Modern Anti-windup Synthesis

by Zaccarian, Luca; Teel, Andrew R.

• ISBN13: 9780691147321
• ISBN10: 0691147329
• Format: Hardcover
• Copyright: 2011-07-11
• Publisher: Princeton Univ Pr

Summary

This book provides a wide variety of state-space--based numerical algorithms for the synthesis of feedback algorithms for linear systems with input saturation. Specifically, it addresses and solves the anti-windup problem, presenting the objectives and terminology of the problem, the mathematical tools behind anti-windup algorithms, and more than twenty algorithms for anti-windup synthesis, illustrated with examples. Luca Zaccarian and Andrew Teel's modern method--combining a state-space approach with algorithms generated by solving linear matrix inequalities--treats MIMO and SISO systems with equal ease. The book, aimed at control engineers as well as graduate students, ranges from very simple anti-windup construction to sophisticated anti-windup algorithms for nonlinear systems. Describes the fundamental objectives and principles behind anti-windup synthesis for control systems with actuator saturation Takes a modern, state-space approach to synthesis that applies to both SISO and MIMO systems Presents algorithms as linear matrix inequalities that can be readily solved with widely available software Explains mathematical concepts that motivate synthesis algorithms Uses nonlinear performance curves to quantify performance relative to disturbances of varying magnitudes Includes anti-windup algorithms for a class of Euler-Lagrange nonlinear systems Traces the history of anti-windup research through an extensive annotated bibliography

Author Biography

Luca Zaccarian is associate professor of control engineering at the University of Rome, Tor Vergata. Andrew R. Teel is a professor in the Electrical and Computer Engineering Department at the University of California, Santa Barbara.

Table of Contents

Preface	p. ix
Algorithms Summary	p. xi
Preparation	p. 1
The Windup Phenomenon and Anti-windup Illustrated	p. 3
Introduction	p. 3
Illustrative examples	p. 4
Summary	p. 21
Notes and references	p. 22
Anti-windup: Definitions, Objectives, and Architectures	p. 23
Preliminaries	p. 23
Qualitative objectives	p. 26
Anti-windup augmentation	p. 32
Quantitative performance objectives	p. 40
Notes and references	p. 47
Analysis and Synthesis of Feedback Systems: Quadratic Functions and LMIs	p. 48
Introduction	p. 48
Unconstrained feedback systems	p. 50
Linear matrix inequalities	p. 51
Constrained feedback systems: global analysis	p. 59
Constrained feedback systems: regional analysis	p. 63
Analysis examples	p. 67
Regional synthesis for external stability	p. 70
Notes and references	p. 73
Direct Linear Anti-Windup Augmentation	p. 75
Static Linear Anti-windup Augmentation	p. 77
Overview	p. 77
Key state-space representations	p. 78
Algorithms providing global guarantees	p. 81
Algorithms providing regional guarantees	p. 98
Notes and references	p. 107
Dynamic Linear Anti-windup Augmentation	p. 109
Overview	p. 109
Key state-space representations	p. 110
Factoring rank-deficient matrices	p. 113
Algorithms providing global guarantees	p. 114
Algorithms providing regional guarantees	p. 141
Notes and references	p. 152
Model Recovery Anti-Windup Augmentation	p. 155
The MRAW Framework	p. 157
Introduction	p. 157
A block diagram/transfer function description	p. 158
A state-space description (linearity not needed)	p. 161
Robust, fragile, or both?	p. 164
Notes and references	p. 167
Linear MRAW Synthesis	p. 174
Introduction	p. 174
Global stability-based algorithms	p. 176
Regional stability and performance algorithms	p. 195
Notes and references	p. 199
Nonlinear MRAW Synthesis	p. 200
Introduction	p. 200
Switching and scheduling linear controllers	p. 201
Model predictive control for anti-windup design	p. 208
Global designs for non-exponentially unstable plants	p. 217
Designs for exponentially unstable plants that maximize the basin of attraction	p. 222
Notes and references	p. 225
The MRAW Structure Applied to Other Problems	p. 226
Rate- and magnitude-saturated plants	p. 226
Anti-windup for dead-time plants	p. 232
Bumpless transfer in multicontroller schemes	p. 235
Reliable control via hardware redundancy	p. 240
Notes and references	p. 243
Anti-windup for Euler-Lagrange Plants	p. 245
Fully actuated Euler-Lagrange plants	p. 245
Anti-windup construction and selection of the stabilizer v	p. 246
Simulation examples	p. 250
Notes and references	p. 268
Annotated Bibliography	p. 269
Overview	p. 269
Problem discovery	p. 269
The first constructive techniques	p. 270
Call for systematization	p. 271
Modern anti-windup schemes	p. 272
Additional references	p. 281
Index	p. 285
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