Abstract
This paper investigates estimating the frequency response of the normalized coprime factors of a possibly unstable transfer function from closed-loop frequency domain experimental data. A stochastic framework has been adopted. The dual Youla-Kucera parametrization approach in closed-loop system identification has been developed to guarantee the normality of the estimated frequency response. A parametrization of all the normalized coprime factors has been established for transfer functions internally stabilizable by a known controller. Based on this parametrization, interpolation conditions have been derived for the measurement errors being consistent with the stabilizing controller and experimental data. An analytic expression has been obtained for the maximum likelihood estimate of the frequency response. The effectiveness of the suggested method is confirmed through numerical simulations.
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