Time-Varying Trajectory Tracking Boundary Control of a Flexible Rotation Beam Based on Servomechanism

In this article, we consider the time-varying trajectory tracking boundary control problem for the flexible rotation beam subject to distributed disturbance. A partial differential equation model for the flexible rotation beam system with the coupling of angle and vibration displacement is established by Hamilton principle. By introducing a servo system generated by the reference signal, a boundary controller is proposed to track the desired time-varying trajectory, which is different from the fixed angular position in most existing work. A Lyapunov-based stability analysis is presented to demonstrate that the tracking error system between the servo system and the original system is uniformly ultimately bounded. Based on the infinite dimensional operator theory, it is proved that the closed-loop system is well posed and all signals remain bounded. Numerical simulations verify the correctness of the theory and the effectiveness of the control strategy. And the experiments based on the Quanser platform demonstrate the same result as well.