Subspace identification of closed loop systems by the orthogonal decomposition method

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.