Sur le contrôle semi-actif des vibrations élastiques d'une grande structure souple.

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Debbabi, Meriem (2009) Sur le contrôle semi-actif des vibrations élastiques d'une grande structure souple. Doctorat Structure et matériaux, Département de génie civil/ LCPC, ENPC p.154.

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Résumé

Le contrôle semi-actif est un domaine de recherche en plein essor vu qu'il joint la stabilité des systèmes contrôlés passivement à la possibilité de contrôle en temps réel permise par les stratégies actives. Dans cette thèse on s'intéresse à un assemblage de poutres modélisées sous l'hypothèse de linéarité et représentant un modèle de pont à hauban en cours de construction.

Cette structure a été contrôlée précédemment par un dispositif formé d'un pendule à masse accordée couplé à un alternateur et à une résistance électrique sous l'hypothèse de petites rotations du pendule. Dans cette thèse on a pour objectif de rendre robuste cet actionneur pour les grandes rotations du pendule. Afin d'y parvenir le travail effectué peut être divisé en quatre points:



Tout d'abord, une étude paramétrique est effectuée afin de mieux comprendre le comportement de l'actionneur en grandes rotations du pendule. Cette étude a permis d'identifier la dépendance du contrôle aux variables et aux paramètres du système.



Puis une étude du contrôle passif du système non linéaire virtuel est effectuée et une loi basée sur le contrôle par séquencement de gain est définie et appliquée à la structure. Ces deux lois montrent la nécessité de la conception d'un contrôle en temps réel.



Ensuite, on définit des lois semi-actives dans l'esprit de la poursuite d'un modèle de référence pour les deux systèmes pendule seul et pont-pendule. Leurs limites et leurs apports sont établis.



Enfin par une stratégie de poursuite on conçoit une loi de contrôle actif et sa version semi-active pour le système non linéaire réel. Cette dernière, permet enfin de réaliser les objectifs de cette thèse i.e avoir un niveau d'amortissement de la structure pont-actionneur électromécanique, pour les grandes rotations du pendule, comparable à celui d'un modèle linéaire.

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Table des Matières

Introduction 1

1 Concepts de base sur la dynamique non linéaire et sur le

contrôle 9

1.1 Introduction - 9

1.2 Outils d’analyse des systèmes non linéaires - 10

1.2.1 Concepts généraux - 10

1.2.2 Analyse de la dynamique non linéaire du pendule - 15

1.3 Méthodes de contrôle non linéaire - 18

1.3.1 Stabilisation par linéarisation - 19

1.3.2 Séquencement de Gain - 19

1.3.3 L’approche Model Reference Adaptive Control (MRAC) . 20

1.3.4 Linear Quadratic Regulation (LQR) - 22

1.3.5 L’approche State-Dependent Riccati Equation

Control(SDRE) - 23

1.3.6 Le contrôle Clipping - 25

1.4 Les amortisseurs semi-actifs en génie civil - 25

1.5 Dissipation électromécanique - 26

2 Présentation du système 27

2.1 Introduction - 27

2.2 Modèle structure - 28

2.3 Dispositif d’amortissement - 33

2.4 Modèle pont-actionneur électromécanique - 35

3 Outils d’analye du système non linéaire 43

3.1 Introduction - 43

3.2 Système simplifié - 44

3.3 Schéma de Newmark semi-explicite - 50

3.3.1 Schéma de Newmark générique - 50

3.3.2 Schéma de Newmark utilisé - 51

4 Stratégies de contrôle passif et séquencement de gain 55

4.1 Introduction - 55

4.2 Etude paramétrique - 56

4.3 Contrôle passif du modèle non linéaire virtuel - 62

4.4 Application de la stratégie de séquencement de gain - 68

5 Stratégie de poursuite pour le modèle non linéaire virtuel 75

5.1 Introduction - 75

5.2 Critère d’optimisation - 76

5.3 Contrôle par tracking du pendule - 77

5.3.1 Loi de contrôle actif - 78

5.3.2 Loi de contrôle semi-actif - 80

5.3.3 Comparaison des lois - 82

5.4 Contrôle par tracking du modèle pont-pendule - 83

5.4.1 Loi de contrôle actif - 84

5.4.2 Loi de contrôle semi-actif - 86

6 Stratégie de poursuite pour le modèle réel 91

6.1 Introduction - 91

6.2 Contrôle par traking du pendule réel - 92

6.2.1 Loi de contrôle semi-actif pour le pendule réel - 92

6.2.2 Loi de contrôle semi-actif pour le pendule avec dispositif idéal - 98

6.3 Contrôle du pont-actionneur électromécanique réel - 99

6.3.1 Loi de contrôle semi-actif par poursuite de l’amortissement 99

6.3.2 Loi de contrôle semi-actif avec dispositif idéal - 102

6.3.3 Loi de contrôle semi-actif par poursuite du courant . . . 105

6.4 Loi semi-active polynomiale - 107

7 Dispositif expérimental 111

7.1 Introduction - 111

7.2 Présentation du dispositif expérimental - 112

7.2.1 Matériel utilisé - 112

7.2.2 Post traitement - 116

7.3 Variation du type d’excitation - 116

7.4 Projet-Programme d’autres validations expérimentales - 119

Conclsion 121

Bibliographie 125

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