An Enhanced Coupling PD with Sliding Mode Control Method for Underactuated Double-pendulum Overhead Crane Systems

An enhanced coupling PD with sliding mode control method, called ECPD-SMC in short, is presented for double-pendulum overhead crane systems in this paper. The proposed method replaces the PD controller with the equivalent part of traditional SMC method, without any system parameters. The ECPD-SMC algorithm is composed of PD control part and the SMC control part. The SMC part is utilized for constructing the frame of a controller, providing strong robustness with uncertain model, different system parameters, and external disturbances. The PD control part is used to stabilize the control system. Moreover, the coupling behavior between the trolley movement and the payload swing is enhanced, and hence, leads to an improved control performance. As shown by Lyapunov techniques and Schur complement, the proposed ECPD-SMC guarantees asymptotic result even in the presence of uncertainties, including model, system parameters, and various disturbances. Some simulation results are included to demonstrate the correctness and superior control performance of the designed controller.