Séminaire de Mécanique d'Orsay

Le Jeudi 25 octobre 2018 à 14h00 - Salle de conférences du LIMSI

Linear iterative method for closed-loop control of quasiperiodic flows

Colin Leclercq

We consider the problem of closed-loop control of linearly unstable flows giving rise to self-sustained oscillations in the fully nonlinear regime. We are interested in cases where the growth of strongly unstable modes generate sig- nificant mean-flow distortion, such that the temporally-averaged mean flow u departs significantly from the base flow u_B . We here aim at reaching back to the base state from the attractor, with the sole knowledge of the mean flow (and not u_B ). We propose to use an iterative approach combining linear models stemming from the linearization of the Navier–Stokes equations about the mean flow and robust linear control approaches. We illustrate the method on 2D incompressible open-cavity flow at Re = 7500 , for which convergence is obtained in 5 steps. A parallel can be drawn with Newton’s iteration as we solve the nonlinear problem of cancelling mean flow distortion with a sequence of linear models and controllers.

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