Modeling and vibration suppression for overhead crane in planar space with nonlinear time-varying actuator faults and uncertain control directions

Bridge cranes used for vertical lifting and horizontal transportation of heavy objects are widely used in engineering. Based on the Hamilton principle, a dynamic model of a bridge crane system in planar space is established for the first time in this paper, and the movement of the main beam and trolley in planar space is considered at the same time. This paper introduces an adaptive fault-tolerant boundary control scheme, grounded in the Nussbaum function, to address the challenges posed by time-varying actuator faults and uncertain control directions. Ultimately, the control scheme can effectively suppress cable vibrations and achieve position tracking for both the main beam and the trolley, so as to provide a strong safety guarantee for the workers operating the bridge crane. The Lyapunov method is utilized to demonstrate the uniform ultimate boundedness of the closed-loop system. Furthermore, the effectiveness of the proposed control method is corroborated by simulation results.