# 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 Leclerc

ONERA

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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