In this paper we propose a virtual closed loop model parameterization to perform system identification. This parameterization is designed to achieve specific goals. We show that the method includes, as special cases, known methods for closed loop identification and also offers additional flexibility. We analyze the ramifications of the new tailor-made parameterization for systems operating in closed loop. The approach exploits a property of Box-Jenkins models in order to minimize the bias arising from feedback and noise model mismatch.
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