Analysis of closed-loop identification with a tailor-made parametrization

An analysis is made of a closed-loop identification scheme in which the parameters of the (open-loop) model are identified on the basis of measurements of input and output signals of a closed-loop transfer function. A parametrization of a closed-loop transfer in terms of the parameters of the open-loop plant model is employed, utilizing knowledge of the implemented feedback controller. This is denoted a tailor-made parametrization as it is tailored to the specific feedback structure at hand. Consistency of the estimate is shown to hold under additional conditions on controller and plant model order. These conditions result from the requirement of a uniformly stable model set. Simulation examples show both the power and the hazard of closed-loop identification with a tailor-made parametrization.