Repetitive controllers represent an attractive solution for systems having periodic reference or disturbance signals with high harmonic content. In order to obtain some performance improvements for three-phase plants, as grid-connected converters, complex repetitive controllers were proposed later in literature. In this article, the advantages of complex repetitive control systems over the real ones are analyzed. In addition, sufficient conditions for the input–output stability of complex repetitive control systems and modified complex repetitive control systems are obtained from the small gain theorem. These stability conditions are then used to derive the stability domains for complex repetitive control systems. Further, a relative stability analysis based on the sensitivity function is introduced. An experimental application based on an active power filter is used to exemplify the effectiveness of the proposed stability analysis.

中文翻译：

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复数nk + m重复控制器应用于空间向量：优势与稳定性分析

对于具有高谐波含量的周期性参考或干扰信号的系统，重复控制器代表了一种有吸引力的解决方案。为了获得一些三相设备的性能改进，作为并网变流器，在后面的文献中提出了复杂的重复控制器。在本文中，分析了复杂重复控制系统相对于真实系统的优势。此外，由小增益定理得到了复杂重复控制系统和修正的复杂重复控制系统输入输出稳定性的充分条件。然后使用这些稳定性条件推导出复杂重复控制系统的稳定性域。此外，引入了基于灵敏度函数的相对稳定性分析。