Equivalent Liénard-type models for a fluid transmission line

Lizeth Torres; Jorge Alejandro Delgado Aguiñaga; Gildas Besançon; Cristina Verde; Ofelia Begovich

doi:10.1016/j.crme.2016.04.004

Equivalent Liénard-type models for a fluid transmission line
[Modèles équivalents de type Liénard pour une ligne de transmission de fluides]

Lizeth Torres ^1,² ; Jorge Alejandro Delgado Aguiñaga ³ ; Gildas Besançon ^4,⁵ ; Cristina Verde ¹ ; Ofelia Begovich ³

¹ Instituto de Ingeniería, Universidad Nacional Autónoma de México, 04510, Coyoacán, Mexico City, Mexico
² Cátedras CONACYT, Mexico
³ Centro de Investigación y de Estudios Avanzados CINVESTAV Unidad Guadalajara, 45019 Zapopan, Jalisco, Mexico
⁴ Université Grenoble Alpes, GIPSA-Lab, 38000 Grenoble, France
⁵ CNRS, GIPSA-Lab, 38000 Grenoble, France

Comptes Rendus. Mécanique, Volume 344 (2016) no. 8, pp. 582-595.

Résumé
Abstract

Cet article envisage principalement la dérivation de modèles de type Liénard pour exprimer le comportement dynamique d'une ligne de transmission de fluides. Le calcul est effectué à partir d'un système hyperbolique quasi linéaire constitué d'une équation de quantité de mouvement et d'une équation de continuité. Dans des études précédentes, il a été montré que transformer les systèmes régis par une équation différentielle de type $\ddot{x} (t) + F_{0} (x (t)) \dot{x} (t) + G_{0} (x (t)) = 0$ dans la forme de Liénard peut s'avérer utile à la conception d'algorithmes d'estimation. Cette affirmation est confirmée dans cet article pour le cas des fluides, car la conception et l'évaluation d'un observateur basé sur un modèle de type Liénard, estimant les paramètres d'une canalisation, y sont présentées. L'approche est illustrée par des résultats de tests en simulation et expérimentaux.

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The main contribution of this paper is the derivation of spatiotemporal Liénard-type models for expressing the dynamical behavior of a fluid transmission line. The derivation is carried out from a quasilinear hyperbolic system made of a momentum equation and a continuity one. An advantage of these types of models is that they are suitable for formulating estimation algorithms. This claim is confirmed in the present paper for the case of fluid dynamics, since the article presents the conception and evaluation of a Liénard model-based observer that estimates the parameters of a pipeline such as the friction factor, the equivalent length and the wave speed. To show the potentiality of the approach, results based on some simulation and experimental tests are presented.

Supplementary Materials:
Supplementary materials for this article are supplied as separate files:

Reçu le : 2016-03-02
Accepté le : 2016-04-13
Publié le : 2016-05-17

DOI : 10.1016/j.crme.2016.04.004

Keywords: Pipelines, Fluid dynamics, Liénard equation, State observers, Parameter identification
Mot clés : Canalisations, Dynamique des fluides, Équation de Liénard, Observateurs d'états, Identification de paramètres

Affiliations des auteurs :

Lizeth Torres ^{1, 2} ; Jorge Alejandro Delgado Aguiñaga ³ ; Gildas Besançon ^{4, 5} ; Cristina Verde ¹ ; Ofelia Begovich ³

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     title = {Equivalent {Li\'enard-type} models for a fluid transmission line},
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Lizeth Torres; Jorge Alejandro Delgado Aguiñaga; Gildas Besançon; Cristina Verde; Ofelia Begovich. Equivalent Liénard-type models for a fluid transmission line. Comptes Rendus. Mécanique, Volume 344 (2016) no. 8, pp. 582-595. doi : 10.1016/j.crme.2016.04.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.04.004/

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