Abstract
The essential feature of conventional proxy-based sliding mode control (PSMC) method is the introduction of a proxy, which is controlled by a normal sliding mode control (SMC) approach to track the desired trajectory. Both the safety problem in conventional stiff position control and the chattering problem in the SMC are overcome by the PSMC strategy. Meanwhile, the stability problem of PSMC is not well addressed for general nonlinear systems. In this paper, a new PSMC method is proposed for robust tracking control of a class of second-order nonlinear systems. A PD type virtual coupling is used and a specified sliding mode controller is designed in the proposed PSMC method. Based on the model of a class of second-order nonlinear systems, the stability of the closed-loop PSMC system is proved by Lyapunov theorem. Numerical simulations were carried out to verify the propose method.
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