A Time-Varying PD Sliding Mode Control Method for the Container Crane Based on a Radial-Spring Damper

For the multi-rope structure of the container crane system and its large mass payload anti-swing positioning problem, an equivalent double-swing model based on radial spring-dampers is established and a time-varying PD sliding mode controller (TVPD-SMC) with improved transient performance is proposed. In particular, the dynamics of the container crane system are first analyzed using the Lagrange method, and an equivalent double pendulum dynamics model of the crane is established. Compared with the traditional double pendulum model, this model ensures the accuracy of modeling without measuring the second pendulum angle. On this basis, an enhanced coupled time-varying sliding mode control method is designed to eliminate the sliding mode control method’s reaching phase and improves the robustness of the controller. Finally, the convergence and stability of the closed-loop system are proved using the Lyapunov technique and the Lasalle invariance theorem, and the simulation results demonstrate the effectiveness of the method.