Design of a sliding mode controller with a nonlinear time-varying sliding surface

In this study, a new sliding surface design approach for second-order systems is proposed that varies the sliding surface in a nonlinear and time-varying fashion. The control law is reformulated by using the new surface that is defined in the new co-ordinate axis. The nonlinear surface is then moved in a proper direction by using a time-varying function. Simulations are performed on a second-order nonlinear model of a two-link planar manipulator system. The results of the new design methodology are compared with a classical sliding mode controller and a sliding mode controller possessing a discretely moving sliding surface. It has been shown that the proposed method has improved the system performance in terms of a decrease in the reaching time, robustness to disturbances and smoother phase plane trajectory. The decrease obtained in the reaching time is quite valuable, as it improves the robustness of the controlled system to external disturbances and parameter variations.