Discrete-Time Sliding-Mode Control With Improved Quasi-Sliding-Mode Domain

In this paper, a new discrete reaching law with improved quasi-sliding-mode domain (QSMD) is proposed and a sliding-mode controller is designed for discrete-time systems with uncertainties. By redefining the change rate as the second-order difference of the system uncertainties and adopting the continuous-approximate function, smaller width of the QSMD can be guaranteed. Moreover, the QSMD of the proposed reaching law is obtained and the system dynamics in and out the QSMD are theoretically analyzed. Perturbation estimation technique is employed to estimate the unknown uncertainties. Thus, no prior knowledge of the uncertainty bound is required. Both numerical simulations and experimental results on a piezoelectric actuator are presented to demonstrate the performance of the proposed method.