Home

QNET Rotary Pendulum Laboratory Manual

1. e n 5 time s b Motor Voltage Figure 5 3 Pendulum response using energy control with E 50 mJ 12 In Control Parameters fix Er to 20 0 mJ and vary the swing up control gain mu between 10 and 100 m s J Describe how this changes the performance of the energy control Answer 5 3 Outcome Solution B 7 As the mu gain increases the amplitude of the pendulum swings be come larger Recall from swing up controller given in 5 6 which is im plemented in the VI that u is the proportional gain 13 Click on the Stop button to stop running the VI 5 4 Hybrid Swing Up Control 20 minl 1 Open the QNET ROTPENT Swing Up Control vi and ensure it is configured as described in Section 6 Make sure the correct Device is chosen 2 Run the QNET ROTPENT Swing Up Control vi The VI should appear similarity as shown in Figure 4 1 3 In the Balance Control Parameters section ensure the following parameters are set e kp theta 6 50 V rad Q QNET ROTPENT Laboratory Manual Instructor Manual v 1 0 GUANSER i 10 11 e kp alpha 80 0 V rad e kd theta 2 75 V rad s e kd alpha 10 5 V rad s In the Swing Up Control Parameters section set e mu 55 m s J e Er 20 0 mJ e max accel 10 m s e Activate Swing Up OFF de pressed Adjust the Angle Energy deg mJ scope scales to see between 250 and 250 see the ROTPEN User
2. 8 Click on the Stop button to stop running the VI 4 5 Balance Control with Friction Compensation 30 min 1 Go through steps 1 7 in Section 4 3 to run the default balance control The pendulum should be balancing QNET ROTPENT Laboratory Manual Instructor Manual v 1 0 DUAN SER 2 In the Signal Generator section set e Amplitude 0 0 deg e Frequency 0 10 Hz e Offset 0 0 deg 3 In the Dither Signal section set e Amplitude 0 00 V e Frequency 2 50 Hz e Offset 0 00 V 4 sSemseey Observe the behaviour of Arm Angle deg in the Angle Energy deg mJ scope Intuitively speaking can you find some reasons why the arm is oscillating Answer 4 5 Outcome Solution B 5 If the procedure was followed correctly and pendulum is balancing they should be able to make the following analysis B 8 Due to static friction found in motor it typically takes at least 2 5 V to get the rotor moving As a result the pendulum has to fall enough such that the balance controller generates over 2 5 V To keep the pendulum balanced the arm has to move back and forth and this is why is oscillates about the offset angle 5 Increase the Amplitude in the Dither Signal section by steps of 0 1 V until you notice a change in the arm angle response 6 From the Voltage V scope and the pendulum motion what is the Dither signal doing Compare the response of the arm with and without the Dithe
3. The LOR theory has been packaged in the LabVIEW Control Design and Simulation Module Thus given a model of the system in the form of the state space matrices A and B and the weighting matrices Q and R the LQR function in the Control Design Toolkit computes the feedback control gain automatically In this experiment the model is already available In the laboratory the effect of changing the Q weighting matrix while R is fixed to 1 on the cost function J will be explored See Wikipedia for more information on optimal control 3 2 Balance Control Design VI The QNET ROTPENT Control Design VI has three tabs Each tab is explained in the following sections 3 2 1 Symbolic Model Tab The Symbolic Model tab shown in Figure 3 1 is used to setup the QNET rotary pendulum model JNET ROTPENT Control Design vi ate Tools Window Hep NET ROTPEN Control Design lh Jp Jeq Mp Ip 2 Mp r 2 3p Geg Jp4 IMp r 2 3p Mp lp g t Jeg Mp r 2 Geq Jp I Mp lp r Kt Km Rm eg Jp Jeq Mp p 2 Mp r 2 Jp Jeq Mp Ip 2 Mp r 2 Jp MESSEN ben M See Jeq Mp Ip 24 Kt Op Mp lp 2 Rm Ieq p Jeq Mp Ip 2 Mp r 2 3p Mp Ip Kt r Rm Qeq 3p Jeq Mp lp 24 Mp r 2 3p Figure 3 1 LabVIEW VI to generate state space model of QNET rotary pendulum 3 2 2 Open Loop Analysis Tab The Open Loop Analysis tab on the VI is used to analyze the open loop stability of the QNET rotary pendulum System shown in Figure 3 2 NET
4. e Amplitude 45 0 deg e Frequency 0 10 Hz e Offset 0 0 deg 11 Observe the behaviour of the system when a square wave command is given to the arm angle Why does the arm initially move in the wrong direction Answer 4 3 Outcome Solution B 7 This is necessary to keep the pendulum balanced If the arm didn t go back a bit before moving forward then the pendulum would have a ten dency to rotates downwards and go unstable The technical answer is the system is non minimum phase 12 Click on the Stop button to stop running the VI 4 4 Implement Designed Balance Control 20 min 1 Go through Section 3 4 and design a balance control according to the given specifications Remark It is recommended to use the experimental determined pendulum moment of inertia that was found in Section 2 5 2 Open the QNET ROTPENT Swing Up Control vi and ensure it is configured as described in Section 6 Make sure the correct Device is chosen 3 Run the QNET ROTPENT Swing Up Control vi The VI should appear similarity as shown in Figure 4 1 4 In the Signal Generator section set e Amplitude 45 0 deg e Frequency 0 20 Hz e Offset 0 0 deg 5 To implement your balance controller enter the control gain found in Section 3 4 in kp theta kp alpha kd theta and kd alpha in the Control Parameters section 6 Manually rotate the pendulum in the upright position until the n Range LED in the Control Indicators
5. gt NI ELVIS I gt NI ELVIS II Quanser QNET Trainers are plug in boards for NI ELVIS to teach introductory controls in undergraduate labs Together they deliver added choice and cost effective teaching solutions to engineering educators All six QNET Trainers are offered with comprehensive ABET aligned course materials that have been developed to enhance the student learning experience To request a demonstration or quote please email info ni com 2012 Quanser Inc All rights reserved LabVIEW is a trademark of National Instruments INFO NI COM INFO QUANSER COM Quanser control solutions for teaching and research are made in Canada
6. 2 Use the rubric for Outcome A Section A 3 to assign a score for each question The rubric gives the descrip tion of levels of achievement 4 exemplary 3 proficient 2 developing and 1 beginning incomplete for each criterion As an example below is a completed sample scoring sheet after evaluating the homework of one student Question A 1 A 2 A 3 1 3 2 2 4 2 3 3 4 3 5 4 6 3 7 3 8 3 9 3 3 10 3 4 11 3 4 Total 10 32 8 3 You can then enter the Total for each performance criterion into the assessment workbook 1 as shown in Figure A 1 A 2 3 How to score the lab reports As mentioned earlier in Section A 1 2 there are various ways in which you can use the material provided in this manual In any case the outcomes targetted by the lab experiments can be assessed from the lab reports submitted by the students These reports should follow the specific template for content given at the end of each laboratory chapter This will provide a basis to assess the outcomes easily The lab activities correspond to the applied part of engineering Therefore outcomes B and K were mapped to the lab activities through their performance criteria The lab reports themselves match outcome G on effective communication skills If you choose to do an individual experiment in your weekly lab sessio then you can ask the students to submit a lab report using the report template provided
7. 2 8 12 8 4 4 4 2 2 3 8 8 8 4 4 4 4 3 4 8 8 8 4 3 4 4 4 5 8 12 10 4 3 4 3 B 6 6 10 10 3 4 3 3 3 7 5 8 10 4 4 3 4 4 8 5 7 12 3 4 2 4 4 9 7 9 12 3 4 3 3 4 10 7 9 10 2 3 4 4 4 Total Possible 8 5 4 4 4 Scaled Average x x Std Dev 0 71 SCORE for K SCORE for B 3 48 D Figure A 4 Computation of single score for outcome G in the assessment workbook 5 DUAN SER A 2 7 Assessment workbook The assessment workbook 1 was developed using Microsoft Excel It is intented to give a general idea for how the assessment scores can be tracked and brought together On purpose we designed the workbook to have no automatic features You can use it as is or customize it in any way you like The assessment workbook has a tab for the Pre Lab Questions and a tab for each of the laboratory chapters Only 10 students were listed assuming you would use samples of student work and not the entire class If you want to add more students you can insert rows into the spreadsheets Note f you insert new rows make sure that the formula ranges in the cells with calculations are correct At the bottom of each pre lab section there is a row entitled Total Possible To count a pre lab assignment in the calculation of the overall scores you need to enter the correct totals here For example to count the Pre Lab for modeling you need to enter 12 44 and 8 Figure A 1 If you want to exclude an assignment from the overall calculation enter 0 as sh
8. Manual 2 for help Make sure the pendulum is hanging down motionless and the encoder cable is not interfering with the pendu lum In the Swing Up Control Parameters set the Activate Swing Up switch to ON pressed down position The pendulum should begin going back and forth If not click on the Disturbance button in the Signal Generator section to perturb the pendulum Turn off the Active Swing Up switch if the pendulum goes unstable or if the encoder cable interferes with the pendulum arm motion f Gradually increase the reference energy Er in the Control Parameters section until the pendulum swings up to the vertical position Answer 5 4 Outcome Solution B 5 Setting the reference energy E between 80 and 85 mJ should be ad equate to swing up the pendulum to its vertical position 5335 what reference energy was required to swing up the pendulum Was this value expected Answer 5 5 Outcome Solution B 9 Between 80 and 85 mJ This is inline with the potential energy of the pendulum that was measured in Step 7 in Section 5 3 when the pendu lum is vertically upwards AGE Click on the Stop button to stop running the VI G SYSTEM REGUIREMENTS Reguired Hardware e NI ELVIS II or NI ELVIS I e Quanser QNET Rotary Inverted Pendulum Trainer ROTPENT See QNET ROTPENT User Manual 2 Required Software e NI LabVIEW 2010 or later e NI LabVIEW Control Design and Simulation M
9. ROTPEN Control Desi 0 t 0 1 x t 0 ut 0 22 374 0 274296 0 8 23713 0 36 2091 0 0703703 0 2 11322 dx dt 1000 0100 Y07 ooi 0001 Figure 3 2 LabVIEW VI used to analyze open loop stability of QNET rotary pendulum system Q QU AN SER INNOVATE EDUCATE QNET ROTPENT Laboratory Manual Instructor Manual v 1 0 3 2 3 Simulation Tab On the Simulation tab shown in Figure 3 3 users can generate the balance control gains for the QNET rotary pendulum system using LQR and simulate the closed loop system 08 Q ROTP ontrol_Desig i File Edit View Project Operate Tools Window Help m ar a a QNET ROTPEN Control Design err status code x NATIONAL dl fo INSTRUMENTS aa GUANSER E Symbolic Model Open Loop Analysis Simulation setpoint anal Generator Cut simulation Control Input V Signal Type 100 154 m e litude 7j der 2d Amplitu g 45 0 g g 2 S 5 Offset j 0 0 deg a s 50 Disturbance CE D 354 10 100 1157 1 1 1 1 1 5 6 7 8 5 6 7 8 3 10 Simulation Time Simulation Time Pendulum dea 10 Optimal Gain K 5 1 00 60 73 1 39 7 99 gt Figure 3 3 LabVIEW VI for QNET rotary pendulum balance control design 3 3 Model Analysis 20 min 1 Open the QNET ROTPENT Control Design vi Run the ONET ROTPENT Control Design vi The front panel of the VI
