Robust sliding-mode control for a gantry crane system subject to external disturbance

This paper devotes to proposing a sliding-mode controller to reject external disturbance and stabilize the gantry crane system which formulated by the partial differential equations (PDEs). The control objectives are transporting trolley hanging with a payload to the specified place while eliminating the oscillation and rejecting the external disturbance in transportation. By applying the operator semigroup theory, it can be proved that proposed controller is well-posed to the gantry crane system. Furthermore, asymptotic stability has been proved through the application of the extended Krasovskii-LaSalles’ invariance principle. Ultimately, numerical simulations are given to illustrate the advance of proposed control scheme and an experiment is conducted to display the feasibility of proposed sliding-mode controller.