Model reduction for control system design
type: Item
instance of: scholarly article
title: Model reduction for control system design
zbMATH Open document ID: 0964.93003
author: Goro Obinata
author: Brian D. O. Anderson
published in: Communications and Control Engineering
publication date: 2001-01-23T00:00:00Z
review text: This book is an exposition on model and controller reduction for linear finite-dimensional systems. There has been a previous version in Japanese edited by the publisher Asakura Shoten. Chapter one provides the ideas of a first set of methods. Truncation, singular perturbations and procedures which appeared in the eighties: Balanced realization and Hankel norm approximation, the latter topic being well developed. The discrete case and some mixed methods are also presented. Chapter two deals with multiplicative approximations. Now, the approximation criterion is based on the Bode plot (amplitude, phase). The results of Green and Glover are presented. There are sections on balanced stochastic truncation (error bounds are established and the case of nonsquare transfer function matrices is examined). The rest of the chapter deals with multiplicative Hankel norm approximation. Traditional design methods lead to controllers of the same order as the plants. The issue is to produce a reduced order controller. The challenge is that one desires that the performance/robustness properties are preserved during reduction. Chapter three presents answers to these problems: Frequency weighted approximation, frequency weighted balanced truncation, frequency weighted Hankel norm reduction, partial fraction expansions, multiplicative versions. The last chapter deals with coprime factorization and one desires that instabilities are not reflected directly (copied) in the reduced controller. A bibliography with 89 entries and a small index end this volume. Each chapter terminates with an example and each section has a summary at its end. This book will be valuable to those interested in having an overview on model and controller reduction.
reviewed by: A. Akutowicz
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 1555435
zbMATH Keywords: balanced realization
zbMATH Keywords: model and controller reduction
zbMATH Keywords: Hankel norm approximation
zbMATH Keywords: multiplicative approximations
zbMATH Keywords: stochastic truncation
zbMATH Keywords: frequency weighted balanced truncation
zbMATH Keywords: frequency weighted Hankel norm reduction
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1555435