Model Reduction for Control System Design

by Obinata, Goro; Anderson, Brian D. O.

• ISBN13: 9781852333713
• ISBN10: 1852333715
• Format: Hardcover
• Copyright: 2000-10-01
• Publisher: Springer Verlag

Summary

Modern methods of filter design and controller design often yield systems of very high order, posing a problem for their implementation. Over the past two decades or so, sophisticated methods have been developed to achieve simplification of filters and controllers. Such methods often come with easy-to-use error bounds, and in the case of controller simplification methods, such error bounds will usually be related to closed-loop properties.This book is the first comprehensive treatment of approximation methods for filters and controllers. It is fully up to date, and it is authored by two leading researchers who have personally contributed to the development of some of the methods. Balanced truncation, Hankel norm reduction, multiplicative reduction, weighted methods and coprime factorization methods are all discussed.The book is amply illustrated with examples, and will equip practising control engineers and graduates for intelligent use of commercial software modules for model and controller reduction.

Table of Contents

Preface	vii
Acknowledgements	ix
Contents	xi
List of Figures	xiii
Key Notation	xv
Methods for Model Reduction	1	(60)
Introduction to Model and Controller Reduction	1	(1)
Model Reduction by Truncation	2	(3)
Singular Perturbation	5	(2)
Reduced Order Models Based on Balanced Realization Truncation	7	(9)
Methods Involving Minimizing an Approximation Error Norm	16	(4)
Hankel Norm Approximation	20	(20)
Markov and Covariance Parameter Matching	40	(4)
Mixed Methods	44	(2)
Model Reduction in Discrete Time Systems	46	(8)
Examples	54	(7)
Multiplicative Approximation	61	(32)
The Multiplicative Approximation Problem	61	(2)
Balanced Stochastic Truncation	63	(4)
Balanced Stochastic Truncation: Theory and Extensions	67	(14)
Multiplicative Hankel Norm Approximation	81	(9)
Example	90	(3)
Low Order Controller Design	93	(36)
Approaches to the Design of Low Order Controllers	93	(3)
Controller and Plant Reduction via Frequency Weighted Approximation	96	(6)
Frequency Weighted Balanced Truncation	102	(10)
Frequency Weighted Hankel Norm Reduction	112	(3)
Frequency Weighted Reduction Using Partial Fractions	115	(3)
Multiplicative Approximation with Frequency Weighting	118	(1)
Sampled-data Controller Reduction	119	(5)
Example	124	(5)
Model and Controller Reduction Based On Coprime Factorizations	129	(30)
Coprime Factorizations: What are they and why use them?	129	(2)
Coprime Fractional Descriptions	131	(6)
Reducing Controller Dimension Using Coprime Fractions	137	(4)
Controller Reduction by H∞-balanced Truncation	141	(4)
Controller Reduction via Coprime Fractions and Frequency Weighting	145	(4)
Controller Reduction via Multiplicative Coprime Factor Approximation	149	(2)
Reducing Controller Dimension to Preserve H∞ Performance	151	(2)
Example	153	(6)
Bibliography	159	(8)
Index	167