Delay-difference Approximation of PD-Controllers. Insights into Improperly-posed Closed-loop Systems

Diego Torres-García (1, 2) , César‐fernando Méndez‐barrios (2) , Silviu-Iulian Niculescu (1, 3) , Alejandro Martínez-González (2)

1 DISCO - Dynamical Interconnected Systems in COmplex Environments
2 UASLP - Universidad Autonoma de San Luis Potosi [México]
3 L2S - Laboratoire des signaux et systèmes

This paper focuses on the study of the behavior of critical roots when a dynamical system is stabilized by a PD-controller, for which the derivative action has been approximated by using two commensurate delays. The use of such an approximation leads to a characteristic quasipolynomial whose coefficients depend explicitly on the delay parameter. The aim of the paper is to address the way the delay parameter may affect the location of the roots of the corresponding characteristic function, and in particular the cases when "small" delays induce instability in the closed-loop systems. Such an analysis is performed by expressing the critical solution of the system as a delay-dependent power series. Illustrative examples complete the presentation.

Mots clés: PD-control; Delay-dependent Coefficients; Improperly-Posed Linear Systems

Domaines: Sciences de l'ingénieur [physics]

Diego Torres-García, César‐fernando Méndez‐barrios, Silviu-Iulian Niculescu, Alejandro Martínez-González. Delay-difference Approximation of PD-Controllers. Insights into Improperly-posed Closed-loop Systems. COSY 2022 - 1st IFAC Workshop on Control of Complex Systems, IFAC, Nov 2022, Bologna, Italy. ⟨10.1016/j.ifacol.2023.01.052⟩. ⟨hal-03958376⟩