleared via the control loop VI s
52. on the Preview Trajectory control and observe the signal on the graph indicator Notice the effect of selecting the Bidirectional Inputs control on signals for which you specify more than one repetition Choose a sinusoidal signal with an amplitude of 1640 counts This amplitude corresponds to an input of 0 5 Volts to the drive motor and 2 6 Newtons to the mass carriage nominally You will learn how to calculate these exact values in the next lab Set the frequency to 2Hz and repeat the signal 8 times Preview the trajectory to check that it is what you expected it is always good practice to preview the test signal before you execute it to make sure you know exactly what will be commanded Once you have confirmed that the commanded trajectory is correct press the Execute Trajectory control The Test Signals vi front panel will close and the Executing Trajectory indicator on the main VI s front panel will light up During this time you will see the plant responding to the command When the trajectory is complete the plot data will be computed as shown by the Computing Plot Data indicator Once complete you may choose which trajectories you wish to view by selecting the corresponding check box If necessary use the zoom features for the graph indicator to get a better view of the data Also select the cursor tool and drag the cursor over the response plot Notice that time and amplitude data is shown in the cursor legend This feature will
53. r running Lab VIEW Real Time OS The PXI 7831R intelligent data acquisition board is connected to the controller through the PXI bus Control loops can be executed on both the Real Time controller and on the intelligent data acquisition board The ECP RIO Adapter cable connects the 68pin VHDCI connector from the MIO connector on the PXI 7831R to the round encoder cable connected directly to the ECP plant The banana plugs connect to the motor drive inputs on the front of the ECP Power supply The ECP Amplifier is then connected to one of ECP s mechanical plants PXI provides a portable computing and acquisition solution that is rugged and rated for enviormnets where normal PC s can t go making it ideal for both laboratory and research applications in many types of environments where determinism and reliability are crucial PXI Control System ETS PXI Advisor for configuring a PXI system from National Instruments 2 This option consists of a Windows PC communicating with a second PC running LabVIEW Real Time OS Real Time OS PC Requirements The PCI 7831R intelligent data acquisition board is connected to the PC through the PCI bus Control loops can be executed on both the Real Time OS running on the PCI and in the RIO intelligent data acquisition board The ECP RIO Adapter cable connects the 68pin VHDCI connector from the MIO connector on the PXJ 7831R to the round encoder cable connected directly to the ECP plant The banana plugs
54. re 10 1 2DOF Spring Mass System 2 Find a state space realization of the system 3 Design and simulate a full state feedback compensator to control the position of the second mass carriage Design your compensator to meet the following performance specifications a Percent overshoot lt 10 b Settling time lt 1sec c Zero steady state error to a step input Available for free at Connexions lt http cnx org content col10302 1 5 gt 61 10 1 3 Lab Procedure Configure the plant as shown in Fig 1 above Code your state feedback compensator into the control loop VI Perform a 3000 count step input and determine if you have met the performance specifications Once you have achieved the desired performance save your plot and turn it in with the rest of your work fe DIE Available for free at Connexions lt http cnx org content col10302 1 5 gt 62 CHAPTER 10 STATE FEEDBACK COMPENSATION OF A 2DOF RECTILINEAR SYSTEM 10 1 4 Post Lab 1 2 Explain how the state feedback gains affect the system s response in terms of its characteristic equation What effect does the compensator have on the zero s of the system If a system has an undesirable zero how can its effect be reduced using only a state feedback compensator Why is full state feedback compensation often unfeasible especially with higher order systems Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 11
