Brief Subspace identification of closed loop systems by the orthogonal decomposition method

Authors:
Tohru Katayama;Hidetoshi Kawauchi;Giorgio Picci
Affiliations:
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan;Department of Information Engineering, University of Padova, 35131 Padova, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2005

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Abstract

In this paper, we consider a problem of identifying the deterministic part of a closed loop system by applying the stochastic realization technique of (Signal Process. 52 (2) (1996) 145) in the framework of the joint input-output approach. Using a preliminary orthogonal decomposition, the problem is reduced to that of identifying the plant and controller based on the deterministic component of the joint input-output process. We discuss the role of input signals in closed loop identification and the realization method based on a finite data, and then sketch a subspace method for identifying state space models of the plant and controller. Since the obtained models are of higher order, a model reduction procedure should be applied for deriving lower order models. Some numerical results are included to show the applicability of the present technique.