Exponential stabilization of flexural sway vibration of gantry crane via boundary control method

This paper aims to develop a boundary control solution for complicated gantry crane coupled motions. In addition to the large angle sway motion, the crane cable has a flexural transverse vibration. The Hamilton principle has been utilized to derive the governing partial differential equations of motion. The control objectives which are sought include: moving the payload to the desired position; reducing the payload swing with large sway angle; and finally suppressing the cable transverse vibrations in the presence of boundary disturbances simultaneously. These simultaneous boundary control objectives make the problem challenging. The proposed control approach is based on the original nonlinear hybrid partial differential equation–ordinary differential equation model without any simplifications of sway motion nonlinearities, coupling effects, and the effect of gravitational force. Using the Lyapunov method, a boundary control law has been designed which guarantees the exponential stability and uniform boundedness of the closed-loop system. In order to demonstrate the effectiveness of the proposed control method, numerical simulation results are provided by applying the finite difference method.