10. experimental procedure in Step 4 in Section 4 5 Il RESULTS Do not interpret or analyze the data in this section Just provide the results 1 Balance control response plot from step 7 in Section 4 4 Ill ANALYSIS Provide details of your calculations methods used for analysis for each of the following 1 Effect of changing offset in Step 8 in Section 4 3 Balance control analysis in Step 9 in Section 4 3 Balance control analysis when tracking step reference in 11 in Section 4 3 Examining the arm oscillation in Step 4 in Section 4 5 Explain what the Dither signal is doing in Step 6 in Section 4 5 O a A OO N Effect of increasing Dither signal frequency in Step 8 in Section 4 5 IV CONCLUSIONS Interpret your results to arrive at logical conclusions for the following 1 Whether the balance controller meets the specifications in Step 7 in Section 4 4 2 Effect of setting the Dither signal to the identified friction parameters in Step 9 of Section 4 5 7 4 Template for Content Swing Up Control I PROCEDURE 1 Energy Control e Briefly describe the main goal of the experiment e Briefly describe the experimental procedure in Step 7 in Section 5 3 2 Hybrid Swing Up Control e Briefly describe the main goal of the experiment e Briefly describe the experimental procedure in Step 9 in Section 5 4 Il RESULTS Do not interpret or analyze the data in this section Just provide the results 1 Pendul
11. for this experiment The template contains the main content sections you aa ONET ROTPENT Laboratory Manual Instructor Manual e Ives d 0 5 O icr Home Insert Page Layout Formulas Data Review View Developer B M Cut Calibri Ju aa S E wrap Tet 43 Copy J Format Painter B Zz U Al 2 E Sd Merge amp Center Clipboard fa Font a Alignment M17 G fe 1 Modelling Position 2 Lab Guestinns Pre Lab Questions 3 ID A 2 A3 N A 3 A 4 2 8 26 4 8 5 2 8 8 26 3 7 6 3 2 4 38 3 8 7 4 2 10 28 2 6 8 5 4 12 24 4 6 9 6 4 10 28 4 7 10 7 6 8 24 2 4 11 8 8 6 28 4 5 12 9 6 8 20 4 8 13 10 6 9 27 3 6 14 Total Possible 8 12 28 4 8 15 Scaled 8 x 2 fH Figure A 1 Pre Lab entry into the assessment workbook for one student would expect in a typical lab report procedure results analysis conclusions Each section of the report template ties back to the activities in the lab and the corresponding assessment indicators It also contains performance criteria related to the format of the report You can score the lab reports using the rubric for outcome G given in Section A 3 and the scoring sheet provided for the experiment in that section Note that each lab report scoring sheet directly corresponds to the lab report content template for that experiment Also note that the rubric for outcome G already contains rubrics for outcomes B and K since these
12. imaginary axis 0 4 0 64 0 8 1 0 i 1 i 1 8 0 6 0 4 0 2 0 0 0 2 0 4 0 6 0 real axis Figure 6 3 QNET ROTPENT Control Design VI Open Loop Analysis tab P 08 Q ROTP ontrol_Desig 5 Eile Edit View Project Operate Tools Window Help aa ae gt s m gp QNET ROTPEN Control Design 16 15 status code f s A NATIONAL 4 Ea INSTRUMENTS izata QUANSER i Symbolic Model Open Loop Analysis Simulation setpoint Signal Generator r SS am deg simulation Control Input V Signal Type 1 9 EE 277 EE o TJ m 27 29 50 4 Amplitude 1 60 0 20 g B z Ber 23 2 Frequency Ao an Hz 21 4 0 Ne 7 Zo y 5 Offset d X 25 4 52 No 0 g y 3 d 44 Disturbance OFF gt 23 75 1 1007 1 1 1 1 sO 1 1 1 1 1 5 6 n 8 9 10 5 6 7 8 9 10 Q 24 rds Simulation Time Simulation Time fioo 0 00 0 00 0 00 Pendulum deg jooo 1 00 000 0 00 10 looo 0 00 1 00 0 00 28 looo 0 00 0 00 1 00 1 R 3 pn 3 1 00 8 o amp Optimal Gain K A 00 86 80 1 52 15 62 m 1 1 1 1 1 6 7 8 9 10 Simulation Time v gt Figure 6 4 QNET ROTPENT Control Design VI Simulationtab ID Label Symbol Description Unit 1 Mp My Mass of pendulum assembly link weight kg 2 Ip lp Center o
13. link angles as well as the applied input motor voltage Table 3 lists and describes the main elements of the ROTPENT Simple Modeling virtual instrument front panel Every element is uniquely identified through an ID number and located in Figure 6 1 3 DUAN SER 07 0NET ROTPENT Simple Modeling vi File Edit View Project Operate Tools Window Help eje wj QNET ROTPEN Simple Modeling INSTRUMENTS evi 4 0 sj 250 0 1 1 Arm Angle deg IGUANSER Angle deg Pendulum Angle deg 100 EE Scopes 1 3 Theta 1 EXNE 2 Current 0 5 A 3 P Voltage 13 y 4 Signal Generator Signal Type yu 5 Amplitude 2 50 y 6 Petey doo kz 7 150 155 160 i 1 5 190 195 200 EE 8 Voltage V Input Voltage W 2 44 Disturbance OFF Figure 6 1 QNET ROTPENT Simple Modeling virtual instrument 6 3 Control Design VI The QNET ROTPENT Control Design VI enables users to design a balance controller and simulate its response The matrices for the state space model of the rotary inverted pendulum system is shown in the Symbolic Model tab and illustrated in Figure 6 2 The values of the variables used in the state space model can be changed In the Open Loop Analysis tab shown in Figure 6 3 the numerical state space model is displayed and the resulting open loop poles are plotted on a phase plane Based on this model a co
14. outcomes appear as an integral part of the report To score the lab report of one student 1 Print the scoring sheet for the Lab Report for the experiment they conducted in the lab One sheet is used per student 2 Use the Content rubric Section A 3 to assign a score for each entry in the scoring sheet The rubric gives the description of levels of achievement 4 exemplary 3 proficient 2 developing and 1 begin ning incomplete for each criterion As an example below is a completed scoring sheet after evaluating the lab report of one student 3 Use the Format rubric Section A 3 for the GS 1 and GS 2 criteria to score the formatting of the report on the same scoring sheet 5 DUANS E R CONTENT FORMAT Item K 1 K 2 B 5 B 6 B 7 B 9 GS 1 GS 2 I PROCEDURE 1 1 Frequency Response Experiment 1 2 Bump Test Experiment 1 3 Model Validation Experiment 1 Il RESULTS 1 2 3 4 Ill ANALYSIS Ill 1 Frequency Response Experiment 1 2 3 I 2 Bump Test Experiment 1 IV CONCLUSIONS 1 Total 4 You can then enter the Total for each performance criterion into the assessment workbook 1 as show in Figure A 2 al B ra D a r G r Y a Modelling Ki K2 B 5 B 6 B 7 amp 9 csi Gs2 1 6 10 12 3 5 3 4 3 2 E r a E 3 8 8 8 4 4 4 4 3 4 8 8 8 4 3 4 4 4 5 8 2 10 4 3 4 3 4 6 6 10
15. periodically documents and demonstrates the degree to which the program outcomes are attained by their students Most programs do this by mapping the outcomes a through k to the courses in the curriculum Then these outcomes are assessed in the courses Finally the assessment results are collected from the courses and compiled into program level data to demonstrate the degree to which the program outcomes are attained by their students If your course is part of a similar assessment effort in your program you probably need to assess the following outcomes in your course A An ability to apply knowledge of mathematics science and engineering B G K An ability to use the techniques skills and modern engineering tools necessary for engineering practice An ability to design and conduct experiments as well as to analyze and interpret data An ability to communicate effectively and These outcomes can be assessed in your course using various assessment tools such as student surveys and assignments or questions targeting specific outcomes To measure achievement of an outcome such as outcome A in the list above typically some performance criteria are defined for the outcome The performance criteria are a set of measurable statements to define each learning outcome They identify the specific knowledge skills attitudes and or behavior students must demonstrate as indicators of achieving the outcome For the
16. purpose of this laboratory curriculum we defined a set of performance criteria for each outcome These criteria are labeled as A 1 A 2 B 3 K 3 as indicated in the rubrics in Section A 3 below We also embedded these performance criteria in the curriculum shown by indicators such as PAR YA A 2 1 Assessment in your course Assessment of outcomes is different than grading A course grade or a grade on an assignment or exam is a composite indicator For example if a student receives B as a grade in your course it is probably difficult to tell his her level of achievement in outcome A versus G One of the purposes of assessment is to measure the level of achievement of these specific skills and knowledge so that improvements can be made in the future offerings of the course So how should you introduce outcomes assessment into your course The outcomes assessment approach described here can be applied to each pre lab homework assignment and lab report of each student throughout the semester This may or may not be feasible depending on your class size In general a representative sample of student work is assessed You can continue to give assignments exams and grade them in the traditional way To introduce assessment into your course you can pick a representative sample of student work and score their work using the scoring sheets and rubrics given in this manual This is a good way to start introducing assessment into your c
17. section turns bright green Ensure the encoder cable does not interfere with the pendulum arm motion 7 sen ane Attach the response found Angle Energy deg mJ and the Voltage V scopes Does your system meet the specifications given in Section 3 4 Answer 4 4 Outcome Solution B 5 If the student was able to get the response given in Figure 4 2 then the procedure to run the VI was done properly K 2 The measured closed loop response of the QNET rotary inverted pendu lum is given in Figure 4 2 This is using the LQR gain given in Equation Ans 3 1 B 9 As shown in Figure 4 2 the arm peak time is around 0 75 seconds the input motor voltage is within 10 5 V and the pendulum oscillates 5 deg about the vertical position So the specifications given in Section 3 4 are satisfied Arm Angle deg MW Pendulum Angle deg Angle Energy deg mJ Pendulum Energy mJ 250 pd iem Te zi WEE er peer i eer 150 Mee eer e mE RI s0 pe Ea 7 100 150 200 250 T J T J T F 1 45 0 45 5 46 0 46 5 47 0 475 48 0 48 5 49 0 49 5 50 0 time s a Rotary Arm Pendulum Angle and Energy Voltage V reset T 15 T T T J J T J 1 45 0 45 5 46 0 46 5 47 0 475 48 0 48 5 49 0 49 5 50 0 time s b Motor Voltage Figure 4 2 Simulated rotary inverted pendulum response
18. time it takes for the pendulum to swing back and forth in a few cycles e g 4 cycles 4 EAJ Find the frequency and moment of inertia of the pendulum using the observed results See Section 2 1 to see how to calculate the inertia experimentally Answer 2 4 Outcome B 5 K 1 Solution If they were able to follow the procedure properly then they should be able to measure the number of cycles After performing the experiment the pendulum goes through 6 cycles in 2 5 s Using Equation 2 3 the frequency is 6 24H f 2 5 i Substituting this and the pendulum parameters defined in 2 in Equation 2 2 0 0270 x 9 81 x 0 153 ap i 107 kg m niae 4 x 242 x n MORE UN 5 EX Compare the moment of inertia calculated analytically in Exercise 1 and the moment of inertia found experimentally Is there a large discrepancy between them QNET ROTPENT Laboratory Manual Instructor Manual Answer 2 5 Outcome Solution B 9 The moment of inertia found analytically is 6 98 x 1074 kg m while the experimentally determined inertia is 1 77 x 1074 kg m This dis crepancy may be due to an inaccuracy when measuring the pendulum frequency or the fact that this frequency is the damped frequency not the undamped natural frequency that the equation to compute the inertia uses 6 Stop the VI by clicking on the Stop button 2 6 Results Fill out Table 1 with your answers
