Modelling and control of overhead cranes with flexible variable-length cable by finite element method

This work considers the modelling problem of the dynamics of overhead cranes with flexible cable and load hoisting or lowering during crane travel. The analysis includes the transverse vibrations of the flexible cable and trolley motion. A set of nonlinear ordinary differential equations governing the motion of the crane system with time-varying spatial domain is derived via the calculus of variation and Hamilton's principle. A variable-domain finite element method is used to discretize the nonlinear system. A proportional- derivative controller is suggested to drive the crane to a desired destination. Numerical simulations are provided to show the effectiveness of the developed model and to illustrate the results.