Modelling and Control of an Overhead Crane with a Variable Length Flexible Cable

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This paper introduces a novel mathematical model that represents an overhead crane with flexible cable and load hoisting/lowering. The model includes the transverse vibrations of the flexible cable. Highly non-linear Partial Differential Equations and Ordinary Differential Equations that govern the motion of the crane system within the time-varying spatial domain are derived via calculus of variation and Hamilton's principle. A proportional derivative control scheme is applied to drive the underlying crane so that the cable and payload swing are damped out. Numerical simulations for the control performance of the considered system are presented for various operating conditions.


Cable swing; Cables — Vibration; Crane motion; Cranes; derricks; etc.; Damping (Mechanics); Differential equations; Flexible cable; Mathematical modeling; Mathematical models; Overhead cranes; Payload swing; Proportional derivative control; Simulation; Transverse vibration; Variable-time modified Galerkin methods


Applied Mathematics | Computer-Aided Engineering and Design | Control Theory | Dynamics and Dynamical Systems | Mechanical Engineering | Non-linear Dynamics


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