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