Frequency domain properties of scalar and multivariable feedback systems
type: Item
instance of: scholarly article
title: Frequency domain properties of scalar and multivariable feedback systems
zbMATH Open document ID: 0637.93035
published in: Lecture Notes in Control and Information Sciences
publication date: 1993-06-05T00:00:00Z
review text: In this monograph, a multivariable control system design method is presented. The method is the so-called frequency response method, which is the straightforward extension of classical methods developed for scalar system design. In the introductory chapter, Chap. 1, it is stressed that classical techniques which are extremely powerful for the design of scalar systems cannot be extended to multivariable systems as they are. It is the goal of this monograph to extend the classical techniques to multivariable systems if at all possible. In Chap. 2, sensitivity and complementary sensitivity functions are introduced. The classical design methods are nothing but to harmonize tradeoffs. One of the tradeoffs is a constraint between the magnitude of both functions. Chap. 3 treats analytical tradeoffs. The case when the plant has minimum zeros and unstable poles are discussed. In Chap. 4, it is emphasized that an alternative method which substitutes the shaping of gain and phase used in classical techniques is necessary for the design of multivariable control systems. In Chap. 5, it is stated that directionality which is essential for multivariable systems prevents the direct extension of classical techniques. The singular value decomposition of the transfer function matrix plays an important role in multivariable systems. In Chap. 6, the concept of phase is reconsidered from a new point of view. In Chap. 7, the relation between properties of open and closed loop systems is considered, which, over some frequency range, have high gains in only some directions, low gains in different directions, or both high and low gains in different directions. In Chap. 8 through Chap. 11, mathematical tools for studying analytical design tradeoffs in multivariable systems are presented. An analytical function is given in Chap. 8. The complex unit sphere is presented in Chap. 9. Differential equations describing how the singular vectors of a matrix transfer function change with frequency are …
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 70G10
Mathematics Subject Classification ID: 93B50
Mathematics Subject Classification ID: 93B17
Mathematics Subject Classification ID: 93B35
zbMATH DE Number: 193003
zbMATH Keywords: multivariable control system design method
zbMATH Keywords: frequency response
zbMATH Keywords: sensitivity
zbMATH Keywords: complementary sensitivity
zbMATH Keywords: tradeoffs
zbMATH Keywords: singular value decomposition
zbMATH Keywords: transfer function
author: J. S. Freudenberg
author: Douglas P. Looze
reviewed by: Kunihiko Ichikawa
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0044565
OpenAlex ID: W1545941242
DOI: 10.1007/BFB0044565
description: scientific article; zbMATH DE number 193003