Boundary cooperative control by flexible Timoshenko arms

This paper discusses a cooperative control problem by two one-link flexible Timoshenko arms. The goal is to control a grasping force to collect an object with the two flexible arms, and to simultaneously suppress the vibrations of the arms. To solve this problem, we propose a boundary controller that is based on a dynamic model represented by a hybrid PDE–ODE model; the exponential stability of the closed-loop system is then proven by the frequency domain method. Finally, several numerical simulations are carried out to investigate the validity of the proposed boundary cooperative controller.