Robust controls for ship-mounted container cranes with viscoelastic foundation and flexible hoisting cable

This study proposes two robust controllers for a ship-mounted container crane based on the back-stepping sliding mode control technique. The ship crane system is operated under complex conditions, in which the disturbances caused by the viscoelasticity of seawater and the flexibility of handling wire ropes are fully considered. With two actuators consisting of a trolley-moving force and container-hoisting torque, the controllers concurrently stabilize six states: trolley displacement, container-lifting motion, container swing, axial container oscillation, ship roll, and heave. The quality of the control algorithms is investigated through simulation. The results show that the responses of the crane are asymptotically stabilized and that the ship vibrations are significantly reduced.