Inverted Pendulum: Analysis, Design and Implementation
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
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
Bibliography: KHALIL SULTAN July 25, 2003