Une représentation d'état pour la commande en boucle fermée des écoulements cisaillés

Johan Carlier 1, 2 Christophe Collewet 1, 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 : In this paper, we propose a generic state representation for the closed-loop control of shear flows. The objective of the control is here to regulate these flows around a steady state. We assume that the actuator acts at the boundaries and that the state of the flow can be reconstructed from image sensors. The methodology followed for the implementation of the closed-loop control consists of linearizing the Navier-Stokes equations around the desired state, spatially discretizing the resulting linear system and determining the feedback gain according to an optimal control law. A state matrix representation is obtained for the periodic channel flow and the spatially developing mixing layer flow. After verifying the representativity in terms of linear stability, the control law is implemented in a nonlinear 3D solver of the Navier-Stokes equations. The simulation results show that the control law stabilizes the periodic channel flow, thereby suppressing the development of the unstable mode, and delays the onset of large eddies in the mixing layer, by rejecting relatively slow endogenous perturbations occurring on the command.
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Johan Carlier, Christophe Collewet. Une représentation d'état pour la commande en boucle fermée des écoulements cisaillés. Congrès Français de Mécanique, Aug 2019, Brest, France. ⟨hal-02283161⟩

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