On the relation between a bias-eliminated least-squares (BELS) and an IV estimator in closed-loop identification

A bias-correction method for closed-loop identification, introduced in the literature as the bias-eliminated least-squares (BELS) method (Zheng & Feng ,Automatica 31 (1995) 1019), is shown to be equivalent to a basic instrumen tal variable estimator applied to a predictor for the closed-loop system. T his predictor is a function of the plant parameters and the known controlle r. Corresponding to the related method using a least-squares criterion, the method is referred to as the tailor-made IV method for closed-loop identif ication. The indicated equivalence greatly facilitates the understanding an d the analysis of the BELS method. (C) 2001 Elsevier Science Ltd. All right s reserved.