19. trainer is shown in Figure 1 1 The motor is mounted vertically in a metal chamber An L shaped arm is connected to the motor shaft and pivots between 180 degrees A pendulum is suspended on a horizontal axis at the end of the arm The pendulum angle is measured by an encoder The control variable is the input voltage to the pulse width modulated amplifier that drives the motor The output variables are the angle of the pendulum and the angle of the motor Figure 1 1 QNET rotary inverted pendulum trainer ROTPENT There are three experiments simple modeling inverted pendulum balance control and swing up control The experiments can be performed independently Topics Covered e Modeling the pendulum e Balance control via state feedback e Control optimization LQR e Friction compensation e Energy control e Hybrid control Prerequisites In order to successfully carry out this laboratory the user should be familiar with the following e Transfer function fundamentals e g obtaining a transfer function from a differential equation e Using LabVIEW to run VIs B DUANS E R e SIMPLE MODELING 2 1 Background This experiment illustrates some control tasks for gantry cranes The gantry is a moving platform or trolley that transports the crane about the factory floor or harbor The load hangs from the crane using wires and is moved by the gantry crane Typically the problem is to move the load quickly and move it to th
20. 10 3 4 3 3 3 7 5 8 10 4 4 3 4 4 8 5 7 12 3 4 2 4 4 9 7 5 2 3 4 3 3 4 10 7 9 10 2 3 4 4 4 Total Possible 8 12 12 4 4 4 4 4 Scaled Average 3 40 310 3 33 340 380 340 3 50 3 50 Std Dev 123 170 163 0 70 063 0 70 on 071 T Figure A 2 Lab report score entries in the workbook for one student A 2 4 Assessment of the outcomes for the course As explained earlier the performance criteria such as A 1 A 2 A 3 are used to describe a set of measurable statements to define each learning outcome Up to this point we explained how to assess each performance criterion using the pre labs the lab reports and the scoring sheets A single score for each outcome can be computed to indicate the level of attainment of that outcome by the entire class One approach is to simply average the scores for the performance criteria for that outcome For example in case of outcome A you can use SCOREA 1 SCORE4 2 SCORE 4_3 3 SCORE A 1 Another possibility is to use a weighted average where some of the performance criteria are considered to be more important than the others In case of outcome A you can use SCORE wi SCOREA 4 4 Ka Oa w3 SCORE4 3 A 2 where w1 wz and ws are weights you can assign on the 0 to 1 scale for the performance criteria A 1 A 2 and A 3 respectively The total of all weights should equal 1 QNET ROTPENT Laboratory Manual Instructor Manual A 2 5 Course Sco
21. 33 z00 250 5 0 1 55 Voltage V Input Voltage W 1 7 0 75 time s 1 8 0 1 8 5 QNET ROTPENT Laboratory Manual Instructor Manual EET ID Label Symbol Description Unit 1 Theta 9 Arm angle numeric display measured by en deg coder on motor 2 Alpha a Pendulum angle numeric display measured deg by encoder on pendulum pivot 3 Current Im Motor armature current numeric display A 4 In Range Balance controller is engaged when this LED is turns bright green 5 Energy Numeric display of the pendulum energy mJ 6 Signal Type Type of signal generated for the arm refer ence signal i e desired angle of arm 7 Amplitude Reference position amplitude input box deg 8 Frequency Reference position frequency input box Hz 9 Offset Reference position offset input box deg 10 Disturbance Visa Apply simulated disturbance voltage V 11 Amplitude Aq Dither signal amplitude input box V 12 Frequency fa Dither signal frequency input box Hz 13 Offset Vao Dither signal offset input box V 14 kp theta kp 6 Arm angle proportional gain input box Virad 15 kp_alpha kpa Pendulum angle proportional gain input box V rad 16 kd theta kao Arm angle derivative gain input box V s rad 17 kd_alpha kaa Pendulum angle derivative gain input box V s rad 18 mu u Proportional gain for energy controller m s2 J 1
22. 4 meets the specifications given in Step 9 11 Stop the VI by clicking on the Stop button QNET ROTPENT Laboratory Manual Instructor Manual setpoint simulation Arm deg Pendulum deg 10 g ES a 3 a 2 E a 07 E 5 10 x T 1 1 1 60 61 62 63 64 65 Simulation Time b Pendulum Link Simulation Time a Rotary Arm Control Input V Amplitude I I 60 61 62 63 64 65 Simulation Time c Motor Voltage Figure 3 4 Simulated rotary inverted pendulum response QNET ROTPENT Laboratory Manual Instructor Manual GUANSER 4 BALANCE CONTROL IMPLEMENTATION 4 1 Background Balancing is a common control task In this experiment we will find control strategies that balance the pendulum in the upright position while maintaining a desired position of the arm When balancing the system the pendulum angle a is small and balancing can be accomplished simply with a PD controller If we are also interested in keeping the arm in a fixed position a feedback from the arm position will also be introduced The control law can then be expressed as u kp o 0 9 kp o T ka 90 ka 4 1 where kp is the arm angle proportional gain amp is the pendulum angle proportional gain kg is the arm angle derivative gain and k4 a is the pendulum angle derivative gain The desired angle of the arm is denoted by 0 and there is no reference for the pendulum angle beca
23. 9 Er E Reference energy for energy controller mJ 20 Max accel Umax Maximum acceleration m s 21 Activate Swing Up When pressed down the energy controller that swings up the pendulum is engaged 22 Mp Mp Mass of pendulum assembly link weight kg 23 Ip ly Center of mass of pendulum assembly m link weight input box 24 Marm Marm Mass of rotary arm kg 25 r r Length from motor shaft to pendulum pivot m 26 Jp Jp Pendulum moment of inertia relative to pivot kg m2 27 Jeq Jeq Equivalent moment of inertia acting on the DC kg m2 motor shaft 28 Kt Ki DC motor current torque constant N m A 29 Rm Rm Electrical resistance of the DC motor arma 2 ture 30 Device Selects the NI DAQ device 31 Sampling Rate Sets the sampling rate of the VI Hz 32 Stop Stops the LabVIEW VI from running 33 Scopes Angle 0 a Scope with measured arm angle in red and deg pendulum angle in blue 34 Scopes Voltage Vin Scope with applied motor voltage in red V O DUANS E R Table 5 QNET ROTPENT Swing Up Control VI Components 7 LAB REPORT This laboratory contains three groups of experiments namely 1 Modeling 2 Balance control design 3 Balance control implementation 4 Swing up control For each experiment follow the outline corresponding to that experiment to build the content of your report Also in Section 7 5 you can find some basic tips for the format of your report 7 1 Template for Conten
24. Device Selects the NI DAQ device 11 Sampling Rate Sets the sampling rate of the VI Hz 12 Stop Stops the LabVIEW VI from running 13 Scopes Angle 0 a Scope with measured arm angle in red deg and pendulum angle in blue 14 Scopes Voltage Vm Scope with applied motor voltage in V red Table 3 QNET ROTPENT Simple Modeling VI Components 08 0NET ROTPENT Control Design vi Elle Edit view Project Operate Tools Window Help 2 eje ONET ROTPEN Control Design QUANSER Symbolic Model Open Loop Analysis Simulation Model Parameters Symbolic A IMp 2 lp 2 r g eq p4 Op Kt Km Mp lp 2 KE Km Rm 40 Jeq Mp lp 2 Mp r 2 Jp Jeq Jp Jeg Mp Ip 2 rA Mp lp g Deq Mp r 2 eq Jp 1 Mp Ip r Ke Km Rm eg Jp4 o Jeq Mp ip 2 Mp r 2 Jp Jeq Mp ip 2 Mp r 2 Jp Mp lp Kt r Rm Jeq Jp Jeq Mp Ip 2 Mp r 2 3p Figure 6 2 QNET ROTPENT Control Design VI Symbolic Model tab E DUANSER 13 08 0NET ROTPENT Control Design vi File Edit View Project Operate Tools Window Help QNET ROTPEN Control Design status code NATIONAL 15 A2 INSTRUMENTS ER Symbolic Model Open Loop Analysis Simulation Open Loop Eguation Pole Zero Map 1 0 0 1 0 0 0 0 IM 0 M 0 8 18 0 22374 0274296 0 a 23713 Mt 0 36 2091 0 0703703 0 2 11322 0 6 1000 Dt 0100 17 0010 0001 0 2 0 0 0 2 4
25. Modeling Pre Lab questions in Section 2 3 DUANS E R 8 2 Simple Modeling Lab Report Student Name CONTENT FORMAT Item K 1 B 5 B 6 B 7 B 9 GS 1 GS 2 I PROCEDURE 1 1 Damping 1 2 Friction 1 3 Moment of Inertia Il RESULTS Ill ANALYSIS 1 2 3 IV CONCLUSIONS Total 1This scoring sheet corresponds to the report template in Section 7 1 QNET ROTPENT Laboratory Manual Instructor Manual E 8 3 Balance Control Design Lab Report Student Name CONTENT FORMAT Item K 1 K 2 K 3 B 5 B 7 B 9 GS 1 GS 2 I PROCEDURE 1 1 Model Analysis 1 2 Control Design and Simulation Il RESULTS Ill ANALYSIS 1 2 3 4 IV CONCLUSIONS 1 2 Total 1This scoring sheet corresponds to the report template in Section 7 2 QNET ROTPENT Laboratory Manual Instructor Manual DUANS E R NNOVATE EDUCATE 8 4 Balance Control Implementation Lab Report Student Name CONTENT FORMAT Item K 1 K 2 B 5 B 7 B 8 B 9 GS 1 GS 2 I PROCEDURE 1 1 Default Balance Control I ja 1 2 Implement Designed Balance Control 2 E 1 3 Balance Control with Friction Compensation Il RESULTS Ill ANALYSIS aj A oj N 6 IV CONCLUSIONS Total 1This scoring sheet corresponds to the report template in Section 7 3 QNET ROTPENT Laboratory Manual Instruct
26. NATIONAL INSTRUMENTS QUANSER INNOVATE EDUCATE INSTRUCTOR WORKBOOK QNET Rotary Inverted Pendulum Trainer for NI ELVIS Developed by Quanser Curriculum designed by Karl Johan str m Ph D Lund University Emeritus Jacob Apkarian Ph D Quanser Paul Karam B A SC Guanser Michel L vis M A Sc Quanser Jeannie Falcon Ph D National Instruments Curriculum complies with ABET ETT T ABET Inc is the recognized accreditor for college and university programs in applied science computing engineering and technology Among the most respected accreditation organizations in the U S ABET has provided leadership and quality assurance in higher education for over 75 years 2011 Quanser Inc All rights reserved Quanser Inc 119 Spy Court Markham Ontario L3R 5H6 Canada info guanser com Phone 1 905 940 3575 Fax 1 905 940 3576 Printed in Markham Ontario For more information on the solutions Quanser Inc offers please visit the web site at http www guanser com This document and the software described in it are provided subject to a license agreement Neither the software nor this document may be used or copied except as specified under the terms of that license agreement All rights are reserved and no part may be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying recording or otherwise without the prior written permiss
