Beam equation with saturating piezoelectric controls

Christophe Prieur 1 Sophie Tarbouriech 2
1 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
Abstract : This paper deals with a controlled beam equation for which the input is subject to magnitude saturation. The 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 output feedback law and a dynamical output feedback control law. 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.
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Submitted on : Friday, June 14, 2019 - 2:27:09 PM
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Christophe Prieur, Sophie Tarbouriech. Beam equation with saturating piezoelectric controls. Joint 8th IFAC Symposium on Mechatronic Systems (MECHATRONICS'19) and 11th IFAC Symposium on Nonlinear Control Systems (NOLCOS'19), Sep 2019, Vienne, Austria. ⟨hal-02156546⟩

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