55. res values compared to your second order model values Can you explain any discrepancies between them Which method do you think is more accurate Available for free at Connexions lt http cnx org content col10302 1 5 gt Chapter 9 Phase Lead Compensation of a Rotational Rigid Body System 9 1 Phase Lead Compensation of a Rotational Rigid Body System 9 1 1 Objectives 1 Use frequency domain techniques to design a phase lead compensator for a rigid rotational disk 1This content is available online at lt http cnx org content m13070 1 1 gt Available for free at Connexions lt http cnx org content coll0302 1 5 gt 55 CHAPTER 9 PHASE LEAD COMPENSATION OF A ROTATIONAL RIGID BODY SYSTEM 9 1 2 Pre Lab 1 Derive the equations of motion for the 1DOF rotational system that you will control in this lab The plant configuration is shown below The disk will be loaded with four 0 5kg brass weights placed at a distance 9 0cm from the center of rotation Figure 9 1 Rotational Rigid Body Plant Configuration 1 Design and simulate a phase lead compensator that satisfies the following performance specifications a Zero steady state error to a step input b Gain margin gt 15 db c Phase Margin gt 45 Available for free at Connexions lt http cnx org content col10302 1 5 gt 57 9 1 3 Lab Procedure Configure the plant for this experiment Code your phase lead compensator into the control loop V
56. rted Pendulum on a Rotating Base By Robert Bishop URL http cnx org content m13068 1 1 Pages 69 73 Copyright Robert Bishop License http creativecommons org licenses by 2 0 Available for free at Connexions lt http cnx org content col10302 1 5 gt ATTRIBUTIONS Control Systems Laboratory This course introduces students to fundamental control systems theory with emphasis on design and imple mentation These labs focus on technical implementation issues of classical control theory in the frequency domain and modern control theory in the state space Design and implementation for this course is done using National Instruments LabVIEW software and hardware for control and Educational Control Products ECP hardware for the plants About Connexions Since 1999 Connexions has been pioneering a global system where anyone can create course materials and make them fully accessible and easily reusable free of charge We are a Web based authoring teaching and learning environment open to anyone interested in education including students teachers professors and lifelong learners We connect ideas and facilitate educational communities Connexions s modular interactive courses are in use worldwide by universities community colleges K 12 schools distance learners and lifelong learners Connexions materials are in many languages including English Spanish Chinese Japanese Italian Vietnamese French Portuguese and Thai Con
57. s The Encoder 2 and Encoder 3 indicators correspond to the second and third mass carriages respectively The Encoder 4 indicator is for the pendulum accessory and will be used later in the course Available for free at Connexions lt http cnx org content col10302 1 5 gt 30 10 11 12 CHAPTER 4 INTRODUCTION TO LAB HARDWARE AND LABVIEW IMPLEMENTATION Whenever you wish to set the encoder readings to zero simply press the Reset Encoders control located on the front panel Try this now Now manually displace the first mass carriage until you engage one of the limit switches Notice how the System Error indicator lights up At this point if any voltage were being output to the drive motor it would be set to zero and remain there until you press the Clear Error control on the front panel Press this control now and observe how the System Error indicator light turns off You are now going to send a commanded trajectory to the plant First power on the amplifier box by pressing the black button Also center the first mass carriage between the two stop bumpers and then reset the encoders Now press the Command Trajectory control on the front panel The front panel for the Test Signals vi subVI will pop open Click through the different types of test signals you can command the system with and notice the different parameters that you can change for each signal Choose one of the signals and enter values for its parameters Then click
58. the system below where G s is the transfer function you found previously Ris gt fs Figure 6 2 Transfer Function Or With k 0 0 find kp and kg such that the closed loop system is critically damped and has a natural frequency of wn 2Hz 6 Now with k 0 find kp and kg such that the closed loop system has a natural frequency of wn 4H z and the following damping ratios 0 2 C 05 1 0 2 0 Available for free at Connexions lt http cnx org content col10302 1 5 gt 41 7 Compute k such that knhwki 7500N m sec 8 Using the Control Design Toolkit write a LabVIEW VI that simulates the step response of the closed loop system The controller gains kp ki and kg should be controls on the front panel so you can change each one individually and see how it affects the system s response Available for free at Connexions lt http cnx org content col10302 1 5 gt 42 CHAPTER 6 RIGID BODY PD AND PID CONTROL 6 1 3 Lab Procedure 1 Configure the plant as shown above in Fig 1 with the first mass carriage free and the other two clamped Load four 0 5kg brass weights onto the carriage No springs should be attached to the carriage Inset a PID controller structure into the control loop VI You should implement the control algorithm in two ways one with the differentiator in the forward loop and the other with the differentiator in an inner feedback loop A good way to do th
