Novel Adaptive Hierarchical Sliding Mode Control for Trajectory Tracking and Load Sway Rejection in 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 trajectory tracking and load sway rejection is a more significant issue for crane systems. For these purposes, the nonlinear dynamics of an overhead crane with double-pendulum effect is derived for the controller design. Then, a novel adaptive hierarchical sliding mode controller is presented. Unlike a traditional approach, the proposed one can make fixed sliding mode surface active to search the state trajectories. Such an adaptive design can make the states of the system to enter the desired sliding surface as soon as possible and, at the same time, can also improve the cart tracking precision. The Lyapunov technique and LaSalle's principle are employed to confirm the stability of the whole system. The experimental results validate that the proposed method has superior control performance and robustness with respect to parameter variations.