μ-Synthesis of an Under-Actuated Bridge Crane

During crane operation, the distribution of load mass may be nonuniform, which leads to the model uncertainty of the crane. Additionally, external disturbances such as wind and friction can cause oscillation of crane loads. A robust control strategy is proposed for an uncertain bridge crane system to address these issues. This strategy aims to accurately locate, quickly transport, and suppress its swing angle. The bridge crane is first modeled as the two degree-of-freedom system to study the control problem, and the load mass and the track friction coefficients are taken as parameter uncertainties. The appropriate performance weight and input weight functions are then designed for the closed-loop system by a concluded procedure. The relationship between the weight-function parameters and the resulting performance is analyzed. According to these weight functions, a μ-synthesis robust controller is designed using the DK-iteration algorithm. The output disturbance is introduced to analyze the pendulum angle suppression and perturbation rejection abilities of the closed-loop system in a shorter period. Finally, the effectiveness of the designed control method is verified by a simulation example.