Sliding-mode-based trajectory tracking and load sway suppression control for double-pendulum overhead cranes

Overhead cranes with double-pendulum effect seem more practical than those with single-pendulum effect. However, in this case, the dynamic performance analysis and the controller design become more difficult. Moreover, achieving both high-precision tracking control and load sway suppression is a more significant issue for crane systems. In order to solve the aforementioned problems, the nonlinear dynamics of a 2-D overhead crane with double-pendulum effect is derived for controller design. Then, a novel sliding mode controller with nonlinear sliding surface is presented. Unlike a traditional linear sliding surface, the nonlinear one can change the damping ratio of the closed-loop system from its initial low value to final high value. The low value can provide a quick response, whereas the high value one can eliminate overshoot to make the cart track the given trajectory more precisely. The stability of the whole system is confirmed by the Lyapunov technique. The numerical simulation and experimental results validate that the proposed method has superior control performance and robustness with respect to parameter variations and external disturbance.