Boundary control and exponential stability of a flexible Timoshenko beam manipulator with measurement delays

This study mainly focuses on the boundary control problem for a novel flexible Timoshenko beam manipulator system with measurement delay terms. The actuator structure of the manipulator consisted of a translational slider and a rotational motor, which are able to provide two inputs to influence different variables in boundary conditions of the Timoshenko partial differential equations. A static feedback boundary controller is proposed to realise exponential stability of the closed-loop system based on C-0-semigroup and fundamental solutions. The controller is independent of the precise knowledge of parameters in the delay terms directly, so it has robustness to time delays in certain degree. Numerical simulations are provided to verify the effectiveness of the proposed control scheme.