Robust control of rubber–tyred gantry cranes with structural elasticity.

• A new mathematical model for rubber–tyred gantry cranes is developed considering the elastic structure. • Two advanced sliding mode controls are proposed to validate dynamic model. • Experiment shows the sufficient accuracy and effective application of modeling and control to cranes. A gantry crane holds strict underactuation and elastic multibody structure, and thus faces challenges in control system design. For model–based control, we develop a three–dimensional dynamic model of rubber–tyred gantry cranes considering the distributed mass and bending deformation of gantry. Such modelling hybridises the lumped model of trolley–bridge–payload motions and continuous model of gantry vibration. We consider a complex operation in which three motors composed of travelling trolley, pushing bridge and hoisting container run simultaneously. We propose two versions of the robust controller, namely, dynamic sliding mode and fast terminal sliding mode for tracking the three motions, eliminating swings of container, and reducing the bending vibration of elastic gantry. Simulation and experiment reveal precision and effective application of our crane modelling to control approaches. The control system effectively tracks and stabilises all outputs and achieves robustness when a crane suffers from the structural and parametric uncertainties. [ABSTRACT FROM AUTHOR]