Properties and Usage of Closed-loop Identiication Methods Properties and Usage of Closed-loop Identiication Methods

System identi cation deals with the construction of mathematical models of dynamical systems using measured data. Closed-loop identi cation is what results when performing the identi cation experiment under output feedback, that is, in closed loop. In this thesis we study a number of closed-loop identi cation 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 di erent methods for closed-loop identi cation. A focus will be on accuracy aspects of di erent closed-loop identi cation 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 tting the model to the data with arbitrary frequency weighting has long been open. We describe and analyze a new method for closed-loop identi cation { 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 identi cation and control. One mainstream approach has been to try to match the identi cation and control criteria by using proper frequency weighting in the identi cation. 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 identi cation step in several identi cation-for-control schemes based on this idea can be performed in a uni ed manner using a simple indirect method. A related approach to identi cation for control is to try to minimize the degradation in closed-loop performance due to control design based on identi ed 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. i