abstract

• This paper aims to explore the advantages and disadvantages associated with implementing derivative action in a PID controller using a delay-difference approximation scheme in continuous time. Despite the simplicity of the approximation, the characteristic function of the closed-loop system is a quasipolynomial including delay-dependent coefficients, which results in a challenging task. The proposed study primarily focuses on the way the controller gains and the delay affect the key characteristics of the dynamics such as asymptotic stability, noise rejection, and closed-loop performance for linear-time-invariant (LTI) minimum-phase second-order systems. Additionally, the paper provides some results concerning the delay margin of the delay-difference approximation of the closed-loop system. Finally, the proposed results are illustrated via numerical examples. © 2024 IEEE.

authors

• Méndez Barrios César Fernando Francisco

publication date

• 2024-01-01

funding provided via

• CONACyT-UASLP; IDEX Paris-Saclay, (ANR-11-IDEX-0003-02); CVU, (929482)  Grant

published in

• 2024 32nd Mediterranean Conference on Control and Automation, MED 2024  Proceedings

keywords

• Asymptotic stability; Continuous time systems; Controllers; Electric control equipment; Linear control systems; Proportional control systems; Three term control systems; Approximation scheme; Characteristics functions; Closed-loop system; Continous time; Controller performance; Controller stabilities; Delay dependent; Difference approximation; PID controllers; Quasipolynomials; Closed loop systems

Digital Object Identifier (DOI)

• 10.1109/MED61351.2024.10566201

PubMed ID

start page

• 616

end page

• 621

volume

issue