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MULTIVARIABLE
FEEDBACK CONTROL
Analysis and design
Sigurd Skogestad
Norwegian University of Science and Technology
Ian Postlethwaite
University of Leicester
Second Edition
This version: August 29, 2001
JOHN WILEY & SONS
Chichester
.
New York
.
Brisbane
.
Toronto
.
Singapore
ii MULTIVARIABLE FEEDBACK CONTROL
BORGHEIM, an engineer:
Herregud, en kan da ikke gjøre noe bedre enn leke i denne
velsignede verden. Jeg synes hele livet er som en lek, jeg!
Good heavens, one can’t do anything better than play in this
blessed world. The whole of life seems like playing to me!
Act one, LITTLE EYOLF, Henrik Ibsen.
iv MULTIVARIABLE FEEDBACK CONTROL
CONTENTS
.......................................... iii
CONTENTS .................................. v
PREFACE ................................... ix
1 INTRODUCTION ............................. 1
1.1 The process of control system design . ................ 1
1.2 The control problem . ........................ 2
1.3 Transfer functions . . . ........................ 3
1.4 Scaling . ............................... 5
1.5 Deriving linear models ........................ 8
1.6 Notation . ............................... 11
2 CLASSICAL FEEDBACK CONTROL ................. 15
2.1 Frequency response . . ........................ 15
2.2 Feedback control . . . ........................ 21
2.3 Closed-loop stability . ........................ 24
2.4 Evaluating closed-loop performance . ................ 27
2.5 Controller design . . . ........................ 39
2.6 Loop shaping . . . . . ........................ 40
2.7 Shaping closed-loop transfer functions ................ 55
2.8 Conclusion . . . . . . ........................ 62
3 INTRODUCTION TO MULTIVARIABLE CONTROL ........ 63
3.1 Introduction . . . . . . ........................ 63
3.2 Transfer functions for MIMO systems ................ 64
3.3 Multivariable frequency response analysis . . . . . ......... 68
3.4 Control of multivariable plants .................... 79
3.5 Introduction to multivariable RHP-zeros . . . . . . ......... 84
3.6 Condition number and RGA . .................... 87
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