Hierarchical global fast terminal sliding-mode control for a bridge travelling crane system

The bridge crane system is a typical under-actuated system that is widely used in production and life. Although various scholars have conducted extensive research on the bridge crane system in recent years, there are still many problems, such as the trajectory planning of the cart and the anti-sway control of the cargo. In order to tackle the problem of the anti-sway control of the cargo, a hierarchical global fast terminal sliding-mode control (H-GFTSMC) is developed in this work. First, the Lagrange equations are used to model the system dynamics. Then, an appropriate hierarchical global fast terminal sliding-mode controller is designed to achieve anti-sway control of the cargo, and it is proved that each sliding-mode surface is progressively stable. A series of simulations were implemented to verify the effectiveness of the control method. The simulation results show that the H-GFTSMC has better control performance compared with the proportional–integral–derivative control method. When changing the cable length or adding non-negligible noise to the system, the H-GFTSMC still has good robustness.