PD sliding mode trajectory tracking control method for a double-pendulum bridge crane considering initial input saturation

To address the significant swinging issues of the hook and load caused by the dual-pendulum effect and initial input saturation in the operation of a two-dimensional double-pendulum bridge crane, a PD sliding mode trajectory tracking control method is proposed. Based on the double-pendulum bridge crane model, the coupled dynamic relationships between the trolley displacement, hook angle, and load angle are analyzed in depth. To ensure the smooth operation of the trolley, the initial driving force is reasonably constrained, and an online trajectory tracking mechanism is introduced to precisely control its motion trajectory. By designing a PD sliding mode controller and incorporating a saturation function, the oscillation phenomenon is effectively suppressed, significantly improving the stability and accuracy of the anti-sway control system. Experimental results show that the proposed control method successfully limits the initial driving force, suppresses the dual swinging effect, reduces the amplitude of the swing, and enhances the stability and safety of the transport process, providing a feasible solution to the swinging problem of bridge cranes.