<p>This paper addresses the positioning and payload swing suppression problem for overhead cranes subject to input time delay and external disturbances, and proposes a delay-compensated discrete terminal sliding mode control method (DC-TSMC). A discrete system model of the overhead crane incorporating input time delay and disturbances is established. A Smith-predictor-based extended state observer (SP-ESO) is designed to simultaneously estimate system states and disturbances, with the disturbance rate of change introduced as an extended state to enhance disturbance tracking capability. Based on the predicted effects of input times delay, a transient-aware adaptive compensation strategy is proposed, which dynamically adjusts fusion weights according to system states to achieve an optimal balance between steady-state accuracy and transient response. A delay-compensated discrete terminal sliding mode controller is designed, achieving finite-time convergence of tracking error through a double-power reaching law. Combined with boundary layer design, chattering is effectively suppressed and disturbance feedforward compensation is realized. The finite-time convergence of closed-loop tracking error and robust stability under interval time delay are rigorously proven via Lyapunov theory. Simulation and experimental results show that the proposed method outperforms existing literature methods, with positioning error within <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(0.02 \, m\)</EquationSource> </InlineEquation>, a maximum payload swing angle of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(3^\circ\)</EquationSource> </InlineEquation>, and fast overshoot-free convergence in simulations. Under actual <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(80 \, ms\)</EquationSource> </InlineEquation> time delay and gust disturbance conditions, the system achieves a steady-state error below <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(0.06 \, m\)</EquationSource> </InlineEquation>, a peak swing angle of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(4.6^\circ\)</EquationSource> </InlineEquation>, and smooth chattering-free control inputs. This method balances positioning anti-sway performance and disturbance rejection, verifying its effectiveness and engineering applicability, and provides an engineering reference for industrial overhead cranes.</p>

Discrete sliding mode control method for overhead cranes with time-delay disturbances based on extended state observer

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发表日期：

2026年8月4日

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Yunsheng Xin,
Ziyue Lv,
Shenzhen Pan,
Xinyu Yan

摘要

This paper addresses the positioning and payload swing suppression problem for overhead cranes subject to input time delay and external disturbances, and proposes a delay-compensated discrete terminal sliding mode control method (DC-TSMC). A discrete system model of the overhead crane incorporating input time delay and disturbances is established. A Smith-predictor-based extended state observer (SP-ESO) is designed to simultaneously estimate system states and disturbances, with the disturbance rate of change introduced as an extended state to enhance disturbance tracking capability. Based on the predicted effects of input times delay, a transient-aware adaptive compensation strategy is proposed, which dynamically adjusts fusion weights according to system states to achieve an optimal balance between steady-state accuracy and transient response. A delay-compensated discrete terminal sliding mode controller is designed, achieving finite-time convergence of tracking error through a double-power reaching law. Combined with boundary layer design, chattering is effectively suppressed and disturbance feedforward compensation is realized. The finite-time convergence of closed-loop tracking error and robust stability under interval time delay are rigorously proven via Lyapunov theory. Simulation and experimental results show that the proposed method outperforms existing literature methods, with positioning error within \(0.02 \, m\) , a maximum payload swing angle of \(3^\circ\) , and fast overshoot-free convergence in simulations. Under actual \(80 \, ms\) time delay and gust disturbance conditions, the system achieves a steady-state error below \(0.06 \, m\) , a peak swing angle of \(4.6^\circ\) , and smooth chattering-free control inputs. This method balances positioning anti-sway performance and disturbance rejection, verifying its effectiveness and engineering applicability, and provides an engineering reference for industrial overhead cranes.