Adaptive Prescribed-Time Recursive Sliding Mode Control of Underactuated Bridge Crane Systems

As a critical piece of equipment in industrial logistics, the operational efficiency of bridge cranes is influenced by their positioning and sway suppression capabilities. Addressing the challenge of positioning and sway suppression in bridge crane systems when load mass is difficult to estimate accurately, an adaptive prescribed-time sliding mode control (PTSMC) is proposed. Firstly, a two-dimensional bridge crane dynamic model is established using the Lagrange method, then transformed into a controllable cascade form. Secondly, a novel sliding mode variable with an explicit time term is designed for achieving prescribed time convergence, while an adaptive law is introduced to estimate unknown loads in real time. Theoretical analysis demonstrates that the proposed method guarantees convergence of the system state to the equilibrium point within the prescribed time. Numerical simulations validate the effectiveness of this strategy, demonstrating that the system can complete trolley positioning and swing angle suppression within the prescribed time. This significantly enhances the dynamic performance and transfer efficiency of the bridge crane.