Séminaire IPAG

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Controllability and stabilization of the beam equation with piezoelectric actuators in presence of saturation and hysteresis

jeudi 11 septembre 2025 - 11h00

Christophe Prieur - Gipsa-Lab
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The objective of this presentation is to review some of control properties we may address for a dynamical model. More specifically, as an introduction, we will first start with a linear, finite-dimensional dynamical model and introduced the different control concepts for a linear ordinary differential equation. Then we will go for the more challenging control problems as those derived a partial differential equation as the one given by the beam equation controlled by a piezoelectric patch. The model is composed by a partial differential equation, describing the deformation dynamics, interconnected with an ordinary differential equation describing the electric charge dynamics. Firstly, the exact controllability problem is solved with various sets of initial conditions. Then the well-posedness of the linear model is stated, together with its global asymptotic stability, when a voltage control law, containing terms of the self-sensing configuration, is applied. Finally, the more realistic assumption of the presence of hysteresis in the electrical domain is introduced. Applying a passive control law, the well-posedness and the global asymptotic stability of the nonlinear closed-loop system are established.

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Hôtes : Jean-Baptiste Le Bouquin

Salle Manuel Forestini, 414 rue de la piscine, 38400 Saint Martin d'Hères