Dynamical modelling and nonlinear control of a 3D crane

Based on Lagrange equations, a 3D crane system dynamic model is derived which describes the simultaneous travelling, traversing, and hoisting motions of the crane, and the resulting load swing. With this dynamic model, this paper presents a nonlinear controller design scheme for the 3D crane payload based on partial feedback linearization technique. By choosing the actuated degrees corresponding to the freedom as the system outputs, the controller is designed to track the trajectories of outputs while providing internal dynamics stability of unactuated degrees. The analysis of the system internal dynamics shows that the stability of the zero dynamics guarantees the stability of the control system. Finally, simulation results are presented showing the effectiveness of the prompted controller design scheme.