Robust adaptive vibration control of a gantry crane system with flexible cable

In this paper, a robust adaptive vibration control method for gantry crane system is proposed considering unknown parameters brought by unknown payload, cable length and tension. The control objective is to transport the cargo to the desired position while suppressing the vibration of the cable in the presence of unknown parameters. For this purpose, a boundary controller is designed with an adaptive law to compensate the parameter uncertainty of the system. The well-posedness of the closed-loop system is proved by means of operator semigroup theory and the asymptotic stability of the closed-loop system is analyzed. Finally, the effectiveness of the proposed control approach is demonstrated through both numerical simulation comparisons and physical experiments.