PID Control Design for First-Order Delay Systems via MID Pole Placement: Performance vs. Robustness

Dan Ma (1) , Islam Boussaada (2, 3, 4) , Jianqi Chen (5) , Catherine Bonnet (4, 2) , Silviu-Iulian Niculescu (2, 4) , Jie Chen (5)

1 School of Information Science & Engineering, Northeastern University Shenyang
2 L2S - Laboratoire des signaux et systèmes
3 IPSA - Institut Polytechnique des Sciences Avancées
4 DISCO - Dynamical Interconnected Systems in COmplex Environments
5 CUHK - City University of Hong Kong [Hong Kong]

The PID control is favored in controlling industrial processes for its ease of implementation. In this paper we present an analytical study, with an aim at stability robustness, tracking performance, and pole placement of first-order unstable plants under PID control. We employ a multiplicity-induced dominancy (MID) strategy to design and tune PID controller gains, which is shown to possess desirable properties that ensure specified decay rate of the closed-loop response and the stability robustness of the closed-loop system in spite of variations in the delay parameter. We also study the tradeoff between delay robustness and tracking performance of PID controllers. We show that under the constraint of steady-state tracking, the maximal delay robustness range can be computed by solving a unimodal pseudo-concave optimization problem.

Mots clés: Time-delay systems; PID control; delay robustness; pole placement; steady-state tracking

Domaines: Automatique / Robotique; Systèmes dynamiques [math.DS]

Dan Ma, Islam Boussaada, Jianqi Chen, Catherine Bonnet, Silviu-Iulian Niculescu, et al.. PID Control Design for First-Order Delay Systems via MID Pole Placement: Performance vs. Robustness. Automatica, 2021, ⟨10.1016/j.automatica.2021.110102⟩. ⟨hal-03427550⟩