abstract

• 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.

authors

• Méndez Barrios César Fernando Francisco
• Niculescu S.-I.
• Torres-García D.

publication date

• 2024-01-01

funding provided via

• CONACyT-UASLP; IDEX Paris-Saclay; CONACyT‐UASLP; CONAHCyT-Mexico; CONAHCyT‐Mexico, (ADI 2022); IDEX Paris‐Saclay, (ANR‐11‐IDEX‐0003‐02); CVU, (929482)  Grant

published in

• International Journal of Robust and Nonlinear Control  Journal

keywords

• delay-dependent coefficients; PD-control; properly-/improperly-posed systems; quasi-polynomials Approximation theory; Characteristic roots; Delay dependent; Delay-dependent coefficient; Difference approximation; Multiple delays; PD control; PD controllers; Properly-/improperly-posed system; Quasipolynomials; SISO systems; Closed loop systems

Digital Object Identifier (DOI)

• 10.1002/rnc.7217

PubMed ID

start page

• 6431

end page

• 6454

volume

• 34

issue

• 10