Adaptive band-limited disturbance rejection in linear discrete-time systems
type: Item
instance of: scholarly article
title: Adaptive band-limited disturbance rejection in linear discrete-time systems
zbMATH Open document ID: 0920.93026
DOI: 10.1155/S1024123X95000111
author: Pierre T. Kabamba
author: A. Galip Ulsoy
author: Foued Ben Amara
published in: Mathematical Problems in Engineering
publication date: 1999-09-23T00:00:00Z
full work available at URL: https://eudml.org/doc/48225
review text: Summary: The problem of adaptively rejecting a disturbance consisting of a linear combination of sinusoids with unknown and/or time varying frequencies for SISO LTI discrete-time systems is considered. The rejection of the disturbance input is achieved by constructing the set of stabilizing controllers using the Youla parametrization and adjusting the Youla parameter to achieve asymptotic disturbance rejection. The first main result in this paper concerns off-line controller design where a controller that achieves regulation is numerically designed off-line based on the assumption that only the sequence of discrete disturbance input values (as opposed to a model of the disturbance) is available. A least squares based optimization algorithm is used in the controller design. As expected, it is shown, under some mild assumptions, that if the off-line designed controller achieves regulation, then it must include a model of the disturbance input. The second main result concerns on-line controller design where recursive versions of the off-line algorithm used above for controller design are presented and their convergence properties analyzed. Conditions under which the on-line algorithms yield an asymptotic controller that achieves regulation are presented. Conditions both for the case where the disturbance input properties are constant but unknown and for the case where they are unknown and time-varying are given. The on-line controller construction amounts to an adaptive implementation of the Internal Model Principle. The performance robustness of the off-line designed controller in the face of plant model uncertainties is investigated. It is shown, under some mild assumptions, that performance robustness is realized provided internal stability is maintained. The performance of the adaptation algorithms is illustrated through a simulation example.
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 93C73
zbMATH DE Number: 1283576
zbMATH Keywords: internal model principle
zbMATH Keywords: adaptive control
zbMATH Keywords: stabilizing controllers
zbMATH Keywords: Youla parametrization
zbMATH Keywords: disturbance rejection
zbMATH Keywords: controller design
zbMATH Keywords: performance robustness
MaRDI profile type: Publication
OpenAlex ID: W2074415325
description: scientific article; zbMATH DE number 1283576