Overhead cranes are underactuated systems with significant model uncertainties that pose major challenges for precise anti-swing control. These uncertainties, including unknown parameters and varying dynamics, severely limit the performance of conventional controllers. To address the control challenge of 7-degree-of-freedom (7-DOF) overhead cranes with variable cable length and double spherical pendulum dynamics, this paper proposes an adaptive sliding mode control method integrated with time-delay estimation. First, a comprehensive dynamic model that accounts for bridge movement, trolley travel, hoisting motion, and spherical swings of both the hook and the payload is established. Then, a sliding surface is constructed based on the coupling analysis between actuated and unactuated dynamics. The core innovation lies in the integration of time-delay estimation with adaptive sliding mode control, where the time-delay estimator provides accurate approximation of unknown system dynamics, while the adaptive mechanism compensates for estimation errors and parameter variations. This dual approach ensures robust performance despite model inaccuracies. Lyapunov stability analysis rigorously confirms the uniform ultimate boundedness of all closed-loop signals under model uncertainties. Experimental tests further show that the designed controller achieves accurate positioning and robust swing suppression, outperforming conventional controllers in challenging working conditions.
Li et al. (2026) studied this question.