Sliding-Mode Controller Based on Fractional Order Calculus for a Class of Nonlinear Systems

This paper presents a new approach of fractional order sliding mode controllers (FOSMC) for a class of nonlinear systems which have a single input and two outputs (SITO). Firstly, two fractional order sliding surfaces S1 and S2 were proposed with an intermediate variable z transferred from S2 to S1 in order to hierarchy the two sliding surfaces. Secondly, a control law was determined in order to control the two outputs. A sliding control stability condition was obtained by using the properties of the fractional order calculus. Finally, the effectiveness and robustness of the proposed approach were demonstrated by comparing its performance with the one of the conventional sliding mode controller (SMC), which is based on integer order derivatives. Simulation results were provided for the cases of controlling a ball-beam and inverted pendulum systems