Weights determine stability of sensitivity-optimal controllers
type: Item
instance of: scholarly article
title: Weights determine stability of sensitivity-optimal controllers
zbMATH Open document ID: 0882.93018
DOI: 10.1016/S0005-1098(97)00016-2
author: Kathryn E. Lenz
published in: Automatica
publication date: 1998-03-02T00:00:00Z
review text: The author discusses the problem of how to choose the dynamic weight in \(H^\infty\) optimality design to ensure stability and minimum-phase property of the optimal controller. It is shown that for a large class of SISO plants including distributed parameter systems with poles and zeros on the imaginary axis and infinity the necessary and sufficient condition for existence of stable \(H^\infty\) optimal controller for weighted sensitivity is stabilizability of the plant by any stable controller. Necessary and sufficient interpolation conditions on the weight ensuring stability of the optimal controller are formulated and a resulting procedure for controller design is presented. The plant is supposed to have at least one zero in the closed right half-plane. The results for weighted mixed sensitivity minimization for the same class of plants are similar but there are not suggestions how to select mixed sensitivity weights. In the case of lumped parameter plants the results simplify and may be easily implemented. The author presents a number of such examples and explains the mathematical simplifications in these cases. The distributed parameter example analyzed in the paper is a flexible beam with free ends.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 1062912
zbMATH Keywords: \(H^ \infty\) optimality design
zbMATH Keywords: distributed parameter systems
zbMATH Keywords: stable controller
zbMATH Keywords: interpolation conditions
zbMATH Keywords: mixed sensivity minimization
zbMATH Keywords: lumped parameter plants
reviewed by: Andrzej Świerniak
MaRDI profile type: Publication
cites work: When is a controller optimal in the sense of ℋ/sub ∞/ loop-shaping?
cites work: Optimal mixed sensitivity for SISO-distributed plants
cites work: Q3922907
cites work: On compensation of nonminimum-phase zeros
cites work: Design of stable controllers attaining low H/sup infinity / weighted sensitivity
cites work: Q3874458
cites work: Properties of optimal weighted sensitivity designs
cites work: Characterizing optimal solutions to weighted mixed sensitivity problems
cites work: When is a controller \(H^{\infty}\)-optimal ?
cites work: Frequency domain analysis and robust control design for an ideal flexible beam
cites work: A Characterization of Badly Approximable Functions
cites work: Properties of optimally robust controllers
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description: scientific article; zbMATH DE number 1062912