Sliding mode control for uncertain discrete-time systems based on fractional order reaching law

Abstract

The design and validation of a new fractional order (FO) reaching law for uncertain discrete-time systems is studied. A sliding mode controller is subsequently constructed by adopting this law. Unlike previous works, the presented reaching law is established on the basis of the Grünwald–Letnikow FO calculus of the switching function. A high-order disturbance compensator is integrated into this reaching law to evaluate and compensate the disturbance. A rigorous theoretical analysis is given to demonstrate the superior performance of the reaching law. Results indicate that the developed method owns the ability to guarantee an O(Tn+1) order ultimate magnitude of the quasi-sliding mode domain. Therefore, the presented method is capable of further mitigating chattering and guaranteeing a further improvement on the control accuracy in comparison with previous reaching law methods. Moreover, sliding mode dynamics of the discrete-time system in and out the vicinities of the sliding surface is analysed in detail. Simulation results are presented to verify the feasibility and effectiveness of the developed method.