Control design for beam stabilization with self-sensing piezoelectric actuators: managing presence and absence of hysteresis

Andrea Mattioni (1) , Christophe Prieur (1) , Sophie Tarbouriech (2)

1 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

This paper deals with the modeling and stabilization of a flexible clamped beam controlled with a piezoelectric actuator in the self-sensing config- uration. We derive the model starting from general principles, using the general laws of piezoelectricity. The obtained model is composed by a PDE, describing the flexible deformations dynamics, interconnected with an ODE describing the electric charge dynamics. Firstly, we show that the derived linear model is well-posed and the origin is globally asymptot- ically stable when a voltage control law, containing the terms estimated in the self-sensing configuration, is applied. Secondly, we make the more realistic assumption of the presence of hysteresis in the electrical domain. Applying a passive control law, we show the well-posedness and the origin’s global asymptotic stability of the nonlinear closed-loop system.

Keywords: Piezoelectric actuator Nonlinear control Partial Differential Equations Asymptotic stability; Piezoelectric actuator; Nonlinear control; Partial Differential Equations; Asymptotic stability

Domains: Systems and Control [cs.SY]

Andrea Mattioni, Christophe Prieur, Sophie Tarbouriech. Control design for beam stabilization with self-sensing piezoelectric actuators: managing presence and absence of hysteresis. Mathematics of Control, Signals, and Systems, In press, ⟨10.1007/s00498-024-00393-6⟩. ⟨hal-04659186⟩