Properties and Usage of Closed-loop Identification Methods

Sammanfattning: System identification deals with the construction of mathematical models of dynamical systems using measured data. Closed-loop identification is what results when performing the identification experiment under output feedback, that is, in closed loop. In this thesis we study a number of closed-loop identification methods, both classical and more recently suggested ones. A common feature of the methods considered is that they all are derived in the prediction error framework. We provide a comprehensive treatment of the statistical properties of the different methods for closed-loop identification. A focus will be on accuracy aspects of different closed-loop identification methods and we show that indirect and joint input-output methods fail to give better accuracy than the direct method.The question of whether is is possible to design a closed-loop method that allows fitting the model to the data with arbitrary frequency weighting has long been open. We describe and analyze a new method for closed-loop identication - the projection method - that has this desirable property. A strong feature of the projection method is that it can be applied to systems with arbitrary feedback mechanisms, just as the direct method. A drawback is that the projection method gives worse accuracy than the direct method.Substantial interest has been devoted to the problem of linking identification and control. One mainstream approach has been to try to match the identification and control criteria by using proper frequency weighting in the identification. Obviously the projection method is well suited for this problem. In the literature various indirect methods have been employed. The motivation for this has been that by using indirect methods the bias error will be shaped by the sensitivity function which generally is considered advantageous. We show how the identification step in several identification-for-control schemes based on this idea can be performed in a unified manner using a simple indirect method.A related approach to identification for control is to try to minimize the degradation in closed-loop performance due to control design based on identified models by carefully tuning the experiment design parameters. We focus on closed-loop issues and starting with a quite general problem formulation we show how to optimally choose the feedback regulator and the reference signal.