Vibration Suppression Control of a Flexible Gantry Crane System with Varying Rope Length

The paper presents a control approach to a flexible gantry crane system. From Hamilton’s extended principle the equations of motion that characterized coupled transverse-transverse motions with varying rope length of the gantry is obtained. The equations of motion consist of a system of ordinary and partial differential equations. Lyapunov’s direct method is used to derive the control located at the trolley end that can precisely position the gantry payload and minimize vibrations. The designed control is verified through extensive numerical simulations.