Boundary Output-Feedback Stabilization of a Timoshenko Beam Using Disturbance Observer

This paper considers a modeling and control problem for a Timoshenko beam under spatiotemporally varying disturbance. The model of the Timoshenko beam is represented by a hybrid model including both partial differential equations and ordinary differential equations. In order to suppress the vibration of the system, boundary control is proposed based on Lyapunov's direct method. Boundary disturbance observers are designed to reduce the effects of the external disturbances. With the proposed boundary control strategies, the states of the system are proven to be uniformly ultimately bounded and converge to a small neighborhood of zero by choosing the design parameters. Simulations are displayed to show the effectiveness of the proposed boundary control.