Control of beam equation with saturating piezoelectric patches



2/07/2020 - 14:00 Mr Christophe Prieur (GIPSA-LAB, CNRS, Grenoble)

This presentation deals with a controlled beam equation for which the input is subject to magnitude saturation. 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 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 asymptotic stability is proven by Lyapunov-based arguments.

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