Identification in Closed Loop: Some Aspects on Direct and Indirect Approaches

"Identification for Control" has drawn significant interest the past few years. The objective is to achieve a model that is suited for robust control design. Thus one has to tailor the experiment and preprocessing of data so that the model is reliable in regions where the design process does not tolerate significant uncertainties. The use of closed loop experiments has been a prominent feature in these approaches, in particular various ways of handling the so-called indirect approach. In this contribution we study a number of recently suggested methods and show how they correspond to different parameterizations. We also show how direct and indirect identification methods for closed loop data are linked together via the noise model. Some new results for bias distribution in closed loop experiments will also be presented