Discrete-time linear parametric identification: An algebraic approach

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

inria-00105673, version 1

Discrete-time linear parametric identification: An algebraic approach

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

2èmes Journées Identification et Modélisation Expérimentale - JIME'2006 (2006)

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 parameter 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-ordermodel 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. Note added on November 17th, 2007.- An improved and extended version is available at http://hal.inria.fr/inria-00188435/fr/

a – Voestalpine mechatronics GmbH - vatron, Linz, Austria
b – Johannes Kepler Universität - Linz, Austria
1: ALIEN (INRIA Futurs)
INRIA – Polytechnique - X
2: Laboratoire d'informatique de l'école polytechnique (LIX)
CNRS : UMR7161 – 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-00105673, version 1
http://hal.inria.fr/inria-00105673
oai:hal.inria.fr:inria-00105673
From: Michel Fliess <>
Submitted on: Wednesday, 11 October 2006 23:09:10
Updated on: Saturday, 17 November 2007 15:48:42

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%% inria-00105673, version 1
%% http://hal.inria.fr/inria-00105673
@inproceedings{fliess:inria-00105673,
    hal_id = {inria-00105673},
    url = {http://hal.inria.fr/inria-00105673},
    title = {{Discrete-time linear parametric identification: An algebraic approach}},
    author = {Fliess, Michel and Fuchshumer, Stefan 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 parameter 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-ordermodel 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. Note added on November 17th, 2007.- An improved and extended version is available at http://hal.inria.fr/inria-00188435/fr/}},
    keywords = {Discrete-time linear systems, z-transform, bilinear Tustin transform, parameter identification, on-line identifier, rapid sampling, computer algebra.},
    language = {English},
    affiliation = {ALIEN - INRIA Futurs , Laboratoire d'informatique de l'{\'e}cole polytechnique - LIX , Institut f{\"u}r Regelungstechnik und Prozessautomatisierung , CINVESTAV},
    booktitle = {{2{\`e}mes Journ{\'e}es Identification et Mod{\'e}lisation Exp{\'e}rimentale - JIME'2006}},
    address = {Poitiers, France},
    note = {An improved and extended version is available at http://hal.inria.fr/inria-00188435/en/ },
    audience = {not specified },
    year = {2006},
    month = Nov,
    pdf = {http://hal.inria.fr/inria-00105673/PDF/Poitiers.pdf},
}

%F inria-00105673, version 1
%0 Conference Proceedings
%U http://hal.inria.fr/inria-00105673
%2 INFO:INFO_CE;INFO:INFO_ES;INFO:INFO_RB;INFO:INFO_SC;MATH:MATH_OC;SPI:AUTO;SPI:MECA:GEME
%T Discrete-time linear parametric identification: An algebraic approach
%A Fliess, Michel
%A Fuchshumer, Stefan
%A Schlacher, Kurt
%A Sira-Ramirez, Hebertt
%+ ALIEN - INRIA Futurs , Laboratoire d'informatique de l'école polytechnique - LIX , Institut für Regelungstechnik und Prozessautomatisierung , CINVESTAV
%X 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 parameter 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-ordermodel 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. Note added on November 17th, 2007.- An improved and extended version is available at http://hal.inria.fr/inria-00188435/fr/
%G English
%8 2006-11-00
%2 not specified
%B 2èmes Journées Identification et Modélisation Expérimentale - JIME'2006
%2 Poitiers
%2 France
%8 2006-11
%K Discrete-time linear systems, z-transform, bilinear Tustin transform, parameter identification, on-line identifier, rapid sampling, computer algebra.
%2 2006
%Z An improved and extended version is available at http://hal.inria.fr/inria-00188435/en/