Robust vibration control for a flexible cable gantry crane system subject to boundary disturbance

This paper addresses the robust vibration control problem for a gantry crane system which is governed by a partial differential equation. The control objectives are to transport the cargo from the initial position to the desired position and suppress the vibration of the cable and payload in the presence of boundary disturbance. To achieve the objectives, a sliding-mode controller is proposed by repressing the boundary disturbance. By using the operator semigroup theory, the well-posedness of the closed-loop system is guaranteed. The asymptotic stability of the closed-loop system is proven by using the extended LaSalle’s invariance principle. Both numerical simulations and experiments are provided to illustrate the effectiveness of the proposed boundary control method.