Grey Box Identification in Closed-loop

The focus in this paper is identification of parameters in closed-loop systems. The system identification approach is based on a reformulation of feedback controllers in terms of its coprime factors. Based on this controller architecture, an auxiliary input is injected into the controller for the identification. The result of this setup is that the closed-loop identification problem is transformed into a standard open-loop identification problem. The models with unknown parameters are given in the form of a linear fractional transformation (LFT) where the direct term gives the nominal system and the other part gives the nonlinear maps of the variation of the unknown parameters into the system. Further, the coprime factors of this system can again be described as LFT of the nominal coprime factors and the parameter variations, i.e. an open-loop LFT identification problem.