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

Authors:
Marion Gilson;Paul Van Den Hof
Affiliations:
Centre de Recherche en Automatique de Nancy (CRAN), CNRS UPRESA 7039, Université Henri Poincaré, Nancy 1, BP 239, F-54506 Vandoeuvre-lès-Nancy Cedex, France;Signals, Systems and Control Group, Department of Applied Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2001

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Abstract

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 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.