In this paper, we consider position and vibration control of a one-link flexible arm with a non-symmetric rigid tip body, of which the mass center does not lie on the centroidal axis of the arm. In this case, the bending vibration and the torsional vibration of the arm are coupled. Firstly, we derive the distributed parameter model using Hamilton's principle. Secondly, on the basis of this model we construct PDS control law using Lyapunov method and examine the asymptotic stability of the closed-loop system. The PDS controller consists of PD feedback of the motor angle and a bending strain (S) feedback of the flexible arm. Finally, some experiments are performed to demonstrate the effectiveness of the proposed controller.