27. UP CONTROL 5 1 Background 5 1 1 Energy Control If the arm angle is kept constant and the pendulum is given an initial position it would swing with constant amplitude Because of friction there will be damping in the oscillation The purpose of energy control is to control the pendulum in such a way that the friction is constant The potential energy of the pendulum is Ep Mp glp 1 cos a 5 1 and the kinetic energy is 1 Ep 3 5 2 The potential energy is zero when the pendulum is at rest at a 0 in Figure 2 2 and equals 2M gl when the pendulum is upright at a 7 The sum of the potential and kinetic energy of the pendulum is 1 E PEL M gl 1 cosa 5 3 Differentiating 5 3 results in the differential equation E J 8 Mp g lp Sin a 5 4 Substituting the pendulum equation of motion given in Equation 2 1 for pendulum acceleration into Equation 5 4 gives E M ul acosa Since the acceleration of the pivot is proportional to current driving the arm motor and thus also proportional to the drive voltage we find that it is easy to control the energy of the pendulum The proportional control law u E E cosa 5 5 drives the energy towards the reference energy Notice that the control law is nonlinear because the proportional gain depends on the pendulum angle o Also notice that the control changes sign when changes sign and when the angle is 90 deg However for energ
28. ass of body i and m is the mass of body i From the free body diagram in Figure 2 2 the resulting nonlinear equation of motion of the pendulum is Jy t Mp gl sin a t Mp ul cos a t 2 1 where J is the moment of inertia of the pendulum at the pivot axis zo M is the total mass of the pendulum assembly u is the linear acceleration of the pivot axis and I is the center of mass position as depicted in Figure 2 2 Thus as the pivot accelerates towards the left the inertia of the pendulum causes it to swing upwards while the gravitation force Mpg and the applied force Mpu the left hand terms in Equation 2 1 pull the pendulum downwards The moment of inertia of the pendulum can be found experimentally Assuming the pendulum is unactuated lin earizing Equation 2 1 and solving for the differential equation gives the expression J My glp P Af g 2 2 where f is the measured frequency of the pendulum as the arm remains rigid The frequency is calculated using Neyc f E 2 3 where n is the number of cycles and At is the duration of these cycles Alternatively J can be calculated using the moment of inertia expression J r dm 2 4 DUANS E R where r is the perpendicular distance between the element mass dm and the axis of rotation In addition to finding the moment of inertia this laboratory investigates the stiction that is present in the system The rotor of the DC motor that moves the ROTPEN system requires a ce
29. creased however 7 Set the third element in the Q matrix to 0 i e Q 3 3 0 8 Examine and describe the change in the Arm deg and Pendulum deg scope 3 DUANS E R Answer 3 4 Outcome Solution B 7 Decreasing this LOR term makes the arm response faster but the pen dulum angle tends to overshoot more The proportional and derivative gains of the pendulum go down when Q 3 3 decreases 9 EN By varying the diagonal elements of the Q matrix design a balance controller that adheres to the following specifications e Arm peak time less than 0 75 s tp lt 0 75 s e Motor voltage peak less than 12 5 V Vm lt 12 5 V e Pendulum angle less than 10 0 deg a lt 10 0 deg Record the Q and R matrices along with the control gain used to meet the specifications in your report Answer 3 5 Outcome Solution K 3 Using the weighting matrices 40 0 0 0 0 Xu C lo 6 99 0001 and R 1 the following gain was generated K 6 32 812 2 76 10 87 Ans 3 1 10 KM Attach the responses from the Arm deg Pendulum deg and Control Input V scopes when using your designed balance controller Does it satisfy the specifications Answer 3 6 Outcome Solution K 2 The simulated closed loop response of the QNET rotary inverted pendu lum is given in Figure 3 4 This is using the LQR gain given in Equation Ans 3 1 B 9 The response in Figure 3
30. e correct position The fast motion necessary for production makes it more difficult to move the load to the correct location given the swinging motions of the crane This problem can be mimicked using the rotary pendulum system by viewing the tip of the L shaped arm as the moving trolley and the pendulum tip as the load being carried In this experiment we will begin by modeling the system and determine strategies to dampen the oscillations of the system M pg Figure 2 1 Free body diagrams of pendulum assembly Figure 2 1 shows the free body diagram of the pendulum assembly that is composed of two rigid bodies the pen dulum link with mass M and length L 1 and the pendulum weight with mass Mp2 and a length L 2 The center of mass of the the pendulum link and the pendulum weight are calculated separately using the general expression f px dz Tem pdx where z is the linear distance from the pivot axis and p is the density of the body The circle in the top left corner of Figure 2 1 represents the axis of rotation or the pivot axis that goes into the page The pendulum system is then expressed as one rigid body with a single center of mass as shown in Figure 2 2 UU ONET ROTPENT Laboratory Manual Instructor Manual i Figure 2 2 Free body diagram of composite pendulum The center of mass of a composite object that contains n bodies can be calculated using n Rm Milem i ia Mia nu where Zem is the known center of m
31. e various Can use software Can use software Cannot use 5 tools to present software tools tools correctly for tools for data software tools for 5 data in useful and their data presentation presentation with data presentation v format graphs advanced only a few or attempts to numerical table features correctly mistakes use them but with i charts diagrams for data many mistakes presentation missing labels So etc E K 3 Uses software Can use software Can use software Can use software Cannot use o 5 features correctly for simulation only a few mistakes attempts to use them but with many mistakes Table 10 OUTCOME K An ability to use the technigues skills and modern engineering tools necessary for engi neering practice O DUANS E R References 1 Quanser Inc Qnet assessment workbook microsoft excel file 2011 2 Quanser Inc QNET Rotary Pendulum Control Trainer User Manual 2011 Six GNET Trainers to teach introductory controls using NI ELVIS gt GNET DC Motor Control Trainer gt GNET HVAC Trainer gt QNET Mechatronic Sensors Trainer teaches fundamentals of DC motor control teaches temperature process control teaches functions of 10 different sensors gt GNET Rotary Inverted gt GNET Myoelectric Trainer gt QNET VTOL Trainer Pendulum Trainer teaches control using principles of teaches basic flight dynamics and control teaches classic pendulum control experiment electromyography EMG
32. et e All grammar spelling correct e References are cited GS 2 Professional e Has cover page with all neces Two of the Four of the Five or more appear sary details title course student Conditions conditions of the condi ance name s etc for the ex for the ex tions for the e Typed emplary emplary exemplary e Report layout is neat category category category Does not exceed specified maxi mum page limit Pages are numbered Equations are consecutively num bered Figures are numbered axes have labels each figure has a descriptive caption Tables are numbered they include labels each table has a descriptive caption No hand drawn sketches diagrams References are cited using correct format were not met were not met were not met Table 9 OUTCOME G Ability to communicate effectively for Lab Report FORMAT tools to simulate physical systems tools and their advanced tools correctly for simulation tools for simulation with software tools for simulation or 4 3 2 1 Code Perf Criteria Exemplary Proficient Developing Beginning or incomplete 2 K 1 Uses software Can use various Can use software Can use software Cannot use 9 tools for analysis software tools tools correctly for tools for analysis software tools for o and their analysis with only a few analysis or 5 advanced mistakes attempts to use c features correctly them but with 2 for analysis many mistakes E K 2 Uses software Can us
33. f mass of pendulum assembly m link weight input box 3 r r Length from motor shaft to pendulum pivot m 4 Jp Jp Pendulum moment of inertia relative to pivot kg m2 5 Jeq Jeq Equivalent moment of inertia acting on the DC kg m2 motor shaft 6 Bp Bp Viscous damping about the pendulum pivot N m s rad 7 Beq Be Equivalent viscous damping acting on the DC N m s rad motor shaft 8 Kt Ki DC motor current torque constant N m A 9 Km Km DC motor back emf constant V s rad 10 Rm Em Electrical resistance of the DC motor arma 9 ture 11 Symbolic A A Rotary pendulum linear state space matrix A 12 Symbolic B B Rotary pendulum linear state space matrix B 13 Symbolic C C Rotary pendulum linear state space matrix C 14 Symbolic D D Rotary pendulum linear state space matrix D 15 Stop Stops the LabVIEW VI from running 16 Error Out Displays any error encountered in the VI 17 Open Loop Equa Numeric linear state space model of rotary tion pendulum 18 Pole Zero Map Maps pole and zeros of open loop rotary pen dulum system 19 Signal Type Type of signal generated for the arm position reference 20 Amplitude Generated signal amplitude input box V 21 Frequency Generated signal frequency input box Hz 22 Offset Generated signal offset input box V 23 Disturbance Via Apply simulated disturbance voltage V 24 Q Q Linear quadratic weighting matrix that defines a penalty on the state 25 R R Linear quadratic weighting matrix that de
34. fines a penalty on the control action 26 Optimal Gain K K State feedback control gain calculated using LQR 27 Arm 9 Scope with reference in blue and measured deg in red arm angles 28 Pendulum a Scope with inverted pendulum angle in blue deg 29 Control Input Vin Scope with applied motor voltage in red V DUANS E R Table 4 QNET ROTPENT Control Design VI Components 08 QNET ROTPENT Swing Up Control vi File Edit View Project ej eu Operate Tools Window Help ONET ROTPEN Swing Up Control eb QUANSER Digital Scopes rm 1 EE 2 m Control Indicators EGRE Signal Generator Signal Type du 6 Amplitude oo deg i Frequency z looo te Offset deg 9 Disturbance QA 0 Dither Signal Amplitude VY Djo oo 1 1 Alpha Voltage In Range Eneray Offset V 99043 Figure 6 5 QNET ROTPENT Swing Up Control VI Frequency Hz js 42 Device Balance Control Parameters kp theta Vjrad TE 4 koaha tired Aoa N kd theta V srad jus kd alpha V sjrad Js 4 T7 Swing Up Control Parameters mu mjs 2 3 D 375 1 8 Er mJ Jos 1 9 max accel m s 2 er 10 2 0 Activate Swing Up qa 1 Model Parameters lo oz7o 22 po 1ss 0 0280 n 30 Jeq fio i Kt 0 0280 28 Rm 113 30 29 Sampling Rate Hz Angle Energy deg mJ 3 Arm Angle deg Pendulum Angle deg Pendulum Energy mJ 200 250
