Global-Equivalent Sliding Mode Control Method for Bridge Crane

A wide application of sliding mode variable structure control as a nonlinear robust control method, has been witnessed in anti-swing positioning control of bridge crane system. Aiming at the problem that the sliding mode variable structure control system of bridge crane is not robust in approaching process, a new Global-Equivalent Sliding Mode Controller (GESMC) based on bridge crane system is proposed. This controller can realize the anti-sway positioning control of the bridge crane system under the condition of uncertain model parameters and external disturbance. The proposed controller, different from the traditional sliding mode control, excels in improving system robustness through keeping the system states in the sliding surface during the whole response process. Specifically, it initiates with the design of a global sliding surface, which can eliminate the sliding mode approach process of the system and achieve global robustness in the system. Afterwards, a new switching function combined with the equivalent sliding mode control method is incorporated to effectively reduce the chattering generated when the system reaches the sliding mode manifold. Its asymptotic stability is proven without a priori knowledge on the bounds of unknown disturbances by using the Lyapunov stability theory. Lastly, the simulation conducted verifies the effectiveness and robustness of the GESMC proposed in this paper and meanwhile demonstrates a comparatively favorable performance for the GESMC in reducing chattering.