Sliding mode control design with time varying sliding surfaces for a class of nonlinear systems

This paper presents sliding mode control (SMC) design for a class of nonlinear systems in which the sliding surface is designed to be linear with time varying slope(s). The sliding surface design is based on the frozen-time approach. The nonlinear system is frozen at each operation step resulting in linear time invariant (LTI) model and the sliding surface is designed for the LTI model. The surface slope is updated at each frozen step which gives, in general, a moving sliding surface. The control term, on the other hand, is designed so that the moving sliding surface is reached in a finite time. Therefore sliding mode is achieved and the nonlinear system is restricted to stay on the moving sliding surface. We demonstrate the design methodology developed in this study on an inverted pendulum model. The simulation results show the success of the method.