35. from above Description Symbol Value Unit Section 2 4 Friction Positive Coulomb Friction Voltage Vip 24 V Negative Coulomb Friction Voltage Vin 2 9 V Section 2 5 Moment of Inertia Calculated inertia ra 6 98 x 1077 kg m Experimentally found inertia anom 177 x 10 kg m Table 1 QNET ROTPENT Modeling results summary E DUANS E R 3 BALANCE CONTROL DESIGN 3 1 Background A rich collection of methods for finding parameters of control strategies have been developed Several of them have also been packaged in tools that are relatively easy to use Linear Quadratic Regulator LAR theory is a technique that is suitable for finding the parameters of the balancing controller in Equation 4 1 in Section 4 Given that the equations of motion of the system can be described in the form t Ax Bu the LQR algorithm computes a control task u to minimize the criterion J a t Qz t u t Ru t dt The matrix Q defines the penalty on the state variable and the matrix R defines the penalty on the control actions Thus when Q is made larger the controller must work harder to minimize the cost function and the resulting control gain will be larger In our case the state vector x is defined x e a 4 al Since there is only one control variable R is a scalar and the control strategy used to minimize cost function J is given by u K z z kp 0 Or kpala T kaob ka
36. ion of Quanser Inc Acknowledgements Quanser Inc would like to thank the following contributors Dr Hakan Gurocak Washington State University Vancouver USA for his help to include embedded outcomes assessment and Dr K J Astr m Lund University Lund Sweden for his immense contributions to the curriculum content Contents 1 2 O DUANS E R Introduction Simple Modeling 2 1 Background 2 2 Simple Modeling Virtual Instrument 2 3 Damping 15 min 24 Friction 15 min 2 5 Moment of Inertia 30 min 2 6 Results Balance Control Design 3 1 Background 3 2 Balance Control Design VI 3 3 Model Analysis 20 min 3 4 Control Design and Simulation 45 min Balance Control Implementation 4 1 Background 4 2 Balance Control VI 4 3 Default Balance Control 30 min 4 4 Implement Designed Balance Control 20 min 4 5 Balance Control with Friction Compensation 30 min Swing Up Control 5 1 Background 5 2 Swing Up Control VI 5 3 Energy Control 30 min 5 4 Hybrid Swing Up Control 20 min System Requirements 6 1 Overview of Files 6 2 Simple Modeling Laboratory VI 6 3 Control Design VI 6 4 Swing Up Control VI Lab Report 7 1 Template for Content Simple Modeling 7 2 Template for Content Balance Control Design 7 3 Template for Content Balance Control Implementation 7 4 Template for Content Swing Up Control 7 5 Tips for Report Format Scoring Sheets 8 1 Simple Modeling Pre Lab Question
37. is but incom attempts to ana analyze data of the data us of data using plete lyze with wrong ing appropriate correct methods methods a methods N B 8 Accounts for Is aware of Is aware of all Is aware of Is unaware of T experimental all potential potential experi some of the any experimen lt uncertainties experimental mental errors potential experi tal errors errors and can mental errors fully account for them with suggestions to improve them B 9 Interprets re Provides clear Provides accu Provides expla No explanation m sults with in depth accu rate explana nationsandcon or conclusions o respect to the rate explana tions and logical clusions but with are provided or 3 original hypoth tions including conclusions some errors they are wrong esis trends and based on data arrives at logical and results conclusions based on data and results Table 7 OUTCOME B An ability to design and conduct experiments as well as to analyze and interpret data O DUANS E R attention to detail Makes precise measurements surements ing to mostly correct measurements 4 3 2 1 Code Perf Crite Exemplary Proficient Developing Beginning or ria incomplete B 1 Identifies Framed a testable Framed a testable Framed a question Incomplete or no hypothesis question correctly question correctly that may or may not testable question to test and explained be testable the anticipated cause and effect expectation leading
38. is then used inside this region and energy control is used outside the region Figure 5 2 is a called a hybrid automaton and for this specific task can be used to describe the system model and the switching logic la amp a s m Swing up la evan energy control amero pasyalan Figure 5 2 Hybrid swing up controller automaton lal gt yvlal gt n The circles in Figure 5 2 are called locations and represent the two different continuous system The arrows are called edges and represent the discrete jumps taken when certain condition are satisfied The angle used in the switching logic in Figure 5 2 is called the upright angle It is defined as zero when the pendulum is about its upright vertical position and expressed mathematically using Qup a mod 27 m The various switching parameters shown in Figure 5 2 can then be set as 2deg n 720deg s y 30deg Given that the pendulum starts in the downward vertical position it is in the swing up location of the hybrid automaton The swing up controller pumps energy into the pendulum until it swings within 2 deg of its upright vertical position Once the pendulum is within that that range and does not exceed 720 deg s in either direction the edge is taken to engage the balance controller It remain in the Balance PD control location until the pendulum goes beyond the 30 deg position range or beyond 720 deg s DUANS E R 5 2 Swing Up Contro
39. iven in this section Assessment of ABET outcomes is incorporated into this manual as shown by indicators such as ESSA These indicators correspond to specific performance criteria for an outcome A 1 Pre lab Questions and Lab Experiments A 1 1 How to use the pre lab questions All or some of the questions in the Pre Lab Questions sections can be assigned to students as homework One possibility is to assign them as a homework one week prior to the actual lab session and ask the students to bring their assignment to the lab session This would help them get ready for the lab session You should encourage them to study the background section of the chapter prior to attempting the pre lab questions Note that solutions for some of the Pre Lab questions are parameters needed for the experiments in the lab session Another possibility is to go over some of these questions either in class or in the lab session together with the students This could generate an interactive learning opportunity for them prior to the lab Finally it is possible to use some of the pre lab questions in your mid term or final exams This would reinforce the concepts covered in the labs connections between the abstract theory and the real hardware and would give you an option to integrate some of the work done in the lab sessions into your exams A 1 2 How to use the laboratory experiments This manual is organized into several laboratory sections Each section contains
40. l VI The virtual instrument used to run the swing up controller on the QNET rotary pendulum system is the same as the balance control given in Section 4 2 shown in Figure 4 1 5 3 Energy Control 30 min 1 Open the QNET ROTPENT Swing Up Control vi and ensure it is configured as described in Section 6 Make sure the correct Device is chosen 2 Run the QNET ROTPENT Swing Up Control vi The VI should appear similarity as shown in Figure 4 1 3 In the Balance Control Parameters section ensure the following parameters are set e kp theta 6 50 V rad e kp alpha 80 0 V rad e kd theta 2 75 V rad s e kd alpha 10 5 V rad s 4 In the Swing Up Control Parameters section set e mu 55 m s J e Er 20 0 mJ e max accel 10 m s e Activate Swing Up OFF de pressed 5 Adjust the Angle Energy deg mJ scope scales to see between 250 and 250 see the ROTPEN User Manual 2 for help 6 Manually rotate the pendulum at different levels and examine the blue Pendulum Angle deg and the green Pendulum Energy mJ in the Angle Energy deg mJ scope The pendulum energy is also displayed numeri cally in the Control Indicators section 7 Inen What do you notice about the energy when the pendulum is moved at different positions Record the energy when the pendulum is being balanced i e fully inverted in the upright vertical position Answer 5 1 Outcome Solution B 5 If they followed the procedure correctly they shou
41. ld be able to perform the following analyssi as well as measure the energy K 1 The pendulum energy increases proportionally with the pendulum angle When being balanced the energy read is 81 0 mJ 8 Click on the Stop button to bring the pendulum down to the gantry position and re start the VI 9 In the Swing Up Control Parameters section turn ON the Activate Swing Up switch the pressed down posi tion 10 If the pendulum is not moving click on the Disturbance button in the Signal Generator section to perturb the pendulum 11 In Swing Up Control Parameters change the reference energy Er between 5 0 mJ and 50 0 mJ As itis varied examine the control signal in the Voltage V scope as well as the blue Pendulum Angle deg and the red Pendulum Energy mJ in the Angle Energy deg mJ scope Attach the response of the Angle Energy deg mJ and Voltage V scopes Answer 5 2 Outcome Solution B 7 The larger the reference energy the large the amplitude of the control signal K 2 The responses shown in Figure 5 3 are using energy control with mu 55 m s J and Er 50 mJ and max accel 10 m s Arm Angle deg aa Pendulum Angle deg Angle Energy deg mJ Pendulum Energy m3 77 250 200 25 time s a Rotary Arm Pendulum Angle and Energy Voltage V neto CT ai F Fs E us 0 0 0 5 1 0 15 2 0
42. m Amplitude J 0 0 deg Frequency J 0 10 Hz Offset J 50 0 deg Disturbance C OFF 2 Dither Signal Amplitude V 9 0 00 Frequency Hz Jj 5 00 Offset V 0 00 QNET ROTPEN Swing Up Control Device NATIONAL 2 INSTRUMENTS evi Balance Control Parameters kp theta Virad 9 6 50 Ko aha Wrad Jano kd theta V s rad J 2 75 kd alpha V s rad 9 10 5 Swing Up Control Parameters mu mjs 2 3 Jj 375 Er m3 D 55 0 max accel mjs 2 9 10 Corr 5 Activate Swing Up Model Parameters Djio oz7o 30 153 5 0 0800 j 0 0826 m J 0 000509 kg m 2 Jj 0 000698 kg m 2 50 0333 N m A Jj 8 70 ohm Sampling Rate Hz m 100 0 Angle Energy deg mJ Arm Angle deg Pendulum Angle deg Pendulum Energy m 250 1 5 D 20 25 time s Voltage v Input voltage V L 10 T59 D D 2 0 25 time s Figure 4 1 LabVIEW VI for QNET rotary pendulum balancing control and swing up 1 Open the QNET ROTPENT Swing Up Control vi and ensure it is configured as described in Section 6 Make sure the correct Device is chosen 2 Run the QNET ROTPENT Swing Up Control vi The VI should appear similarity as shown in Figure 4 1 3 In the Signal Generator section set e Amplitude 0 0 deg e Frequency 0 10 Hz e Offset 0 0 deg 4 In the Balance Control Parameters section set e kp theta 6 5 V rad e kp alpha 80 V rad e kd theta 2 75 V rad
43. mental rors and can fully ac rors mental errors Ej uncertain count for them with ties suggestions to im prove them K 1 Uses soft Can use various Can use software Can use software Cannotuse software ware tools software tools and tools correctly for tools for analysis tools for analysis for analysis their advanced fea analysis with only a few or attempts to use tures correctly for mistakes them but with many analysis mistakes B 9 Interprets Provides clear Provides accurate Provides explana No explanation or a results with in depth accurate explanations and tions and conclu conclusions are pro 9 respect to explanations in logical conclusions sions but with some vided or they are 2 the original cluding trends and based on data and errors wrong E hypothesis arrives at logical results 8 conclusions based O DUANS E R on data and results Table 8 OUTCOME G Ability to communicate effectively for Lab Report CONTENT 4 3 2 1 Code Perf Exemplary Proficient Developing Beginning or Criteria incomplete GS 1 Content e Each of the required sections is Two of the Three of the Four or none presen completed conditions conditions of the condi tation e If necessary subsections are used for the ex for the ex tions for the well or e All necessary background princi mplary emplary exemplary ganized ples and information for the experi Category category category ment are given were not met were not met were not m
