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

Abstract

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.