Discrete-Time Sliding-Mode Control with Enhanced Power Reaching Law

This paper presents the design, analysis, and verification of a novel reaching law for discrete-time sliding-mode control. The control gains of the reaching law are automatically regulated by the power function and the exponential term that dynamically adapts to the variation of the switching function. The reaching law also employs the perturbation estimation and the difference function to redefine the change rate as the second-order difference of the uncertainty. Compared with previous methods, the proposed reaching law has the capability to amend the control gains in a wise manner, further mitigate chattering, and guarantee a smaller width of the quasi-sliding-mode domain (QSMD). In order to describe the system dynamics in the reaching phase and the sliding phase with respect to control gain values, both the decrement band and the QSMD (ultimate band) of the proposed reaching law are theoretically analyzed. The reaching steps for the switching function to converge toward the sliding surface are also obtained. The effectiveness of the proposed method is verified through numerical simulations and experimental investigations on a piezoelectric actuator.