Boundary state feedback controller design for timoshenko beams with clamped end and pinned end

This work presents a boundary controller design for exponentially stabilizing Timoshenko beams with clamped end or pinned end. The beam is slender and has a small amount of Kelvin-Voigt damping. We apply the backstepping technique to design a state-feedback controller using actuation only at the beam base. The controller requires the solution of a linear hyperbolic PDE, which can be obtained by applying the successive approximation or finite difference methods. We use Zakian’s I
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recursion technique to solve for the closed-loop dynamics. Simulation results show that the response converges rapidly to the steady state value.