Modelling and control of an overhead crane with a variable length flexible cable

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...