Delay‐difference approximations of PD‐controllers. Improperly‐posed systems in multiple delays case

Summary In this paper, we study the behavior of characteristic roots of a class of strictly proper LTI SISO systems that are subject to a PD controller for which the derivative action has been implemented by means of a delay‐difference approximation scheme that uses multiple delays. To such an end,...

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Published inInternational journal of robust and nonlinear control Vol. 34; no. 10; pp. 6431 - 6454
Main Authors Méndez‐Barrios, César‐Fernando, Torres‐García, Juan‐Diego, Niculescu, Silviu‐Iulian
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 10.07.2024
Wiley
Subjects
Approximation
Automatic Control Engineering
Computer Science
delay‐dependent coefficients
Mathematics
PD‐control
properly‐/improperly‐posed systems
quasi‐polynomials
SISO (control systems)
Systems and Control
PD control
Delay-dependent coefficients
Improperly-posed systems
Quasi-polynomials
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Summary:Summary In this paper, we study the behavior of characteristic roots of a class of strictly proper LTI SISO systems that are subject to a PD controller for which the derivative action has been implemented by means of a delay‐difference approximation scheme that uses multiple delays. To such an end, the improperly‐posed case is discussed in depth, that is, the situations where “small delays” induce instability in the closed‐loop system. The effect of adding more delays on the improperly‐posed case is analyzed and a methodology for determining the set of parameters that produces such a situation for a given number of delays is derived. Some illustrative examples complete the presentation.
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ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.7217