Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be fully understood when operating in closed-loop. In this paper, we address the consistency of the simplified refined instrumental variable method for continuous-time systems (SRIVC) and its closed-loop variant CLSRIVC when they are applied on data that is generated from a feedback loop. In particular, we consider feedback loops consisting of continuous-time controllers, as well as the discrete-time control case. This paper proves that the SRIVC and CLSRIVC estimators are not generically consistent when there is a continuous-time controller in the loop, and that generic consistency can be achieved when the controller is implemented in discrete-time. Numerical simulations are presented to support the theoretical results.

中文翻译：

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闭环连续时间系统辨识的精化工具变量方法的一致性分析


改进的工具变量方法已广泛用于开环和闭环设置中连续时间系统的识别。然而，这些方法在闭环运行时的理论特性仍有待完全理解。在本文中，我们解决了连续时间系统的简化精化工具变量法（SRIVC）及其闭环变体 CLSRIVC 在应用于反馈环路生成的数据时的一致性。特别是，我们考虑由连续时间控制器组成的反馈回路以及离散时间控制情况。本文证明了当循环中存在连续时间控制器时，SRIVC 和 CLSRIVC 估计器不具有通用一致性，而当控制器以离散时间实现时，可以实现通用一致性。提出了数值模拟来支持理论结果。