Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2002-003 (February 12, 2002)
Subspace Identification of Closed Loop Systems by Orthogonal Decomposition Method
by Tohru Katayama, Hidetoshi Kawauchi, Tohru Inoue, and Giorgio Picci
We consider the problem of identifying closed loop systems by
applying the stochastic realization technique of (Picci and Katayama,
1996b) to the joint input-output process. It is assumed that the
exogenous input is feedback-free and persistently exciting (PE).
We show that under the preliminary orthogonal decomposition, the
identification of closed loop system is divided into two subproblems:
the deterministic identification of plant and controller, and the
stochastic identification of noise filter. The subspace method of
computing the deterministic and stochastic components of the joint
input-output process is presented, and then subspace methods of
identifying the deterministic and stochastic components are derived
by adapting the standard subspace methods both components. In each
case, a model reduction procedure should be applied for deriving
lower order models from obtained higher order non-minimal models by
canceling poles and zeros situated closely. Some numerical results
are included to show the applicability of the present technique.