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

Michel Fliess 1, 2 Stefan Fuchshumer 3 Markus Schöberl 4 Kurt Schlacher 3 Hebertt Sira-Ramirez 5
1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
3 Institut für Regelungstechnik und Prozessautomatisierung
4 Institut für Regelungstechnik und Prozessautomatisierung
5 CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional
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
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Article dans une revue
Journal Européen des Systèmes Automatisés (JESA), Lavoisier, 2008, 42 (2-3), pp.210--232
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Michel Fliess, Stefan Fuchshumer, Markus Schöberl, Kurt Schlacher, Hebertt Sira-Ramirez. An introduction to algebraic discrete-time linear parametric identification with a concrete application. Journal Européen des Systèmes Automatisés (JESA), Lavoisier, 2008, 42 (2-3), pp.210--232. 〈inria-00188435v2〉

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