Sliding mode control for fractional order plants via limit cycle prediction

This paper presents some results on frequency-domain analysis of the sliding mode controller for fractional order linear time invariant system. The controlled plant is transformed into a nonlinear feedback system consisting of a linear fractional order plant and a nonlinear switching function. Describing function method is used for prediction of limit cycle of the nonlinearity in the control law. The frequency and amplitude of the limit cycle are used to obtain the switching control gain. This analysis provides a method to select a switching gain to suppress the oscillations.