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.

中文翻译：

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具有增强功率趋近律的离散时间滑模控制


本文介绍了一种新颖的离散时间滑模控制趋近律的设计、分析和验证。趋近律的控制增益由幂函数和动态适应开关函数变化的指数项自动调节。趋近律还利用摄动估计和差分函数将变化率重新定义为不确定性的二阶差分。与之前的方法相比，所提出的趋近律能够以明智的方式修正控制增益，进一步减轻抖振，并保证更小的准滑模域（QSMD）宽度。为了描述到达阶段和滑动阶段相对于控制增益值的系统动力学，对所提出的到达律的递减带和QSMD（最终带）进行了理论分析。还获得了切换函数向滑动面收敛的到达步骤。通过数值模拟和压电执行器的实验研究验证了该方法的有效性。