New insights in closed-loop identification with bias-eliminated least-squares (BELS)

A bias-correction method for closed-loop identification, introduced in the literature as the bias-eliminated least squares (BELS) method [9], is shown to be equivalent to a basic instrumental variable 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 as the tailor-made IV method for closed-loop identification. The indicated equivalence greatly facilitates the understanding and the analysis of the BELS method.