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Tower cranes are typical underactuated systems, characterized by high-state coupling and lack of available control inputs, resulting in major challenges for the dynamics analysis. A dynamic model of tower cranes without simplifications is established, where the nonlinearities, unknown frictions, and wind disturbances are emphatically considered. Based on the developed model, an adaptive robust sliding mode control (ARSMC) scheme is proposed, which can achieve accurate payload positioning and sufficient swings suppression, even in the presence of unknown frictions and wind disturbances. Specifically, a sliding mode surface and a suppression function are designed to eliminate payload swings; a sliding mode convergence law is constructed to alleviate the chattering problem; the robustness of the controller is enhanced by designing an estimation strategy of wind disturbances; an effective parameter estimation is presented to improve the adaptive ability of unknown parameters. The stability of the closed-loop system is proved by utilizing the Lyapunov technique and LaSalle’s invariance principle. Finally, the effectiveness of the tower crane model and the superiority of the ARSMC are verified by multiple comparative simulations.
Hou et al. (2024) studied this question.