44. most of sons are clearly Some are miss them are miss listed ing ing B 4 Formulates ex Developed a Developed cor Attempted but Could not perimental plan sophisticated rect experimen could not com develop an to investigate a experimen tal procedure to pletely develop accurate ex phenomenon tal procedure test the hypoth an experimental perimental complete with esis procedure to procedure details of every step to test the hypothesis test the hypoth esis Continued on the next page 4 3 2 1 Code Perf Criteria Exemplary Proficient Developing Beginning or incomplete B 5 Follows ex Follows ex Follows exper Follows ex Follows ex perimental perimental imental proce perimental perimental procedures procedures dures leading procedures procedures carefully with to correct mea with some mis with many mis B great atten surements takes leading to takes leading to tion to detail mostly correct mostly wrong 5 Makes precise measurements measurements o measurements B 6 Documents data Systematically Documents all Documents No data are collected documents all data and with data with some documented or data in an ex accurate units mistakes in the there are major emplary way units or some mistakes in the and by using data missing units accurate units Data organi zation needs improvement B 7 Uses appropri Excellent in Appropriate Some data anal No analysis or ate methods to depth analysis level of analysis ys
45. nd plane RHP move further into the RHP when the inertia is decreased This implies that it s is easier to stabilize or bal ance an inverted pendulum that has a larger moment of inertia Which makes sense from a practical standpoint e g it s easier to balance a broom stick with one hand then it is a pencil 9 Reset the pendulum moment of inertia Jp back to 1 77 x 1074 kg m 10 Stop the VI by clicking on the Stop button 3 4 Control Design and Simulation 45 minl 1 Open the ANET ROTPENT Control Design vi gt WwW N Select the Simulation tab Run the VI The VI running is shown Figure 3 3 In the Signal Generator section set e Amplitude 45 0 deg e Frequency 0 20 Hz e Offset 0 0 deg 5 Set the Q and R LQR weighting matrices to the following e Q 1 1 10 i e set first element of Q matrix to 10 e R 1 Changing the Q matrix generates a new control gain 6 EZS The arm reference in red and simulated arm response in blue are shown in the Arm deg scope How did the arm response change How did the pendulum response change in the Pendulum deg scope Answer 3 3 Outcome B 5 K 1 Solution If the VI was ran correctly they should be able to make the following observations The arm response becomes faster i e peak time decreases mainly due to the increased arm proportional gain In the pendulum tends to deflect form its vertical position more as the gain is in
46. ng E notation graphs 2 diagrams etc 2 are used lt A 3 Explains results Explains the Explains the Some There are no result in the result in the explanation of explanations of context of the context of the the result is the result or an completed completed provided but it attempt was calculations by calculations does not made to provide providing Logical demonstrate an explanation complex conclusions are logical but it is reasoning and drawn reasoning incomplete or interpretations wrong Clear logical conclusions are drawn Table 6 OUTCOME A An ability to apply knowledge of mathematics science and engineering O DUANS E R 4 3 2 1 Code Perf Criteria Exemplary Proficient Developing Beginning or incomplete B 1 Identifies hy Framed a Framed a Framed a ques Incomplete or pothesis to testable ques testable ques tion that may no testable test tion correctly tion correctly or may not be question and explained testable the anticipated cause and effect expecta tion leading to the question 5 B 2 Identifies inde All variables All variables Most variables None or only a 8 pendent and are identified are identified are identified few variables a dependent correctly expla correctly correctly are identified variables nations about correctly their relations are provided B 3 Lists assump All assumptions All assumptions Assumptions No assumptions tions made and their rea are listed are listed but listed or
47. ntroller to balance the rotary inverted pendulum system can be designed using the Linear Quadratic Regulator LOR optimization technique as shown in the Simulation tab in Figure 6 4 The resulting closed loop inverted pendulum system can be simulated Table 4 lists and describes the main elements of the ROTPENT Control Design virtual instrument user interface Every element is uniquely identified through an ID number and located in figures 6 2 6 3 and 6 4 6 4 Swing Up Control VI The QNET Rotary Pendulum Trainer Swing Up Control VI implements an energy based control that swings up the pendulum to its upright vertical position and a state feedback controller to balance the pendulum when in its upright position The main elements of the VI front panel are summarized in Table 5 and identified in Figure 6 5 through the corresponding ID number Description 1 Theta 9 Arm angle numeric display measured by deg encoder on motor 2 Alpha a Pendulum angle numeric display mea deg sured by encoder on pendulum pivot 3 Current Im Motor armature current numeric display A 4 Voltage Vin Motor input voltage numeric display V 5 Signal Type Type of signal generated for the input voltage signal 6 Amplitude Generated signal amplitude input box V 7 Frequency Generated signal frequency input box Hz 8 Offset Generated signal offset input box V 9 Disturbance Via Apply simulated disturbance voltage V 10
48. odule e ELVIS II Users NI ELVISmx installs required NI DAQmx drivers e ELVIS I Users NI DAQmx ELVIS CD 3 0 1 or later installed il Caution Ifthese are not all installed then the VI will not be able to run Please make sure all the software and hardware components are installed If an issue arises then see the troubleshooting section in the QNET ROTPENT User Manual 2 6 1 Overview of Files File Name Description QNET ROTPENT User Manual pdf This manual describes the hardware of the QNET Rotary Pendulum Trainer system and how to setup the system on the ELVIS QNET ROTPENT Workbook Stu This laboratory guide contains pre lab questions and lab dent pdf experiments demonstrating how to design and implement controllers on the QNET DCMCT system LabVIEW QNET ROTPENT Simple Modeling vi Apply voltage to DC motor and examine the arm and pen dulum responses QNET ROTPENT Control Design vi Design and simulate LOR based balance controller QNET ROTPENT Swing Up Control vi Swing up and balance pendulum QNET DCMCT Workbook Instructor pdf Same as the student version except it includes the exer cise solutions Table 2 Instructor design files supplied with the QNET ROTPENT Laboratory 6 2 Simple Modeling Laboratory VI The QNET ROTPENT Simple Modeling VI is shown in Figure 6 1 It runs the DC motor connected to the pendulum arm in open loop and plots the corresponding pendulum arm and
49. or Manual pg 8 5 Swing Up Control Lab Report Student Name CONTENT FORMAT Item K 1 K 2 B 5 B 7 B 9 GS 1 GS 2 I PROCEDURE 1 1 Energy Control 1 2 Hybrid Swing Up Control Il RESULTS Ill ANALYSIS 1 2 3 IV CONCLUSIONS Total 1This scoring sheet corresponds to the report template in Section 7 4 QNET ROTPENT Laboratory Manual Instructor Manual GUANSER Appendix A CINET Instructor s Guide Every laboratory in this manual is organized into four parts Background section provides all the necessary theoretical background for the experiments Students should read this section first to prepare for the Pre Lab guestions and for the actual lab experiments Virtual Instrument introduces the LabVIEW Virtual Instrument that is to be used for the lab experiment Lab Experiments section provides step by step instructions to conduct the lab experiments and to record the col lected data The lab may also include a set of pre lab questions that need to be done prior to the lab experiments System Requirements section describes all the details of how to configure the hardware and software to conduct the experiments It is assumed that the hardware and software configuration have been completed by the instructor or the teaching assistant prior to the lab sessions However if the instructor chooses to the students can also configure the systems by following the instructions g
50. ourse Disclaimer The opionions expressed or the assessment techniques described here have not been endorsed by ABET in any way DUANS E R Recall that for fulfillment of Criterion 3 a program must document the assessment process Programs collect sam ple student work in the academic year prior to the site visit by an ABET team You can retain the sample homeworks lab reports their scoring sheets and the assessment workbook as evidence for the ongoing assessment effort in your course This collection can then be given to the assessment committee in your program to be incorporated into the program level evidence they will compile prior to the ABET site visit A 2 2 How to score the pre lab questions If you choose to assign the pre lab questions as homework then the outcome targetted by these questions can be assessed using the student work The pre lab questions require students to apply their math and engineering science knowledge through calculations and problem solving strategies Therefore outcome A was mapped to the pre lab questions through its performance criteria If you assign the pre lab questions as homework you can score the returned homeworks using the rubric for outcome A given in Section A 3 and the scoring sheet provided for that pre lab in that chapter To score homework of one student 1 Print the scoring sheet for the Pre Lab Questions section you assigned as homework One sheet is used per student
51. own in Figure A 5 Of course if you are excluding a pre lab then do not enter any scores for the students under those columns K L M N o P Q Overall Pre Lab Questions Beam and Ball Pre Lab Questions 2 88 2 00 3 25 3 75 3 09 3 91 3 64 2 82 532822 3 20 SON SSRN SNES Os Jes SP ATOR eee 5883 20 Average 2 99 3 41 3 06 std Dev f 0 56 0 44 0 65 SCORE for A wojo y 4 ORD 0 to O Figure A 5 Enter 0 to exclude or correct totals to include a Pre Lab assignment in the calculation of the overall Scores A 3 Rubrics 4 3 2 1 Code Perf Criteria Exemplary Proficient Developing Beginning or incomplete A 1 Has strategies Uses a Uses an Has a strategy Uses a wrong to solve the sophisticated appropriate for solution but strategy or there problem strategy strategy for content is no evidence Employs refined solution knowledge has of a strategy s and complex Content some Content 9 reasoning to knowledge is conceptual knowledge has S arrive at the used correctly errors many errors 2 solution es A 2 Performs Arrived at Arrived at Arrived at No answer or calculations correct answer correct answer correct answer arrived at wrong 9 Calculations are with correct Calculations are answer S complete calculations mostly correct Calculations are o Precise math but there are mostly or il language some minor completely symbolic errors wro
