Tracking approach of double pendulum cranes with variable rope lengths using sliding mode technique

Cranes are widely employed for transportation in many industrial fields. However, strong couplings and high nonlinearities increase difficulty of designing effective control methods for crane systems. Additionally, complex environments may bring uncertainties and unfavorable factors for the control problem. In this paper, we design an effective tracking approach for double pendulum cranes considering variable rope lengths problem by using sliding mode technique, to further improve the robustness and achieve the control objectives of accurate tracking, while effective suppression for double pendulum swing is also ensured. We design a proper sliding mode surface containing all state variables, which effectively suppresses swing angles of the payload and the hook. Then, the time delay estimator technique is used to estimate parameter uncertainty-related terms and the estimation errors are effectively tackled by using sliding mode technique. The effectiveness is rigorously proved by Lyapunov stability theory. At last, comprehensive simulations are implemented to show the proper performance.