EE 4443/5329. LAB 3: Control of Industrial Systems. Simulation and Hardware Control (PID Design) The Inverted Pendulum. (ECP Systems-Model: 505)

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1 EE 4443/5329 LAB 3: Control of Indutrial Sytem Simulation and Hardware Control (PID Deign) The Inverted Pendulum (ECP Sytem-Model: 505) Compiled by: Nitin Swamy

2 CONTENTS 1. INTRODUCTION SAFETY ISSUES PLANT DESCRIPTION Inverted pendulum apparatu mechanical decription THE ROD DISPLACEMENT SYSTEM TRANSFER FUNCTION OPEN LOOP SYSTEM ANALYSIS QUESTIONS Quetion CONTROLLER SYNTHESIS Controller Deign Specification Quetion IMPLEMENTATION OF THE CONTROLLER ON THE REAL TIME HARDWARE Quetion TABLE OF FIGURES... 9

3 1. INTRODUCTION Thi i the firt in the erie of lab experiment that relate to control of real indutrial ytem. The intent of thee experiment i to introduce the tudent to realworld problem in control, uch a ytem nonlinearitie and modeling error. The lab will involve a two-fold approach. A model of the indutrial plant to be control will be provided. The tudent will firt ue thi mathematical model to deign a uitable controller for the ytem that will tabilize key ytem parameter. The deign will be validated by imulation. After confirming that the deign meet given pecification, the tudent will then implement their deign on the actual hardware. Comparion will be made after the experiment i run between the imulation and the actual implementation. 2. SAFETY ISSUES Do not turn the ECP equipment on without the conent of the intructor. Make ure that there i enough room between you and the hardware.do not deviate from the given pecification. Failure to comply with thi may reult in eriou damage to the hardware and ha the rik of peronal injury a well! 3. PLANT DESCRIPTION 3.1 Inverted pendulum apparatu mechanical decription The ECP ytem inverted pendulum mechanical layout i hown in Fig. 1. A it can be een, there are two ytem involved. One ytem i inverted pendulum angular movement and the other i the rod diplacement. Thoe two are coupled into complex mechanical ytem. There i only one actuator for the whole ytem, DC ervomotor. Drive haft angle and liding rod diplacement are meaured uing encoder. Encoder output i the number of count.

4 Fig. 1: Inverted pendulum apparatu 4. THE ROD DISPLACEMENT SYSTEM TRANSFER FUNCTION Lab 3 deal with the rod diplacement conventional control. The implified tranfer function in Laplace domain for the rod diplacement ubytem i given in equation ( 4-1 ): k hw G() = m1j 4 J oe + (m l 2 1 o + (m l 1 o m g m 2lc ) J 2 c 2 l )g m 1 g J 2 ( 4-1 ) where: Laplace operator m 1 = kg m 2 = kg

5 g = kgm -2 J = kgm 2 J oe = kgm 2 l o = 0.33 m l c = m k hw = x hardware gain 5. OPEN LOOP SYSTEM ANALYSIS QUESTIONS The anwer on the quetion below hould be included in the lab report. The anwer hould be hort, but tudent hould explain how the concluion in the anwer were drawn. For example, if the quetion i: "I the open loop ytem table?", the anwer cannot be imply ye or no, but tudent hould explain how that concluion wa drawn, what calculation how that the ytem i table or untable or what characteritic of the ytem how that ytem i table or untable. The anwer hould be illutrated by the matlab routine, graph, calculation reult and procedure, o it i clear how the analyi wa conducted. If Matlab wa ued to obtain needed reult, give the matlab program and routine ued to olve the problem. Write them with uitable comment. 5.1 Quetion 1. I open loop ytem given in ( 4-1 ) table or untable? 2. I open loop ytem given in ( 4-1 ) controllable? 3. I open loop ytem given in ( 4-1 ) obervable? 6. CONTROLLER SYNTHESIS For the lab 3 the controller ynthei hould be conducted uing root locu method. The tudent hould ue root locu method to find uitable compenator. Then the cloed loop ytem hould be analyzed. The imulation of the cloed loop ytem ha to be conducted and the imulation reult hould be given a the part of the lab report. 6.1 Controller Deign Specification The following pecification need to be met while deigning the controller: 1. Peak overhoot in % ( POV) Maximum control effort < 1.3 Volt ( Practical limitation of hardware! ) 3. Settling time T < 15 econd 4. Steady tate error 1.4 %.

6 6.2 Quetion The quetion after the quetion No 1 hould be anwered only if the anwer for the quetion 1 i "ye". 1. I it poible to deign the controller for the ytem given in ( 4-1 )? 2. Ue root locu method to deign the controller (compenator). Decribe the deign procedure. Be ure that the compenator can be realized (no zero can be ued that are not compenated by the pole). In the report write the compenator in it mathematical form. 3. Plot the root locu of the cloed loop ytem. How it can be een that the cloed loop ytem i table from the root locu plot? 4. Include the cloed loop pole and zero in the report. Can you draw ome concluion on the ytem repone baed on the cloed loop pole and zero? 5. Simulate the cloed loop ytem tep repone. The input tep value hould be 500 count. Plot the tep repone. 6. Analyze the tep repone. Give the peak value, ettling time and natural frequency of the ytem. Compare the repone with the pole and zero of the ytem. Are the reult of the imulation a expected? Explain how you have obtained the peak value, ettling time and natural frequency. Illutrate with figure if neceary. 7. Plot the error, the rod diplacement and the control output for the time pan t = IMPLEMENTATION OF THE CONTROLLER ON THE REAL TIME HARDWARE The controller obtained hould be implemented on the real time hardware. Lab etup i conited of ECP model 505 (inverted pendulum) with the Mini PMAC V1.16D card inide PC. The oftware ued for the real time control i QRTS ECP extenion form Matlab R12/Simulink 4. It work under Real Time Workhop and Real Time Window Target for Simulink 4. The Simulink block diagram i hown in Fig. 2.

7 &! "! # Fig. 2: Simulink block diagram for running QRTS ECP extenion Student hould ue their own compenator (block "comp"). The reference value hould be tep of 500 count at t = 0 and then tep from 500 count to 0 at t = 15. The whole experiment hould be conducted for the time pan t = 30. The reference value time plot i hown in Fig. 3. $% ' ( ) * Fig. 3: Reference value for the experiment Mini Pmac Server Module (green block) i the hardware interface module ued to run the hardware. By double click on that module you can change number of encoder that will be read from the hardware etup.

8 Safety module (red block) are ued to protect the hardware from the poible damage due to controller improper operation. The controller deigned a a part of the olution for the ection 6 hould be in the place of the block "controller" in Fig Quetion 1. Implement you own compenator and run the experiment with the given reference value for Plot the rod diplacement, reference value, control effort and the control error. 3. What can you conclude from the experiment reult? Are there ignificant nonlinearitie preent in the real ytem? 4. Compare the obtained plot from the experiment with the theoretical analyi reult form ection 5. Are there ignificant difference? If o, what could caue them? What you could ay about the model given in ection 5 baed on the comparion of the experiment and imulation reult?

9 8. TABLE OF FIGURES Fig. 1: Inverted pendulum apparatu... 4 Fig. 2: Simulink block diagram for running QRTS ECP extenion... 7 Fig. 3: Reference value for the experiment... 7

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