It is seen that when the hook mass is larger than the load mass or the load has distributed mass property, the load sway of the crane system presents as double-pendulum effect. In this situation, crane system has two different natural frequencies so that the sway characteristic becomes more complex and greatly increases the difficulty of the dynamic performance analysis and controller design. Moreover, the rope length changes significantly affect the stability and control performance of the crane system. In order to solve the aforementioned problems, the linear dynamics of a two-dimensional overhead crane with double-pendulum effect is derived based on a disturbance observer, and is decoupled for controller design by modal analysis. Next, a state feedback controller is presented to achieve robust control performance for a given range of rope length changes. The controller gains are obtained via linear matrix inequality optimization method. Finally, numerical simulations and experimental results validate that the proposed method has superior control performance.
