Closed-Loop Identification of MIMO Systems: A New Look at Identifiability and Experiment Design
- 1 January 2010
- journal article
- Published by Elsevier BV in European Journal of Control
- Vol. 16 (3), 228-239
- https://doi.org/10.3166/ejc.16.228-239
Abstract
This paper addresses a question that has been posed to us: “Is it necessary to excite all reference signals for the identification of a multivariable system operating in closed loop with a linear time-invariant controller?” In this paper, we follow a careful re-examination of the notions of identifiability and informative experiments for multi-input multi-output (MIMO) closed-loop systems, which provides a negative answer to this question. Our analysis also allows to establish conditions on the controller complexity that guarantee existence of a unique global minimum of the identification criterion in the absence of external excitation; these conditions extend to the MIMO case conditions that were known for the SISO case. We illustrate our results for 2-input 2-output systems by presenting various possible experiment designs that produce a unique global minimum for the identification criterion.Keywords
This publication has 16 references indexed in Scilit:
- Closed-loop identification of multivariable systems: With or without excitation of all references?Automatica, 2008
- Least costly identification experiment for controlAutomatica, 2006
- On the Kalman—Yakubovich—Popov lemmaSystems & Control Letters, 1996
- Pseudo-canonical forms, identifiable parametrizations and simple parameter estimation for linear multivariable systems: Parameter estimationAutomatica, 1984
- Uniquely identifiable state-space and ARMA parametrizations for multivariable linear systemsAutomatica, 1984
- Identifiability of linear stochastic systems operating under linear feedbackAutomatica, 1982
- Identifiability of MIMO linear dynamic systems operating in closed loopAutomatica, 1977
- Identification of processes in closed loop—identifiability and accuracy aspectsAutomatica, 1977
- Identifiability conditions for linear multivariable systems operating under feedbackIEEE Transactions on Automatic Control, 1976
- Identifiability conditions for linear systems operating in closed loop†International Journal of Control, 1975