Iterative identification and control using non-normalized coprime factors with application in wafer stage motion control

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 ν-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.