52. procedure in Step 6 in Section 3 4 ll RESULTS Do not interpret or analyze the data in this section Just provide the results 1 LQR matrices and control gain found in Step 9 in Section 3 4 2 Simulated closed loop response plot from Step 10 in Section 3 4 Ill ANALYSIS Provide details of your calculations methods used for analysis for each of the following 1 Open loop poles in Step 6 in Section 3 3 2 Effect of changing moment of inertia on open loop poles in Step 8 in Section 3 3 3 Effect of changing LQR elements on response in Step 6 in Section 3 4 4 Effect of changing different LQR element on the response in Step 8 in Section 3 4 IV CONCLUSIONS Interpret your results to arrive at logical conclusions for the following 1 Does lowering the moment of inertia of the pendulum have the expected result Step 8 in Section 3 3 2 Does the simulation match the specifications in Step 10 in Section 3 4 E DUANS E R 7 3 Template for Content Balance Control Imple mentation I PROCEDURE 1 Default Balance Control e Briefly describe the main goal of the experiment e Briefly describe the experimental procedure in Step 8 in Section 4 3 2 Implement Designed Balance Control e Briefly describe the main goal of the experiment e Briefly describe the experimental procedure in Step 7 in Section 4 4 3 Balance Control with Friction Compensation e Briefly describe the main goal of this experiment e Briefly describe the
53. r signal Answer 4 6 Outcome Solution K 1 The Dither signal applied a sinusoidal voltage signal to the motor This is added to the balance control signal Adding the Dither reduces the amount of arm oscillation For example without the Dither the arm would oscillate between 25 and 40 degrees When adding a Dither with 3 50 V at 2 50 Hz the arm would oscillate between 5 and 13 degrees 7 Increase the Frequency in the Dither Signal section starting from 1 00 to 10 0 Hz 8 How does this effect the pendulum arm response Answer 4 7 Outcome Solution B 7 In general increasing the frequency minimizes the amount the arm os cillation about a certain angle For example the arm will tend to move back and forth more with a Dither of 3 0 V at 1 0 Hz then with a Dither of 3 0 V at 2 5 Hz However increasing the Dither frequency too much causes the pendulum arm to vibrate without improving the swing that much 9 EX Set the Dither Signal properties according to the friction measured in Section 2 4 How does this effect the pendulum arm response QNET ROTPENT Laboratory Manual Instructor Manual Answer 4 8 Outcome Solution B 9 By using the identified Coulomb friction the oscillatory arm angle re sponse should be minimized optimally 10 Click on the Stop button to stop running the VI QNET ROTPENT Laboratory Manual Instructor Manual GUANSER i 5 SWING
54. re for outcome A The assessment workbook 1 incorporates the simple average approach as shown in Figure A 3 K L M N o P Q R Overall Pre Lab Questions Beam and Ball Pre Lab Questions gt w j NN RP Oo P Oc co Co CO wicoleo NN co b oO c co Oc o w S Ee bad bil Pel bad ill sal Real o w 3 04 3 38 3 13 N Average Std Dev r r 0 47 0 40 0 62 SCORE for A Figure A 3 Computation of single score for outcome A in the assessment workbook A 2 6 Course Scores for outcomes B K and G Similarly the simple average approach is also used for outcomes B K and G Referring to the rubrics in Section A 3 it should be noted that outcome G contains performance criteria for both B and K to assess the content of the report In addition there are two performance criteria GS 1 and GS 2 to assess the format of the report The scores for all of these performance criteria are averaged to arrive at the single score for outcome G For example the single score for outcome G in Figure A 4 for the Modelling experiment was calculated using SCOREg AVERAGE Sx 1T SK 2 Sp_5 Sp_6 Sp_7 Sp_9 Ses_1 Sas 2 A 3 where Sy Sos are the scaled average scores for K 1 through GS 2 in the workbook B c D E F G H I J K Modelling ort Content Report Format ID K 1 mi B 6 B 7 B 9 GS 1 GS 2 1 6 10 12 3 5 3 4 3
55. rtain amount of current to begin moving In addition the mass from the pendulum system requires even more current to actually begin moving the system The friction is particularly severe for velocities around zero because friction changes sign with the direction of rotation See Wikipedia for more information on center of mass inertia pendulum and friction 2 2 Simple Modeling Virtual Instrument The virtual instrument for studying the physics of the pendulum when in the gantry configuration is shown in Figure 2 3 07 QNET ROTPENT Simple Modeling vi Eile Edit View Project Operate Tools Window Help gt QNET ROTPEN Simple Modeling NATIONAL Device Sampling Rate Hz INSTRUMENTS yr i 250 0 Ae IEN IGU NSER Angle deg Pendulum Angle deg 100 Digital Scopes Theta iis Ru deg Current o0 f A Voltage o1 y Signal Generator Signal Type m Amplitude Joco y Frequency Jo zs Hz 100 5 0 Offset j 0 00 y Voltage V Disturbance OFF Figure 2 3 LabVIEW VI for modeling QNET rotary pendulum 2 3 Damping 15 minl 1 Ensure the QNET ROTPENT Simple Modeling VI is open and configured as described in Section 2 2 Make sure the correct Device is chosen 2 Run the QNET ROTPENT Simple Modeling vi shown in Figure 2 3 3 Hold the arm of the rotary pendulum system stationary and manually perturb the pendulum 4 While still holding the arm examine the respon
56. s 8 2 Simple Modeling Lab Report 8 3 Balance Control Design Lab Report 8 4 Balance Control Implementation Lab Report 8 5 Swing Up Control Lab Report QNET Instructor s Guide AA Pre lab Questions and Lab Experiments A 2 Assessment for ABET Accreditation A 3 Rubrics CO Ooo b 1 INTRODUCTION Regulation and servo problems are very common but feedback can be used in many other useful ways The name task based control is used as a common classification of a wide variety of problems For instance stabilization of an unstable system can be considered a task based problem However it is a borderline example since it can also be viewed as a regulation problem The Segway transporter is a typical example where stabilization is a key task In that case stabilization is also merged with the steering functions Other examples are damping of a swinging load on a crane stabilization of a rocket during take off and the human posturing systems There are many examples of task based control in aerospace such as automatic landing and orbit transfer of satellites Robotics is a rich field for task based control with challenges such as collision avoidance motion planning and vision based control Task based control is typically more complicated than regulation and servoing but they may contain servo and regulation functions as sub tasks We have chosen the rotary pendulum system to illustrate task based control The QNET rotary inverted pendulum
57. s e kd alpha 10 5 V rad s 5 In the Swing Up Control Parameters section set e mu 55 m s2 J e Er 20 0 mJ e max accel 10 m s2 e Activate Swing Up OFF de pressed 6 Adjust the Angle Energy deg mJ scope scales to see between 250 and 250 see Reference 2 for help Q QUAN SER QNET ROTPENT Laboratory Manual Instructor Manual v 1 0 7 Manually rotate the pendulum in the upright position until the n Range LED in the Control Indicators section turns bright green Ensure the encoder cable does not interfere with the pendulum arm motion 8 GMN Vary Offset and observe the Arm Angle deg response in the Angle Energy deg mJ scope Do not set the Offset too high or the encoder cable will interfere with the pendulum arm motion Answer 4 1 Outcome Solution B 5 If the VI was ran correctly and the pendulum is being balance then they should be able to make some observations below K 1 The Offset input box in the Signal Generator generates a constant set point The rotary arm is stabilized about the set offset angle 9 As the pendulum is being balanced describe the red Arm Angle deg and the blue Pendulum Angle deg responses in the Angle Energy deg mJ scope Answer 4 2 Outcome Solution K 1 Both are stabilized but students may notice that the rotary arm tends to rotate back and forth about the set offset angle 10 In the Signal Generator section set
58. se of Pendulum Angle deg in the Angle deg scope This is the response from the pendulum system 5 Repeat 3 above but release the arm after several swings 6 Inn Examine the Pendulum Angle deg response when the arm is not fixed This is the response from the rotary pendulum system Given the response from the pendulum and rotary pendulum system which converges faster towards angle zero Why does one system dampen faster than the other Answer 2 1 Outcome Solution B 5 If the procedure was followed correctly they should be able to draw some conclusions based on examined responses B 7 The rotary pendulum system converges to angle zero more rapidly The rotary pendulum system is naturally more damped due to the coupling effect between the rotary arm and pendulum link 7 Stop the VI by clicking on the Stop button 2 4 Friction 15 minl 1 Run the QNET ROTPENT Simple Modeling vi 2 In the Signal Generator section set e Amplitude 0 V e Frequency 0 25 Hz e Offset 0 0 V 3 Change the Offset in steps of 0 10 V until the pendulum begins moving Record the voltage at which the pendulum moved 4 Repeat Step 3 above for steps of 0 10 V 5 In Enter the positive Vfp and negative voltage Vn values needed to get the pendulum moving Why does the motor need a certain amount of voltage to get the motor shaft moving Answer 2 2 Outcome Solution B 5 If the procedure was followed correctl
59. several experiments which are for the most part independent of each other Therefore one possible way to use this material is to conduct the individual experiments in your weekly lab sessions Another possibility is to divide the class into teams and have each team conduct an experiment given in a section A g Assessment for ABET Accreditation In the United States accreditation is a peer review process Educational institutions or programs volunteer to un dergo this review periodically to determine if certain criteria are being met The Accreditation Board for Engineering and Technology ABET is responsible for the specialized accreditation of educational programs in applied science computing engineering and technology ABET accreditation is assurance that a college or university program meets the quality standards established by the profession for which it prepares its students It is the responsibility of the program seeking accreditation to demonstrate clearly that the program meets a set of criteria One of these criteria is the Criterion 3 Program Outcomes Engineering programs must demonstrate that their students attain program outcomes a through k Much more information about this can be found in the Criteria for Engineering Accreditation document ABET publishes on its website annually http www abet org For fulfillment of Criterion 3 a program must show that there is an assessment and evaluation process in place that
