Commande en boucle fermée d'une couche de mélange soumise à des perturbations exogènes

Christophe Collewet 1 Johan Carlier 2
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : This paper deals with the closed-loop control of a fluid flow subjected to exogenous disturbances. The goal is to maintain it in a desired state whatever the external disturbances. The main idea consists of linearizing the Navier-Stokes equations about the desired state to obtain a linear state formulation. The components of the state vectors are the stream function evaluated at different points of the space. It is assumed that it can be estimated via image techniques. First we show that, since the mixing layer is an under-actuated system, the disturbance can only be attenuated but not rejected. Therefore, a control law is proposed to cope with our problem. It writes as the sum of two terms. The first one allows to impose a behavior in regulation while the second one describes a behavior in rejection. We show that this second term writes simply as a feedback gain that has to apply to the perturbation value. Consequently, we propose a disturbance observer to derive the control law. Next, we prove the stability of our observer based control scheme. Simulations results on the DNS solver Incompact3d validate our control scheme and show that it overcomes a control law only based on a state feedback.
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Submitted on : Tuesday, September 10, 2019 - 12:11:40 PM
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Christophe Collewet, Johan Carlier. Commande en boucle fermée d'une couche de mélange soumise à des perturbations exogènes. CFM 2019 - 24e Congrès Français de Mécanique, Aug 2019, Brest, France. pp.1-15. ⟨hal-02189111v2⟩

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