Reduced normal forms for nonlinear control of underactuated hoisting systems

Nearly every cargo that is transported by ship is boxed in standardized containers. The land to ship and ship to land handling of containers is performed by container cranes. These cranes dominate the throughput of the containers in ports. The operators need to be well-trained and skilled because of the requirements of the task to load or unload the ships. During container handling, the crane-load system can be compared to a pendulum of rope length L and deflection φ. It is referred to as an underactuated system. Whenever the fixed point of the pendulum is displaced, the load starts oscillating. In the nonlinear dynamics literature, one finds the field of resonant coupling to transfer energy from actuated controllable modes to underactuated uncontrollable modes. This work presents a novel normal form approach in order to identify the mode coupling. The proposed method decomposes a nonlinear control system into controllable and uncontrollable subsystem. Only the normal form terms in the controllable subsystem are utilized to design a general controller. Simulation results are given to highlight the load oscillation suppression.