Inverted Pendulum: Analysis, Design and Implementation

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Inverted Pendulum
Analysis, Design and Implementation

IIEE Visionaries

Document Version 1.0

Reference:
The work included in this document has been carried out in the Instrumentation and Control Lab at the Institute of Industrial Electronics Engineering, Karachi, Pakistan.

CONTENTS

4

W HAT'S INSIDE T HIS REPORT
(CONTENTS IN DETAIL)
CONTENTS IN DETAIL THE AUTHORS
ü ü

4
… … 3 6

ABOUT THE AUTHOR TECHNICAL ADVISOR

PREFACE INTRODUCTION
ü ü

… …

9 12

INTRODUCTION TO INVERTED PENDULUM APPLICATIONS OF INVERTED PENDULUM o SIMULATION OF DYNAMICS OF A ROCKET VEHICLE o MODEL OF A HUMAN STANDING STILL ü PROBLEM DESCRIPTION

MATHEMATICAL WORK
ü



19

MATHEMATICAL ANALYSIS o SETUP DESCRIPTION o INVERTED PENDULUM SYSTEM EQUATIONS o ACTUATION MECHANISM o TRANSFER FUNCTION OF THE W HOLE SYSTEM ü SYSTEM P ARAMETERS

ANALYSIS OF UNCOMPENSATED SYSTEM
ü ü ü ü ü ü POLE ZERO MAP OF UNCOMPENSATED OPEN LOOP S YSTEM IMPULSE RESPONSE OF UNCOMPENSATED OPEN LOOP S YSTEM ROOT LOCUS OF THE UNCOMPENSATED S YSTEM STEP RESPONSE OF UNCOMPENSATED OPEN LOOP S YSTEM SIMULINK M ODEL FOR THE OPEN LOOP IMPULSE RESPONSE SIMULINK M ODEL FOR THE OPEN LOOP STEP RESPONSE



26

COMPENSATION DESIGN
ü HOW CAN THE COMPENSATION BE DESIGNED? (POSSIBLE OPTIONS)



34

ROOT LOCUS SYSTEM DESIGN
ü W HY COMPENSATION IS REQUIRED? ü COMPENSATION GOALS ü COMPENSATION DESIGN T HE SISO DESIGN T OOL ü W HAT IS THE SISO DESIGN TOOL ü IMPORTING MODELS INTO THE SISO DESIGN TOOL ü OPENING THE SISO DESIGN TOOL ü DESIGN SPECIFICATIONS ü ROOT LOCUS DESIGN WITH SISO DESIGN TOOL ü ADDING POLES AND ZEROS TO THE COMPENSATOR ü PROCEDURE



36

ANALYSIS OF COMPENSATED SYSTEM
ü ü ü ü ü ü ü POLE-ZERO MAP OF COMPENSATED OPEN LOOP S YSTEM ROOT LOCUS OF THE COMPENSATED S YSTEM POLE-ZERO MAP OF COMPENSATED CLOSED-LOOP S YSTEM IMPULSE RESPONSE OF PID COMPENSATED SYSTEM STEP RESPONSE OF PID COMPENSATED S YSTEM CONCLUSION OF COMPENSATION ANALYSIS SIMULINK M ODEL FOR CLOSED-LOOP STEP RESPONSE OF COMPENSATED SYSTEM ü SIMULINK M ODEL FOR CLOSED-LOOP IMPULSE RESPONSE OF COMPENSATED SYSTEM ü SIMULINK M ODEL FOR RESPONSE TO DISTURBANCE IN THE FORCE ON THE CART OF COMPENSATED S YSTEM ü SIMULINK M ODEL FOR RESPONSE TO DISTURBANCE IN THE POSITION OF INVERTED BROOM OF COMPENSATED S YSTEM



43

PRACTICAL IMPLEMENTATION
ü CONTROLLER IMPLEMENTATION ANALOG PID CONTROLLER DESIGNS ü DESIGN 1: IDEAL PID ALGORITHM ü DESIGN 2: P ARALLEL PID ALGORITHM ü DESIGN 3: SERIES PID ALGORITHM



56

PRACTICAL RESULTS
ü EXPERIMENTAL DATA

… … …

61 63 65

CONCLUSION APPENDIX

ü M-FILE FOR D ATA OF THE INVENTED PENDULUM SYSTEM ü M-FILE FOR OPEN LOOP & CLOSED LOOP (UNCOMPENSATED) TRANSFER FUNCTION OF IP S YSTEM ü M-FILE FOR ANALYSIS OF THE UNCOMPENSATED INVERTED PENDULUM S YSTEM ü M-FILE FOR CLOSED LOOP COMPENSATED TRANSFER FUNCTION OF IP S YSTEM ü M-FILE FOR ANALYSIS OF THE COMPENSATED INVERTED PENDULUM SYSTEM ü M-FILE FOR PLOT OF E XPERIMENTAL DATA OBTAINED THRU 8051-B ASED DAQ CARD

BIBLIOGRAPHY
ü BOOKS ü PAPERS ü W EB



72

AUTHORS

œ

ABOUT THE AUTHOR
The “INVERTED PENDULUM, ANALYSIS, DESIGN AND IMPLEMENTATION ” is a collection of MATLAB functions and scripts, and SIMULINK models, useful for analyzing Inverted Pendulum System and designing Control System for it. This collection is developed by:

K HALIL SULTAN
Khalil Sultan is currently pursuing the B.E. degree in Industrial Electronics at the Institute of Industrial Electronics Engineering (IIEE), PCSIR, NEDUET, Karachi, Pakistan. He is a STUDENT MEMBER of the IEEE, Inc. and INSTITUTION OF ENGINEERS, PAKISTAN IEP. He is the author of another Simulink Blockset “SERVO SYSTEM BLOCKSET” which can also be looked at MATLAB CENTRAL FILE E XCHANGE at http://www.mathworks.com/matlabcentral/fileexcha nge/loadFile.do?objectId=3087&objectType=FILE He is also the author of another Simulink Block “SINGLE PULSE GENERATOR ” which can also be looked at MATLAB CENTRAL FILE...
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