Tracking sensitivity and achievable \(\mathcal H_{\infty}\) performance in preview control
type: Item
instance of: scholarly article
title: Tracking sensitivity and achievable \(\mathcal H_{\infty}\) performance in preview control
zbMATH Open document ID: 1077.93017
author: D. Kharzeev
published in: Automatica
publication date: 2005-01-26T00:00:00Z
review text: In this paper, a general class of finite preview linear tracking control systems for plants with closed right half complex plane (RHP) zeros is considered. A tracking sensitivity function with important implications for the fidelity of reference tracking is defined. This tracking sensitivity function exhibits different tradeoffs from the standard unity feedback configuration of a feedback loop. The authors then review, for the ideal linear case, how preview control can be used to generate perfect asymptotic tracking performance, including plants with an unstable inverse. This result is examined from the perspective of time domain integrals, and their interpretation in terms of open RHP zeros, settling time and undershoot tradeoffs. It turns out that preview control does indeed permit a small amount of initial undershoot, at a time well ahead of a step reference change occurring, whilst still permitting a short settling time. This situation does give some different tracking performance tradeoffs to the unity feedback case, save that nonminimum phase plant zeros impose design limitations in essentially the same manner as in the unity feedback case. For the case where only a finite preview of the reference trajectory is available, additional frequency domain interpretations can be made. Interpolation conditions and a resultant Poisson frequency domain integral are examined. Following this, the same interpolation conditions are used to examine results on the achievable \(\mathcal H_\infty\) performance for a finite preview control scheme. These results extend the work of U.~Shaked and C.~E.~de Souza and others on \(\mathcal H_\infty\) tracking to the preview case.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93B51
zbMATH DE Number: 2131072
zbMATH Keywords: sensitivity and performance limitations in automatic control systems
zbMATH Keywords: reference tracking problems
zbMATH Keywords: finite preview linear tracking control systems for plants with closed right half complex plane zeros
zbMATH Keywords: \(\mathcal H_\infty\) infinity performance
zbMATH Keywords: tracking sensitivity function
zbMATH Keywords: ideal preview tracking
zbMATH Keywords: time domain integrals
zbMATH Keywords: frequency domain integral inequalities
zbMATH Keywords: \(\mathcal H_\infty\) tracking performance
zbMATH Keywords: resultant Poisson frequency domain integral
MaRDI profile type: Publication
full work available at URL: j.automatica.2004.02.019
OpenAlex ID: W1982228097
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DOI: 10.1016/J.AUTOMATICA.2004.02.019
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description: scientific article; zbMATH DE number 2131072