Closed-loop Identiication Revisited { Updated Version R E Gl Ertek N Ik a U T O M at Ic Co N T R O L Closed-loop Identiication Revisited { Updated Version ?

Technical reports from the Automatic Control group in Linkping are available by anonymous ftp at the address ftp.control.isy.liu.se. This report is contained in the compressed postscript le 2021.ps.Z. Abstract Identiication of systems operating in closed loop has long been of prime interest in industrial applications. The problem ooers many possibilities, and also some fallacies, and a wide variety of approaches have been suggested, many quite recently. The purpose of the current contribution is to place most of these approaches in a coherent framework, thereby showing their connections and display similarities and diierences in the asymptotic properties of the resulting estimates. The common framework is created by the basic prediction error method, and it is shown that most of the common methods correspond to diierent parameterizations of the dynamics and noise models. The so called indirect methods, e.g., are indeed "direct" methods employing noise models that contain the regulator. The asymptotic properties of the estimates then follow from the general theory and take diierent forms as they are translated to the particular parameterizations. In the course of the analysis we also suggest a projection approach to closed-loop identiication with the advantage of allowing approximation of the open loop dynamics in a given, and user-chosen frequency domain norm, even in the case of an unknown, non-linear regulator.