Fractional Order Exponential Type Discrete-time Sliding Mode Control

In this paper, a new fractional order exponential type reaching law (FOE-RL) is presented for the uncertain discrete-time system. The FOE-RL is constructed by adopting the exponential term and the Grünwald-Letnikov fractional order (FO) calculus of the switching function and the sign function. Compared to the integer order reaching laws (IO-RLs), the proposed reaching law is capable of regulating the system trajectory converging to a specified band whose width can be smaller than the upper bound of change rate of the disturbance and even approach zero. Hence, the proposed method has the ability to further suppress chattering and enhance the control accuracy compared to other reaching law strategies. The decrement band and the quasi-sliding mode domain (QSMD) of the uncertain system are analyzed. The sliding surface can be reached in finite steps, even though the system is suffering from uncertainties and disturbances. Numerical simulation examples are given to testify the validity of the presented method.