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Riccati-less approach for optimal control and estimation: An application in 2D Boundary Layers
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.ORCID iD: 0000-0001-7864-3071
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The control of Tollmien-Schlichting (TS) in a 2D boundary layer is analysed by using numerical simulations. Full-dimensional optimal controllers are used in combination with a set-up of spatially localised inputs (actuators and disturbance) and outputs (sensors).

The Adjoint of the Direct-Adjoint (ADA) algorithm, recently proposed by Pralits & Luchini (2010), is used to efficiently compute the linear quadratic Regulator (LQR) controller; the method is iterative and allows to by-pass the solution of the corresponding Riccati equation, unfeasible for high-dimensional systems. We show that an analogous iteration can be cast for the estimation problem; the dual algorithm is referred to as Adjoint of the Adjoint-Direct (AAD). By combining the solutions of the estimation and control problem, full dimensional, model-free, linear gaussian Quadratic (LQG) controllers are obtained and used for the attenuation of the disturbances arising in the boundary layer flow.

The full dimensional controllers turn out to be an excellent benchmark for evaluating the performance of the optimal control/estimation design based on open-loop model reduction. We show the conditions under which the two strategies are in perfect agreement by focusing on the issues arising when feedback configurations are considered. An analysis of the finite amplitude disturbances is also carried out by addressing the limitations of the optimal controllers, the role of the estimation and the robustness to the nonlinearities arising in the flow of the control design.

National Category
Other Engineering and Technologies not elsewhere specified
URN: urn:nbn:se:kth:diva-117912OAI: diva2:603865

QS 2013

Available from: 2013-02-07 Created: 2013-02-07 Last updated: 2013-02-07Bibliographically approved
In thesis
1. Active Control and Modal Structures in Transitional Shear Flows
Open this publication in new window or tab >>Active Control and Modal Structures in Transitional Shear Flows
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Flow control of transitional shear flows is investigated by means of numerical simulations. The attenuation of three-dimensional wavepackets of Tollmien-Schlichting (TS) and streaks in the boundary layer is obtained using active control in combination with localised sensors and actuators distributed near the rigid wall. Due to the dimensions of the discretized Navier-Stokes operator, reduced-order models are identified, preserving the dynamics between the inputs and the outputs of the system. Balanced realizations of the system are computed using balanced truncation and system identification.

We demonstrate that the energy growth of the perturbations is substantially and efficiently mitigated, using relatively few sensors and actuators. The robustness of the controller is analysed by varying the number of actuators and sensors, the Reynolds number, the pressure gradient and by investigating the nonlinear, transitional case. We show that delay of the transition from laminar to turbulent flow can be achieved despite the fully linear approach. This configuration can be reproduced in experiments, due to the localisation of sensing and actuation devices.

The closed-loop system has been investigated for the corresponding twodimensional case by using full-dimensional optimal controllers computed by solving an iterative optimisation based on the Lagrangian approach. This strategy allows to compare the results achieved using open-loop model reduction with model-free controllers. Finally, a parametric analysis of the actuators/ sensors placement is carried-out to deepen the understanding of the inherent dynamics of the closed-loop. The distinction among two different classes of controllers – feedforward and feedback controllers - is highlighted.

A second shear flow, a confined turbulent jet, is investigated using particle image velocimetry (PIV) measurements. Proper orthogonal decomposition (POD) modes and Koopman modes via dynamic mode decomposition (DMD) are computed and analysed for understanding the main features of the flow. The frequencies related to the dominating mechanisms are identified; the most energetic structures show temporal periodicity.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. vii, 72 p.
Trita-MEK, ISSN 0348-467X ; 2013:03
Flow control, flat-plate boundary layer, optimal controllers, model reduction, turbulent jet, POD, DMD, Koopman modes
National Category
Fluid Mechanics and Acoustics
urn:nbn:se:kth:diva-117916 (URN)978-91-7501-640-5 (ISBN)
Public defence
2013-02-22, Sal E3, Osquars Backe 14, KTH, Stockholm, 10:15 (English)

QC 20130207

Available from: 2013-02-07 Created: 2013-02-07 Last updated: 2013-02-07Bibliographically approved

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Semeraro, OnofrioHenningson, Dan Stefan
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