APPLICATION OF A SUBSPACE MODEL IDENTIFICATION TECHNIQUE TO IDENTIFY LTI SYSTEMS OPERATING IN CLOSED-LOOP

In this paper we reformulate the identification of linear time-invaria nt (LTI) systems operating in a closed-loop with an LTI compensator to an open-loop multi-input-multi-output (MIMO) (state space model) iden tification problem, followed by a model reduction step. The open-loop identification problem consists of the identification of a MIMO state space model, describing the deterministic transfer from freely excitab le inputs to measurable (constrained) signals in the loop. This proble m is solved by the recently proposed MOESP (MIMO output-error state sp ace model) identification technique, described in Verhaegen and Dewild e (Int. J. Control, 56, 1187-1210, 1992). The described state space ap proach does not constrain the delay structure of the controller-plant combination; it delivers an estimate of the controller and it allows a n analytical reduction of the obtained state space model of the system (or controller) to half its original system order. The open-loop iden tification problem only requires the selection of the combined model a nd controller order; the individual model and controller order selecti on is performed in the subsequent model reduction step. Furthermore, s pecializing the presented approach to the identification of a SISO sys tem provided useful information regarding where to inject the signal i n the loop in order to enhance numerical robustness. The reliability o f the outlined approach and the usefulness of the obtained insights ar e highlighted in two illustrative numerical examples.