Sliding mode controller design with fractional order differentiation: applications for unstable time delay systems

This paper presents a design method for a sliding mode controller with the contribution of a fractional order differential operator. The conventional sliding mode controller has been widely studied in different control applications. This paper proposes that the fractional order differential operator enlarges the output span of the classical sliding mode controller to obtain a better-fitting control signal for enhanced control performance. The sliding surface and the equivalent control law are modified with the addition of a fractional differential operator and a conventional one. The proposed sliding mode controller with fractional order differentiation is applied to the unstable time delay systems successfully. Illustrative examples are presented to demonstrate the performance of the proposed design method.