Precise Modelling of a Gantry Crane System Including Friction, 3D Angular Swing and Hoisting Cable Flexibility

A crane system offers a typical control problem being an under actuated MIMO system. In this paper the precise modelling of a 2D gantry crane system with 3 DOF is considered. First a simple dynamic model of the system is obtained using Lagrange’s equations of motion. Then, friction non-linearities were added to the model, which were found to decrease the output magnitudes from reference values. The model was further improved by considering the possibility of 3D angular swing which showed more accurate transient responses. Finally, the dynamics of hoisting cable flexibility was added to the system resulting in a complex model requiring time consuming simulation. But, significant change was seen in the angular swing output which will significantly affect controller performance. The models considering either flexibility or 3D load swing are comparatively less complex than the combined model. The precise model to be considered is a trade-off between safety (minimum swing angle) and precise load handling.