The payload swing of an overhead crane needs to be controlled properly to improve efficiency and avoid accidents. However, the swing angle is usually very difficult to control to zero degrees or for it to even remain within an acceptable range because the overhead crane is a complex nonlinear underactuated system, especially when the actual working environment is accompanied by strong disturbances and great uncertainty. To resolve this, a real-time anti-swing closed-loop control strategy is proposed that considers external disturbances. The swing angle is measured in time and it functions with the load displacement as feedback inputs of the closed-loop system. The nonlinear model of the crane is simplified by a linear system with virtual disturbances, which are estimated by the equivalent input disturbance (EID) method. Both simulation and experimental results for a 2-D overhead crane system are investigated to illustrate the validity of the proposed method.

Concerning the robust model predictive control (MPC) for constrained systems with polytopic model characterization, some approaches have already been given in the literature. One famous approach is an off-line MPC, which off-line finds a state-feedback law sequence with corresponding ellipsoidal domains of attraction. Originally, each law in the sequence was calculated by fixing the infinite horizon control moves as a single state feedback law. This paper optimizes the feedback law in the larger ellipsoid, foreseeing that, if it is applied at the current instant, then better feedback laws in the smaller ellipsoids will be applied at the following time. In this way, the new approach achieves a larger domain of attraction and better control performance. A simulation example shows the effectiveness of the new technique.