Anti-sway control of an overhead crane with persistent disturbances by Lyapunov method

An overhead crane is an underactuated system with less driving force than its degrees of freedom, which suffers from such factors as complex coupling between states, continuous disturbances, and so on. This paper designs an energy-based adaptive controller, which, together with a constructed fuzzy observer, makes an overhead crane stable at an “inclined” equilibrium point. Specifically, based on Lagrange's method, the traditional model for a crane is transformed into a novel dynamic equation expressed in new coordinates, based on which, uncertain disturbance within the system is then estimated by constructing a fuzzy observer, and an energy-based adaptive controller is subsequently designed to achieve satisfactory control performance. The closed-loop system is proven to be asymptotically stable by Lyapunov techniques and LaSalle's invariance theorem. Finally, some simulation results are included to show the advantages of the proposed control strategy.