Vibration control of a flexible single-link robot: A backstepping controller for distributed parameter systems

In this paper, a two-degree-of-freedom-control concept for a flexible single-link robot is considered offering trajectory tracking as well as vibration damping. The robot - a flexible link with tip mass attached to a moving cart - is modeled as distributed parameter system including structural damping. The proposed forward controller is designed based on the exact modal approximation of the system dynamics. Based on the infinite dimensional error dynamics formulated in strict feedback form, a backstepping controller is designed that guarantees passivity. Input Shaping is used for planning the desired trajectories. Measurement results at a laboratory experiment show the feasibility of this approach.