Output regulation for a cascaded network of 2 × 2 hyperbolic systems with PI controller

Ngoc-Tu Trinh (1) , Vincent Andrieu (1) , Cheng-Zhong Xu (1)

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique

We are concerned with the PI control/regulation design for a cascaded network of multi systems governed by hyperbolic partial differential equations. The PI controllers have both control inputs and measured outputs situated on the junctions. The stability analysis of closed-loop network is carried out in the L 2 topology by using the Lyapunov direct method. Then the output regulation is proven based on the stability of closed-loop systems. We finally work out detailed PI controller design for a practical cascaded network of n hydraulic Saint-Venant models as well as numerical simulations to validate theoretical results.

Mots clés: cascaded network; Saint-Venant equations; PI controllers; Hyperbolic PDE systems; Lyapunov functional; exponential stability; output regulation

Domaines: Automatique / Robotique; Automatique; Systèmes et contrôle [cs.SY]

Ngoc-Tu Trinh, Vincent Andrieu, Cheng-Zhong Xu. Output regulation for a cascaded network of 2 × 2 hyperbolic systems with PI controller. Automatica, 2018, 91, pp.270-278. ⟨10.1016/j.automatica.2018.01.010⟩. ⟨hal-02056784⟩