Closed-loop system identification using the dual Youla control parametrization

Identification of an unknown plant operated in a closed-loop environment in the presence of external disturbance is considered. Under closed-loop experiment, the objectives of system identification are not only to obtain a best fit of the unknown plant but also to make close prediction or estimation of closed-loop system responses. By using the a priori information of a known stabilizing controller and the dual Youla control parametrization, identification of an unknown plant in a closed-loop system can be simplified to that of an open-loop reduced system. It is shown that the output prediction errors of the estimates for both the original plant and the reduced system are equal. Furthermore, if the feedback controller is of normalized coprime factorization, then to find a best fit of the reduced system amounts to establishing a nominal closed-loop system with which the signals of the true closed-loop system can be predicted in a least squares sense. In addition, the optimal experimental designs for reducing bias distribution of the estimate of the reduced system, fitting of closed-loop frequency responses, and estimating the unknown plant expressed by coprime factors are coincidental.