Boundary control of a Timoshenko beam with prescribed performance

This paper focuses on the boundary control of a Timoshenko beam with a tip mass in space. Compared with an Euler–Bernoulli beam model, the coupling of the Timoshenko beam's transverse vibration and its cross-sectional rotation makes it difficult to develop the controller. The Timoshenko beam is essentially a distributed parameter system, the motion of which can be described using partial differential equations. A prescribed performance function is introduced to the boundary control strategy to guarantee the transient and steady tracking errors. By applying the proposed controller, the outputs are ultimately restricted within a small residual set, which is arbitrarily predefined, and the minimum convergence rate can be ensured. The stability of the boundary control is analyzed using the LaSalle's invariance principle and the theoretical solutions of the Timoshenko beam model. Finally, the performance of the presented boundary controller is verified by numerical case studies.