A Novel Exponential Reaching Law of Discrete-Time Sliding-Mode Control

In this paper, a novel reaching law for discretetime sliding-mode control is proposed. The reaching law is established based on an exponential term that dynamically adapts to the variation of the switching function. The difference function is also employed to redefine the change rate as the second-order difference of the disturbance. Unlike existing works, the proposed reaching law is able to guarantee smaller width of the quasi-sliding-mode domain (QSMD) while decreasing the reaching time in the same time. The ultimate magnitude of the QSMD in proposed method is of the order O(T-3). Moreover, the reaching steps for the system to converge to the sliding surface are obtained and the system dynamics in and out the QSMD are theoretically analyzed. Both numerical simulations and experimental investigations on a piezoelectric actuator are employed to validate the effectiveness of the proposed method.