Vibration suppression of an underwater crane with bounded input

This article investigates the problem of vibration suppression and position tracking of the underwater crane system subject to input constraints. Underwater, the vehicle carrying the flexible loads moves along the guide rails to complete tasks. Under the original distributed parameter model, the backsteeping method is adopted to design a boundary control scheme to suppress the elastic deformation of the flexible load and drive the vehicle and the guide rail to a specified position. The Nussbaum function is introduced to handle the input constraint. Both the Lyapunov stability analysis and simulation illustrate that the proposed control scheme ensures the uniformly ultimately bounded stability of the underwater crane system.