Fixed-Time Robust Stabilization Control of Underactuated Bridge Crane System with Matched Disturbance

The bridge crane is a commonly used heavy-duty hoisting equipment. It is an underactuated mechanical system that has one control input and two degrees of freedom. This paper studies the stabilization control problem for this mechanical system with an external unknown matched disturbance. A fixed-time robust stabilizing control method is developed. Firstly, the system's motion equations are established using the Euler-Lagrange modelling method. Secondly, some appropriate state variables are chosen to change the system to be a quasi-integrator chain system. And then, a terminal sliding surface is constructed for the chained system. And a sliding mode controller is designed to make the sliding surface converge to zero within a fixed time. This ensures that the bridge crane system is robustly stabilized at the target value within a fixed time. Finally, the effectiveness of the presented control method is verified through numerical examples.