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Contrôle frontière par modèle interne de systèmes hyperboliques :
application à la régulation de canaux d'irrigation

Abstract : This work deals with the control of systems described by Partial Derivative Equations. Internal Model Control (IMC) structure is extended to infinite dimension non linear hyperbolic systems, with boundary control. PDE considered are the Saint-Venant equations which describe the free face water flows. The model used is a linearization around a permanent flow whose coefficients depend on the space variable. The slopes and frictions are taken non null, variable phenomena along the channel are taken into account.
Analysis and control synthesis are made, considering the closed loop system as a perturbation of the open loop one. The perturbations are related to the operators, the semigroups and the spectrum in a Hilbert space. The hyperbolic operator Ae(x) dx+ Be(x) is characterized explicitly without preliminary transformation, in dimension one of space, where operators Ae(x) and Be(x) are bounded.
For the control synthesis, an internal model boundary control structure is used, after writting it into an abstract Kalmanian form. The stability analysis of the closed loop, by the perturbation theory in infinite dimension, gives sufficient conditions to adjust the law parameters in case of an integral law and/or proportional one.
Results, in simulation and experimental (Valence's channel), show the well approach feasibility. It was tested in the mono-reach and multi-reaches cases.
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https://tel.archives-ouvertes.fr/tel-00011627
Contributor : Valérie dos Santos Martins <>
Submitted on : Thursday, February 16, 2006 - 2:07:27 PM
Last modification on : Thursday, June 25, 2020 - 10:44:15 AM
Long-term archiving on: : Saturday, April 3, 2010 - 10:25:12 PM

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  • HAL Id : tel-00011627, version 1

Citation

Valérie dos Santos Martins. Contrôle frontière par modèle interne de systèmes hyperboliques :
application à la régulation de canaux d'irrigation. Mathématiques [math]. Université d'Orléans, 2004. Français. ⟨tel-00011627⟩

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