The paper addresses the problem of chattering elimination in sliding mode control for sampled data dynamical systems and proposes an innovative control scheme. The key to the proposed control method is utilizing a pregenerated nonswitching type reference sliding variable profile to control the disturbed plant. As sampled data systems contain sample-and-hold devices in their input and output channels, we carry out a discrete time analysis. We consider the discretization effects on the controller in two aspects: the pace of convergence of the system and the ultimate band width. Consequently, in the reference sliding variable generator, we analyse two reaching laws, differently adapting to changes of the controller’s frequency. We prove that this approach not only minimizes the chattering phenomenon but also provides a reduction of the quasi-sliding mode band width, which in general case remains of O(T) order. Furthermore, the proposed control method incorporates a disturbance compensation algorithm, which results in the ultimate band width of O(T²) order. Finally, we also show that a certain selection of the sliding plane guarantees limitation of all the state variables’ errors to O(T²) order as well. Therefore, the proposed control algorithm significantly improves the system’s robustness.

中文翻译：

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基于无抖动参考滑动变量的SMC

该论文解决了采样数据动力学系统滑模控制中抖振消除的问题，并提出了一种创新的控制方案。提出的控制方法的关键是利用预生成的非切换式参考滑动变量轮廓来控制受干扰的工厂。由于采样数据系统在其输入和输出通道中包含采样保持设备，因此我们进行了离散时间分析。我们从两个方面考虑离散化对控制器的影响：系统的收敛速度和最终带宽。因此，在参考滑动变量生成器中，我们分析了两个到达定律，它们分别适应于控制器频率的变化。O（T）阶。此外，所提出的控制方法结合了干扰补偿算法，从而导致最终带宽为O（T ²）阶。最后，我们还表明，对滑动面的某种选择也保证了将所有状态变量的误差限制为O（T ²）阶。因此，提出的控制算法大大提高了系统的鲁棒性。