Anti-sway control of variable rope length container crane based on phase plane trajectory planning

An overhead crane system is a complex time-varying system if it includes simultaneous hoisting and moving operations. To address the problem that time-varying systems usually have no exact analytical solution, an anti-swing method based on linear approximation of the phase plane trajectory is proposed. Specifically, the phase plane trajectory of the swing angle is first analyzed and it is found that the double-step acceleration method with unequal acceleration amplitude and acceleration time has a combination of limit loops in the phase plane trajectory of the swing angle when the rope length varies, so the average rope length of each section is used to approximate the natural oscillation frequency. Next, the input shaping technique is used to shape the input signal into the desired output signal so that the load swing angle can follow the planned trajectory. The desired acceleration amplitude and switching time are then derived based on the geometric relationship between the swing angle in the phase plane and the specific physical constraints. Finally, the feasibility of the proposed method is verified by numerical simulations.