Sliding mode control based on three-sliding-surface for an inverted pendulum system

This paper proposes an effective method to balance the confliction between higher steady-state precision and stronger robustness in sliding-mode control systems. Based on the relationship between steady-state precision and sliding-mode surface parameters, three sliding surfaces are used in the design of sliding-mode control (SMC). The first and the second sliding-mode surfaces are mainly responsible for guaranteeing the finite-time reachability, the finite-time convergence of the control system states towards a vicinity around the equilibrium origin along the predesigned sliding-mode surface, while the third sliding-mode surface is used to further reduce the terminal steady-state error. Both the performances of the states reaching phase and sliding-mode moving phase of SMC can be feasibly coordinated. A chattering-free sliding-mode control with higher steady-state precision has been developed for a second-order nonlinear inverted pendulum tracking system. Simulation and Comparison results are presented to verify the effectiveness of the proposed approach. Compared with the conventional SMC, the proposed SMC can not only eliminate chattering but also provide higher steady-state accuracy. The robustness of the proposed SMC is also satisfactory.