60. shown in Figure 3 1 Select the Symbolic Model tab gt O N The Model Parameters array includes all the rotary pendulum modeling variables that are used in the state space matrices A B C and D c1 Select the Open Loop Analysis tab shown in Figure 3 2 6 EZA This shows the numerical linear state space model and a pole zero plot of the open loop inverted pendulum system What do you notice about the location of the open loop poles How does that affect the system Recommended In the Model Parameters section it is recommended to enter the pendulum moment of inertia Jp be determined experimentally in Section 2 5 Answer 3 1 Outcome Solution B 5 If the VI was ran correctly they should be able to draw some conclusions based on the pole locations B 7 The inverted rotary pendulum system is unstable because there is one pole in the right hand plane 7 In the Symbolic Model tab set the pendulum moment of inertia Jp to 1 0 x 107 kg m 8 MGM Select the Open Loop Analysis tab How did the locations of the open loop poles change with the new inertia Enter the pole locations of each system with a different moment of inertia Are the changes of having a pendulum with a lower inertia as expected Answer 3 2 Outcome K 1 B 9 Solution The poles are at 9 0 9 2 0 35 0 for J 1 7 x 1074 kg m and 11 11 3 0 35 0 for Jp 1 0 x 10 kg m The poles in the right ha
61. t Simple Modeling PROCEDURE 1 Damping e Briefly describe the main goal of the experiment e Briefly describe the experiment procedure in Step 6 in Section 2 3 2 Friction e Briefly describe the main goal of the experiment e Briefly describe the experiment procedure in Step 5 in Section 2 4 3 Moment of Inertia e Briefly describe the main goal of the experiment e Briefly describe the experiment procedure in Step 4 in Section 2 5 Il RESULTS Do not interpret or analyze the data in this section Just provide the results 1 Provide applicable data collected in this laboratory from Table 1 Ill ANALYSIS Provide details of your calculations methods used for analysis for each of the following 1 Damping analysis in step 6 in Section 2 3 2 Finding friction in step 5 in Section 2 4 3 Calculating moment of inertia of pendulum in step 4 in Section 2 5 IV CONCLUSIONS Interpret your results to arrive at logical conclusions for the following 1 How well does the experimentally derived moment of inertia compare with analytically derived value in step 5 of Section 2 5 UU ng NEN 7 2 Template for Content Balance Control Design I PROCEDURE 1 Model Analysis e Briefly describe the main goal of the experiment e Briefly describe the experimental procedure in Step 6 in Section 3 3 2 Control Design and Simulation e Briefly describe the main goal of the experiment e Briefly describe the experimental
62. th accurate with some mistakes mented or there are lected an exemplary way units in the units or some major mistakes in and by using accu data missing Data the units rate units organization needs improvement K 2 Uses soft Can use various Can use software Can use software Cannot use soft 2 ware tools software tools and tools correctly for tools for data pre ware tools for data a to present their advanced fea data presentation sentation with only a presentation or c data in use tures correctly for few mistakes attempts to use ful format data presentation them but with many graphs mistakes missing numeri labels etc cal table charts diagrams K 3 Uses soft Can use software Can use software Can use software Cannot use software ware tools tools and their ad tools correctly for tools for simulation tools for simulation to simulate vanced features simulation with only a few or attempts to use physical correctly for simula mistakes them but with many systems tion mistakes B 7 Uses appro Excellent in depth Appropriate level of Some data analysis No analysis or at priate meth analysis of the data analysis of data us but incomplete tempts to analyze ods to ana using appropriate ing correct methods with wrong methods lyze data methods B 8 Accounts Is aware of all poten Is aware of all poten Is aware of some of Is unaware of any 2 for exper tial experimental er tial experimental er the potential experi experimental errors ES i
63. to the question B 2 Identifies All variables are All variables are Most variables are None or only a few indepen identified correctly identified correctly identified correctly variables are identi dent and explanations about fied correctly o dependent their relations are 3 variables provided 9 B 3 Lists as All assumptions and All assumptions are Assumptions are No assumptions e sumptions their reasons are listed listed but some are listed or most of a made clearly listed missing them are missing B 4 Formulates Developed a sophis Developed correct Attempted but could experimen ticated experimental experimental pro not completely tal plan to procedure complete cedure to test the develop an experi investigate with details of every hypothesis mental procedure to a phe step to test the hy test the hypothesis nomenon pothesis Could not develop an accurate experi mental procedure B 5 Follows ex Follows experi Follows experimen Follows experimen Follows experimen perimental mental procedures tal procedures lead tal procedures with tal procedures with procedures carefully with great ing to correct mea some mistakes lead many mistakes lead ing to mostly wrong measurements Continued on the next page 4 3 2 1 Code Perf Crite Exemplary Proficient Developing Beginning or ria incomplete B 6 Documents Systematically doc Documents all data Documents data No data are docu data col uments all data in and wi
64. um response from Step 11 in Section 5 3 Ill ANALYSIS Provide details of your calculations methods used for analysis for each of the following 1 Energy at different pendulum position in Step 7 in Section 5 3 2 Effect of changing reference energy in Step 11 in Section 5 3 3 Effect of changing proportional gain in Step 11 in Section 5 3 IV CONCLUSIONS Interpret your results to arrive at logical conclusions for the following 1 Reference energy required to swing up pendulum in Step 10 of Section 5 4 5 DUANS E R 7 5 Tips for Report Format PROFESSIONAL APPEARANCE Has cover page with all necessary details title course student name s etc Each of the required sections is completed Procedure Results Analysis and Conclusions e Typed e All grammar spelling correct e Report layout is neat e Does not exceed specified maximum page limit if any e Pages are numbered Equations are consecutively numbered Figures are numbered axes have labels each figure has a descriptive caption e Tables are numbered they include labels each table has a descriptive caption Data are presented in a useful format graphs numerical table charts diagrams e No hand drawn sketches diagrams References are cited using correct format 8 SCORING SHEETS 8 1 Simple Modeling Pre Lab Questions Student Name Question A 1 A 2 A 3 i Total 1This scoring sheet is for the Simple
65. use the desired position is zero There are many different ways to find the controller parameters As discussed in Section 3 1 one method is based on LQR optimal control Initially however the behaviour of the system will be explored using default parameters When balancing the pendulum over a fixed point the arm tends to oscillate about that reference because of the friction present in the motor Due to friction the motor will not move until the control signal is sufficiently large and the generated torque is larger than the stiction see Section 2 1 for more details This means that the pendulum has to fall a certain angle before the motor moves and the net result is an oscillating motion Friction can be compensated by introducing a Dither signal at the input voltage of the DC motor The Dither signal used has the form Va Aasin fat Vao where A is the voltage amplitude f4 is the sinusoid frequency and Vag is the offset voltage of the signal See Wikipedia for more information on PID and friction 4 2 Balance Control VI The virtual instrument used to run the balance controller and the swing up shown later on the QNET rotary pen dulum system is shown in Figure 4 1 4 3 Default Balance Control 30 min 08 QNET ROTPENT Swing Up Control vi Operate Tools Window Help gt Q Digital Scopes e ETE h REI deo vo DENN Control Indicators In Range lll Energy 7 mJ Signal Generator Signal Type
66. y they should be able to draw some conclusion based on examined responses B 7 The positive and negative Coulomb friction voltages recorded are Vs 2 1 V and Vy 2 9 V These results will vary between QNET ROTPEN systems To overcome the friction in the motor a certain amount of current is required to make the rotor move The amount of voltage in either direction varies between 1 0 V and 3 0 V 6 Stop the VI by clicking on the Stop button 2 5 Moment of Inertia 3O min 2 5 1 Pre Lab Questions 1 LARRYA Find the moment of inertia acting about the pendulum pivot using the free body diagram Make sure you evaluate numerically using the parameters defined in the QNET ROTPEN User Manual 2 Q DUAN SER Answer 2 3 Outcome A 1 A 2 Solution Use Equation 2 4 with the pendulum free body diagram given in Figure 2 1 to find its moment of inertia Using Equation 2 4 on the FBD in Figure 2 1 Lpi LpidLp2 Jd n dr p r dr 0 L pl 1 1 3 Mni Lor Mp2 Lgi Mp3 Lg Lp2 3 Mp2 LA When evaluated with the pendulum parameters given in the QNET Ro tary Pendulum User Manual 2 Jp 6 98 x 1074 kg m 2 5 2 In Lab Exercises 1 Run the QNET_ROTPENT_Simple_Modeling vi 2 Inthe Signal Generator section set e Amplitude 1 0 V e Frequency 0 25 Hz e Offset 0 0 V 3 Click on the Disturbance toggle switch to perturb the pendulum and measure the amount of
67. y to change quickly the magnitude of the control signal must be large As a result the following swing up controller is implemented in the LabVIEW VI u Sat u Er E sign cos a 5 6 where is a tunable control gain and the sat function saturates the control signal at the maximum acceleration of the pendulum pivot umar See Wikipedia for more information on potential energy kinetic energy control theory and nonlinear control 5 1 2 Hybrid Swing Up Control The energy swing up control in 5 5 or 5 6 can be combined with the balancing control law in 4 1 to obtain a control law which performs the dual tasks of swinging up the pendulum and balancing it As illustrated in Figure 5 1 this can be accomplished by switching between the two control systems Oar RENT Labor an NAN Swing up energy control Rotary Pendulum u f E a L4 Switching strategy see Balance Control u K x x Figure 5 1 Swing up hybrid control This system can be modeled as a hybrid system Hybrid systems are systems with both continuous and discrete parts There are two continuous part the closed loop system using the swing up energy controller and the closed loop system using the PD balance controller The switching strategy is the discrete element that chooses which controller or system to run The switching logic can be obtained by determining a region in state space where the balancing works well Balancing control

QNET Rotary Pendulum Laboratory Manual

Contents

Download Pdf Manuals

Related Search

Related Contents