Model reduction for control system design
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.
frequency weighted Hankel norm reduction
scientific article; zbMATH DE number 1555435