A novel low chattering sliding mode controller

The purpose of this paper is to design a high performance sliding mode controller through the use of a new switching function. This method uses the idea of boundary layer sliding mode while taking the boundary layer width as a function of the angle between the state trajectory and the sliding surface which we call approach angle. By incorporating the approach angle into the switching function, the overall sliding mode controller guarantees the asymptotical stability of the system while having only a slight amount of chattering. This method overcomes the shortcomings of a pure discontinuous switching such as excessive chattering, while maintaining its benefit that is the asymptotical stability is guaranteed. The proposed method is used to control an inverted pendulum. It is also compared with a pure switching function. Simulation results show that the new sliding mode controller has good control performance with negligible chattering.