Stabilizing Control of Bridge Crane System Using Fixed‐Time Hierarchical Sliding Mode Method

ABSTRACT The bridge crane system has been widely used in industrial production. This mechanical system is a typical underactuated system that has one control input and two degrees of freedom (DOF). This paper discusses the stabilizing control problem for this 2‐DOF underactuated mechanical system. A fixed‐time hierarchical sliding mode control method is developed. The method first constructs two first‐level sliding surfaces and a second‐level sliding surface for the bridge crane system. Then, a sliding mode controller is designed to stabilize the second‐level sliding surface at the origin within a fixed time. It guarantees the fixed‐time convergence of two first‐level sliding surfaces at the origin. This further enables the fixed‐time stabilization of the bridge crane system to be achieved. Compared with existing methods, our presented control method can stabilize the bridge crane system at the desired position within a fixed time. As a result, the system's stabilizing time is independent of its initial conditions. In addition, it can be predicted in advance and can be limited by a fixed constant. Numerical simulation experiment results verify the effectiveness of the presented method.