An introduction to algebraic discrete-time linear parametric identification with a concrete application

Michel Fliess; Stefan Fuchshumer; Markus Schöberl; Kurt Schlacher; Hebertt Sira-Ramirez

inria-00188435, version 2

An introduction to algebraic discrete-time linear parametric identification with a concrete application

Michel Fliess () ^1, 2, Stefan Fuchshumer^a^, 3, Markus Schöberl^b^, 4, Kurt Schlacher^b^, 3, Hebertt Sira-Ramirez ⁵

Journal Européen des Systèmes Automatisés 42, 2-3 (2008) 210--232

Résumé : An algebraic framework for continuous-time linear systems identification introduced in the literature some years ago has revealed as an interesting alternative way for on-line parametric identification. The present contribution aims at conveying those ideas to linear time-invariant discrete-time systems, with particular emphasis attached to application issues. To this end, an on-line linear identifier for n-th order systems is evolved, re-sorting to the operational representation of the dynamics. Being discussed on the basis of a fifth-order model of a drive-train, the numerical condition of the obtained setting of the identifier is found to suffer significantly with decreasing sampling times. A setting not experiencing these numerical problems is finally introduced by means of a re-parametrization of the identifier via application of the bilinear Tustin transform. The already implemented computer programs, where computer algebra plays an important role, are available.

a – Voestalpine mechatronics GmbH - vatron, Linz, Austria
b – Johannes Kepler Universität - Linz, Austria
1 : Laboratoire d'informatique de l'école polytechnique (LIX)
CNRS : UMR7161 – Polytechnique - X
2 : ALIEN (INRIA Futurs)
INRIA – Polytechnique - X
3 : Institut für Regelungstechnik und Prozessautomatisierung
Johannes Kepler Universität Linz
4 : Institut für Regelungstechnik und Prozessautomatisierung
Johannes Kepler Universität Linz
5 : CINVESTAV
IPN

inria-00188435, version 2
http://hal.inria.fr/inria-00188435
oai:hal.inria.fr:inria-00188435
Contributeur : Michel Fliess <>
Soumis le : Mercredi 9 Avril 2008, 10:32:45
Dernière modification le : Mercredi 9 Avril 2008, 22:58:32

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%% inria-00188435, version 2
%% http://hal.inria.fr/inria-00188435
@article{fliess:inria-00188435,
    hal_id = {inria-00188435},
    url = {http://hal.inria.fr/inria-00188435},
    title = {{An introduction to algebraic discrete-time linear parametric identification with a concrete application}},
    author = {Fliess, Michel and Fuchshumer, Stefan and Sch{\"o}berl, Markus and Schlacher, Kurt and Sira-Ramirez, Hebertt},
    abstract = {{An algebraic framework for continuous-time linear systems identification introduced in the literature some years ago has revealed as an interesting alternative way for on-line parametric identification. The present contribution aims at conveying those ideas to linear time-invariant discrete-time systems, with particular emphasis attached to application issues. To this end, an on-line linear identifier for n-th order systems is evolved, re-sorting to the operational representation of the dynamics. Being discussed on the basis of a fifth-order model of a drive-train, the numerical condition of the obtained setting of the identifier is found to suffer significantly with decreasing sampling times. A setting not experiencing these numerical problems is finally introduced by means of a re-parametrization of the identifier via application of the bilinear Tustin transform. The already implemented computer programs, where computer algebra plays an important role, are available.}},
    keywords = {Discrete-time linear systems, z-transform, bilinear Tustin transform, parameter identification, on-line identifier, rapid sampling, computer algebra},
    language = {Anglais},
    affiliation = {Laboratoire d'informatique de l'{\'e}cole polytechnique - LIX , ALIEN - INRIA Futurs , Institut f{\"u}r Regelungstechnik und Prozessautomatisierung , CINVESTAV},
    publisher = {Herm{\`e}s - Lavoisier},
    pages = {210--232},
    journal = {Journal Europ{\'e}en des Syst{\`e}mes Automatis{\'e}s},
    volume = {42},
    number = {2-3 },
    audience = {internationale },
    year = {2008},
    pdf = {http://hal.inria.fr/inria-00188435/PDF/Discridentif-JESA.pdf},
}

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