Exponential stabilization of a clamped Timoshenko beam with actuation on a tip mass

In this paper, we consider the stabilization of a clamped beam with torque and force actuation on a mass situated at the other side of the beam. We show how to derive the model starting from the Principle of Least Action and we rewrite it as the interconnection between two port-Hamiltonian systems: an infinite dimensional system and a finite dimensional one. Therefore, we propose a control law that allows to exponentially stabilize the origin of the closed-loop system. Further, we show how to explicitly compute, from the system and control parameters, the exponential decreasing rate of the system's norm along time. For a sake of conciseness, we only sketch the theoretical proofs. Finally, we provide some numerical simulations illustrating the closed-loop performances with different choices of the control parameters.