59. tification for the Rectilinear Plant 5 1 System Identification for the Rectilinear Plant 5 1 1 Objectives e Review of the behavior of second order systems e Understand the importance of system identification e Understand the concept of hardware gain and why it will play a crucial role in controller design 1This content is available online at lt http cnx org content m13066 1 1 gt Available for free at Connexions lt http cnx org content coll0302 1 5 gt 33 34 CHAPTER 5 SYSTEM IDENTIFICATION FOR THE RECTILINEAR PLANT 5 1 2 Pre Lab 1 Derive the equations of motion for the 1DOF spring mass system with friction damping shown below and find the transfer function Simulate the unforced natural response in LabVIEW to an initial displacement of 3 0cm look for the Initial Response function in the Control Design Toolkit Determine the natural frequency from the plot Use the following parameters M 3 0kg k 350N m c 4 0Nsec m Figure 5 1 1DOF Spring Mass System with Friction Damping Available for free at Connexions lt http cnx org content col10302 1 5 gt 35 5 1 3 Lab Procedure w Power on the PXI and while it s booting up configure the plant as explained in the next step Clamp the second and third mass carriages and attach the medium stiffness spring between the first and second carriage as shown in Fig 2 Secure four 0 5kg brass weights to the first and second carriages Le m T lo 2
60. tp creativecommons org licenses by 2 0 Module Rigid Body PD and PID Control By Robert Bishop URL http cnx org content m13069 1 1 Pages 39 43 Copyright Robert Bishop License http creativecommons org licenses by 2 0 Available for free at Connexions lt http cnx org content col10302 1 5 gt 75 76 Module Collocated Noncollocated Control of 2DOF Rectilinear System By Robert Bishop URL http cnx org content m13063 1 1 Pages 45 49 Copyright Robert Bishop License http creativecommons org licenses by 2 0 Module System Identification for the Torsional Plant By Robert Bishop URL http cnx org content m13065 1 1 Pages 51 54 Copyright Robert Bishop License http creativecommons org licenses by 2 0 Module Phase Lead Compensation of a Rotational Rigid Body System By Robert Bishop URL http cnx org content m13070 1 1 Pages 55 58 Copyright Robert Bishop License http creativecommons org licenses by 2 0 Module State Feedback Compensation of a 2DOF Rectilinear System By Robert Bishop URL http cnx org content m13067 1 1 Pages 59 62 Copyright Robert Bishop License http creativecommons org licenses by 2 0 Module Inverted Pendulum on a Translating Base By Robert Bishop URL http cnx org content m13064 1 1 Pages 63 67 Copyright Robert Bishop License http creativecommons org licenses by 2 0 Module Self Erecting Inve
61. w to see how the PID controller for this example was implemented a ECP 210 1DOF PID vi Block Diagram File Edit Ts on Tools Browse Window Help m E ie skint Ror 2015 borg prerrtmennrnnnenennnnmnnannnatnnannnansnnintmnnnnnmnnnnannmnnenni Encoder Feedback Analog Output 0 eye Desired Position RT Target 146 6 105 10 Figure 3 4 Partial block diagram view of Example VI ECP 210 1DOF PID vi Section 3 1 2 1 Starting Point VI s for Each Plant The encoder measurement is subtracted from the reference signal to generate the error signal which is sent through the PID algorithm Finally the control effort signal calculated by the PID is sent to the analog output channel that drives the plant motor It can be seen that programming other controllers such as phase lead LQR etc could be easily accom plished by deleting the current algorithm and coding a new one in its place To perform experiments for the open loop case useful when studying the system s natural dynamics or when performing system identification you may simply delete the feedback control algorithm and connect the reference trajectory point directly to the analog output Recall that the analog output channels on the reconfigurable I O board have a range of 10V to 10V and a 16 bit DAC resolution Therefore in the Available for free at Connexions lt http cnx org content col10302 1 5 gt CHAPTER 3 CONTROL LAB

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