Flatness-based control revisited: The <i>HEOL</i> setting

Cédric Join; Emmanuel Delaleau; Michel Fliess

doi:10.5802/crmath.674

Article de recherche - Théorie du contrôle

Flatness-based control revisited: The HEOL setting
[Revoir la commande par platitude : la méthode HEOL]

Cédric Join ^1,² ; Emmanuel Delaleau ³ ; Michel Fliess ^4,²

¹ CRAN (CNRS, UMR 7039), Université de Lorraine, Campus Aiguillettes, BP 70239, 54506 Vandœuvre-lès-Nancy, France
² AL.I.E.N., 7 rue Maurice Barrès, 54330 Vézelise, France
³ ENI Brest, UMR CNRS 6027, IRDL, 29200 Brest, France
⁴ LIX (CNRS, UMR 7161), École polytechnique, 91128 Palaiseau, France

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1693-1706.

Résumé
Abstract

On présente les fondations algébriques de la méthode HEOL qui combine commande par platitude et bouclage intelligent, c’est-à-dire deux avancées de l’automatique ayant fait leur preuve en pratique, y compris industrielle. On résoud ainsi plusieurs questions pendantes sur les bouclages à propos de la platitude et de la commande sans modèle. Théorie élémentaire des modules, corps différentiels ordinaires, et la généralisation à ces corps des différentielles de Kähler permettent une définition intrinsèque du système linéaire tangent. Les manipulations algébriques associées au calcul opérationnel conduisent à l’homéostat et aux correcteurs intelligents, illustrés par simulations numériques.

We present the algebraic foundations of the HEOL setting, which combines flatness-based control and intelligent controllers, two advances in automatic control that have been proven in practice, including in industry. The result provides a solution to many pending questions on feedback loops concerning flatness-based control and model-free control (MFC). Elementary module theory, ordinary differential fields and the generalization of Kähler differentials to differential fields provide an intrinsic definition of the tangent linear system. The algebraic manipulations associated with the operational calculus lead to homeostat and intelligent controllers. They are illustrated via some computer simulations.

Reçu le : 2024-01-10
Accepté le : 2024-08-08
Publié le : 2024-11-25

DOI : 10.5802/crmath.674

Classification : 93B25, 93B52, 93C15
Keywords: Flatness-based control, model-free control, intelligent controllers, differential algebra, module theory
Mots-clés : Commande par platitude, commande sans modèle, contrôleurs intelligents, algèbre différentielle, théorie des modules

Affiliations des auteurs :

Cédric Join ^{1, 2} ; Emmanuel Delaleau ³ ; Michel Fliess ^{4, 2}

¹ CRAN (CNRS, UMR 7039), Université de Lorraine, Campus Aiguillettes, BP 70239, 54506 Vandœuvre-lès-Nancy, France
² AL.I.E.N., 7 rue Maurice Barrès, 54330 Vézelise, France
³ ENI Brest, UMR CNRS 6027, IRDL, 29200 Brest, France
⁴ LIX (CNRS, UMR 7161), École polytechnique, 91128 Palaiseau, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {C\'edric Join and Emmanuel Delaleau and Michel Fliess},
     title = {Flatness-based control revisited: {The} {\protect\emph{HEOL}} setting},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1693--1706},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.674},
     language = {en},
}

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Cédric Join; Emmanuel Delaleau; Michel Fliess. Flatness-based control revisited: The HEOL setting. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1693-1706. doi : 10.5802/crmath.674. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.674/

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