Optimal control of overhead cranes

A nonlinear dynamic model of an overhead crane which represents simultaneous travel, traverse, and hoisting/lowering motions is considered. Nonlinear feedback forms of control are studied, and numerical results are obtained in such a way that specified boundary conditions and the functional constraints for the states and controls are satisfied while minimizing the sway and final time. The results show that the crane can be transferred to a desired position in the shortest possible time while minimizing the sway of the load not only during transfer but also at final time using the suggested control scheme. Several numerical results of the controls, objectives, and of the states are presented which indicate that the proposed method works well.