This paper deals with modelling and control of an overhead crane with a flexible cable. The developed dynamical model includes both transverse vibrations of the flexible cable and large swing angles of cable while the trolley is moving horizontally. To carry out the modelling, Rayleigh-Ritz discretization method is used to achieve an ordinary differential equation (ODE) model for transverse deflection of the cable with finite generalized degrees of freedom. Using the Euler–Lagrange formulation, a nonlinear dynamic model of the crane system with a flexible cable is obtained. The control objective is to move the payload position to the desired point and at the same time, to reduce the payload swing and to suppress the cable's transverse vibration. To this end, a static state feedback control combined with integral error feedback is proposed. Simulations are performed using the developed nonlinear model under various conditions to illustrate the effectiveness of the proposed control system.
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