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Apprentissage statistique de modèles réduits non-linéaires par approche expérimentale et design de contrôleurs robustes: le cas de la cavité ouverte

Abstract : This thesis deals with the design of a closed-loop controller of a subsonic cavity flow. The objective is to build a controller that only relies on observable dynamics and that handles situations where the flow field is excited by unknown external random disturbances. For this, two strategies have been defined: the identification of a non-linear model representing flow dynamics from only measurable information and the design of a robust linear compensator, based on the H∞ control theory, that incorporates robustness properties in the objective function definition. The first part has been devoted to the identification of a non-linear model with data obtained from an experiment conducted at the ONERA S19 subsonic (M = 0.1) wind tunnel on the Chalais-Meudon site. In order to provide a full description of the fluid motion, in particular its frequency content, the natural (without control) flow has been characterized by hot-wire and unsteady pressure measurements and time-resolved Particle Image Velocimetry (PIV) snapshots. Time-filtering has been successfully applied to the PIV snapshots in order to focus on the large-scale low-frequency dynamics of the flow. This step has been shown critical to deal with turbulent flows characterized by high-frequency noise. The obtained POD modes have been used as a projection basis of the velocity field and the associated trajectories fitted to a Non-Linear Auto-Regressive eXogeneous (NLARX) model structure by an identification process. It turns out that the obtained models are not robust, in the sense that they do not manage to reproduce the dynamics of a validation data-set once fitted to a given learning data-set. It has been shown that this failure is due to the strong non-linearities observed in the cavity flow and that render identification methods impracticable. The second part has been devoted to the design of a robust controller from numerical simulations of an incompressible square cavity flow at different Reynolds numbers in transitional regime. Various control design methods have been tested and assessed with respect to several robustness measures. It was found that the traditional Linear Quadratic Gaussian (LQG) controller exhibits poor robustness to external perturbations and that loop-transfer recovery (LTR) techniques and "worst-case" controllers improve robustness but not sufficiently to cope with the strong non-linearities in the flow. To this aim, a compensator design that optimizes the robustness properties with respect to unstructured input-multiplicative and input-to-output uncertainties is presented. The latter shows an important increase in robustness with respect to the introduction of perturbations of the stable part of the input-output relation even though a cost is payed in terms of performances. A strategy to deal also with perturbations of the unstable part of the dynamics, as obtained for example by change in Reynolds numbers, has been introduced.
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Contributor : Claudio Ottonelli <>
Submitted on : Thursday, September 18, 2014 - 3:22:31 PM
Last modification on : Friday, June 26, 2020 - 2:02:05 PM
Document(s) archivé(s) le : Friday, December 19, 2014 - 1:50:56 PM


  • HAL Id : pastel-01065782, version 1



Claudio Ottonelli. Apprentissage statistique de modèles réduits non-linéaires par approche expérimentale et design de contrôleurs robustes: le cas de la cavité ouverte. Mechanics of the fluids [physics.class-ph]. Ecole Polytechnique X, 2014. English. ⟨pastel-01065782⟩



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