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Closed-loop system identification via a tailor-made IV method

A bias-correction method for closed-loop identification, the bias-eliminated least squares (BELS) method, is shown to be equivalent to a basic instrumental variable (IV) estimator applied to a predictor for the closed-loop system. This predictor is a function of the plant parameters and the known controller. Corresponding to the related method using a least squares criterion, the method is referred to is the tailor-made IV method for closed-loop identification. The indicated equivalence greatly facilitates the understanding and the analysis of the BELS method.