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Variance results for identification of cascade systems
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control. (System Identification Group)ORCID iD: 0000-0002-1927-1690
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0002-9368-3079
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0002-3672-5316
2009 (English)In: Automatica, ISSN 0005-1098, Vol. 45, no 6, 1443-1448 p.Article in journal (Refereed) Published
Abstract [en]

The objective of this contribution is to analyze statistical properties of estimated models of cascade systems. Models of such systems are important in for example cascade control applications. The aim is to present and analyze some fundamental limitations in the quality of an identified model of a cascade system under the condition that the true subsystems have certain common dynamics. The model quality is analyzed by studying the asymptotic (large data) covariance matrix of the Prediction Error Method parameter estimate. The analysis will focus on cascade systems with three subsystems. The main result is that if the true transfer functions of the first and second subsystem are identical, the output signal information from the second and third subsystems will not affect the asymptotic variance of the estimated model of the first subsystem. This result implies that for a cascade system with two subsystems, where the dynamics of the first subsystem is a factor of the dynamics of the second one, the output signal information from the second subsystem will not improve the asymptotic quality of the estimate of the first subsystem. The results are illustrated by some simple FIR examples.

Place, publisher, year, edition, pages
PERGAMON-ELSEVIER SCIENCE LTD , 2009. Vol. 45, no 6, 1443-1448 p.
Keyword [en]
System identification, Cascade systems, Variance analysis
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-26521DOI: 10.1016/j.automatica.2009.01.020ISI: 000267199500011OAI: diva2:387459
17th IFAC World Congress Seoul, SOUTH KOREA, JUL 06-11, 2008
NOTICE: this is the author’s version of a work that was accepted for publication in Automatica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Automatica, VOL 45, ISSUE 6, 13 March 2009, DOI: 10.1016/j.automatica.2009.01.020. QC 20110114Available from: 2012-01-19 Created: 2010-11-25 Last updated: 2013-09-05Bibliographically approved

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Wahlberg, BoHjalmarsson, HåkanMårtensson, Jonas
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