Adaptive Boundary Control of a Gantry Crane System with Parametric Uncertainty

In this study, an adaptive boundary control method is investigated for the gantry crane system with parametric uncertainty and boundary disturbance. Firstly, utilizing Hamilton’s principle, the governing equation and boundary conditions described by partial differential equations and ordinary differential equations are derived. Then, two cooperative adaptive boundary controllers and two adaptive laws are designed to suppress the vibration of the flexible cable and compensate for the unknown mass of the trolley and payload of the system. Besides, the stability of the gantry crane system is presented by Lyapunov’s direct method and rigorous mathematical analysis. With the proposed control scheme, the uniform ultimate boundedness of the gantry crane system is achieved. Finally, numerical simulation results are given to demonstrate the advantages and feasibility of the proposed control approach.