Summary A finite time disturbance observer (FTDO) based adaptive hierarchical sliding mode control (AHSMC) is proposed for 4‐DOF tower crane systems with unknown external disturbances. More specifically, to overcome the unknown disturbances, an FTDO combined with the designed adaptive observation error is presented to estimate both matched and unmatched disturbances. Then a new error dynamics taking into account the unmatched disturbances is defined, based on which, a novel nonsingular fast terminal sliding mode (FTSM) surfaces is designed to improve the convergence of system states. Finally, in order to ensure the stability of each subsystem, an AHSMC law incorporating the suggested FTSM‐type reaching law is presented to realize the anti‐sway and positioning control of tower crane system. The finite‐time stability analysis of the closed‐loop system is derived by Lyapunov technique, and simulation results verify the effectiveness of the presented control strategy.

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To address the challenging problem of fixed-time anti-sway and positioning control for tower cranes with uncertain disturbances and input saturation, a novel fixed-time anti-saturation robust algorithm is proposed. First, on the basis of a newly designed fixed-time convergence system, a fixed-time disturbance observer (FTDO) is developed to estimate the matched and unmatched disturbances. Then, an anti-saturation compensator is employed to deal with the input saturation and make the control input leave the saturated region rapidly. Upon which, a novel non-singular fast terminal sliding mode surface is presented. Furthermore, in order to ensure the stability of each subsystem, a hierarchical sliding mode surface taking into account unmatched disturbances and input saturation is designed. Finally, the FTDO based hierarchical sliding mode control law is introduced to improve the transient control performance and robustness of tower cranes. The fixed-time convergence of the closed-loop system is proved by Lyapunov technique. Numerical simulations for four scenarios demonstrate the validity of the presented control scheme and fastest convergence speed in comparison to the recently proposed fixed-time control methods.

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