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

Abstract

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.

Payload motion control for a varying length flexible gantry crane

“…Before proceeding to derive mathematical model of the gantry crane, some important assumptions are specified as follows [20]:…”

“…The dynamics of flexible cable are also described by the wave equation and a finite-time stabilization controller is designed for the crane in [17]. Moreover, control of the flexible cable crane with variable cable length is also considered in [18][19][20]. In these works, the authors concentrate to the ultimate goal which is achieving the payload to desired position and minimizing swinging angle in steady state.…”