Journal Article

On the geometry of stability regions of Smith predictors subject to delay uncertainty

Constantin-Irinel Morărescu, Silviu-Iulian Niculescu and Keqin Gu

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 24, issue 3, pages 411-423
Published in print September 2007 | ISSN: 0265-0754
Published online November 2006 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnl032
On the geometry of stability regions of Smith predictors subject to delay uncertainty

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In this paper, we present a geometric method for describing the effects of the ‘delay-induced uncertainty’ on the stability of a standard Smith predictor control scheme. The method consists of deriving the ‘stability crossing curves’ in the parameter space defined by the ‘nominal delay’ and ‘delay uncertainty’, respectively. More precisely, we start by computing the ‘crossing set’, which consists of all frequencies corresponding to all points on the stability crossing curve, and next we give their ‘complete classification’, including also the explicit characterization of the ‘directions’ in which the zeros cross the imaginary axis. This approach complements existing algebraic stability tests, and it allows some new insights in the stability analysis of such control schemes. Several illustrative examples are also included.

Keywords: delay stability; robustness; Smith predictor

Journal Article.  0 words. 

Subjects: Mathematics

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