Robustness against model uncertainty is essential in model-based controller design. It is well known that a relatively small uncertainty in lightly damped poles and zeros can result in a large distance measured in the $\nu $ -gap metric, leading to conservative robust stability and performance guarantees. This paper aims to develop an identification and control procedure that results in less conservative robust stability and performance conditions for linear systems with lightly damped poles and zeros. To achieve this, a connection is established between a distance measure based on a nonnormalized coprime factorization of the system and existing identification criteria in closed-loop system identification. A nominal model of the system is determined by minimizing this distance measure by means of a frequency-domain identification algorithm. Then, a controller synthesis method is proposed that addresses both nominal performance as robust stability. Improved robustness by using the proposed approach compared to existing approaches is confirmed in an experimental example for a system with lightly damped poles and zeros.

中文翻译：

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非归一化互质因子的迭代辨识与控制及其在晶圆台运动控制中的应用

在基于模型的控制器设计中，针对模型不确定性的鲁棒性至关重要。众所周知，在轻阻尼的零极点和零点上相对较小的不确定性会导致以$ \ nu $ -gap度量值度量的距离较大，从而导致保守的鲁棒稳定性和性能保证。本文旨在开发一种识别和控制程序，以使带有弱阻尼极点和零点的线性系统的鲁棒稳定性和性能条件不那么保守。为此，在基于系统的非规范化互质分解的距离度量与闭环系统识别中的现有识别标准之间建立了联系。通过使用频域识别算法最小化此距离度量来确定系统的标称模型。然后，提出了一种控制器综合方法，将标称性能作为鲁棒稳定性来解决。在具有弱阻尼极点和零点的系统的实验示例中，与现有方法相比，通过使用所提出的方法提高了鲁棒性。