This article focuses on the boundary control for a lifting system during the loading process. A lifting system during the loading process is essentially a non-conservative system. The system dynamics are modelled based on the extended Hamilton’s principle. We consider the unmeasurable impact force caused by the uncertain materials falling velocity as a boundary disturbance and design a disturbance observer to eliminate its effect. The control system needs to guarantee the output constraints that the boundary vibration and dynamic tension fluctuation are both suppressed in a constrained scope of the desired value. Two appropriate boundary backstepping control schemes are proposed by actuators acting on different boundaries to realize the output constraints and to ensure the stability of the closed-loop system in theory. Numerical simulations are provided to illustrate the effectiveness of the proposed control laws in suppressing the cage vibration and rope dynamic tension fluctuation amplitude.

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