Beam equation with saturating piezoelectric controls

Christophe Prieur (1) , Sophie Tarbouriech (2)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

This paper deals with a controlled beam equation for which the input is subject to magnitude saturation. A partial differential equation describes the dynamics of the deflection of the beam with respect to the rest position. The input is the voltage applied on an actuator located in a given interval of the space domain. Two kinds of control are considered: a static controller and a dynamical one. In both cases, the saturated control is indeed applied to the beam equation. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical beam equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a generalized sector condition to tackle the control nonlinearity, the semi-global asymptotic stabilization system is proven by Lyapunov-based arguments.

Mots clés: infinite-dimensional systems; saturation; well-posedness; semi-global asymptotic stability; output feedback control; Lyapunov function

Domaines: Automatique / Robotique

Christophe Prieur, Sophie Tarbouriech. Beam equation with saturating piezoelectric controls. MECHATRONICS 2019 - NOLCOS 2019 - 8th IFAC Symposium on Mechatronic Systems - 11th IFAC Symposium on Nonlinear Control Systems, Sep 2019, Vienne, Austria. ⟨10.1016/j.ifacol.2019.11.757⟩. ⟨hal-02156546⟩