In this paper, we consider a boundary control problem governed by the two-dimensional Burgers’ equation for a configuration describing convective flow over an obstacle. Flows over obstacles are important as they arise in many practical applications. Burgers’ equations are also significant as they represent a simpler form of the more general Navier–Stokes momentum equation describing fluid flow. The aim of the work is to develop a reduced-order boundary control-oriented model for the system with subsequent nonlinear control law design. The control objective is to drive the full order system to a desired 2D profile. Reduced-order modeling involves the application of an $L2$ optimization based actuation mode expansion technique for input separation, demonstrating how one can obtain a reduced-order Galerkin model in which the control inputs appear as explicit terms. Controller design is based on averaging and center manifold techniques and is validated with full order numerical simulation. Closed-loop results are compared to a standard linear quadratic regulator design based on a linearization of the reduced-order model. The averaging∕center manifold based controller design provides smoother response with less control effort and smaller tracking error.

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# Reduced-Order Model-Based Feedback Control of Flow Over an Obstacle Using Center Manifold Methods

Coşku Kasnakoğlu

,
Coşku Kasnakoğlu

Department of Electrical and Electronics Engineering,

kasnakoglu@etu.edu.tr
TOBB University of Economics and Technology

, Ankara 06560, Turkey
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R. Chris Camphouse

,
R. Chris Camphouse

Carlsbad Programs Group, Performance Assessment and Decision Analysis Department,

Sandia National Laboratories

, Carlsbad, NM 88220
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Andrea Serrani

Andrea Serrani

Department of Electrical and Computer Engineering,

The Ohio State University

, Columbus, OH 43210
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Coşku Kasnakoğlu

Department of Electrical and Electronics Engineering,

TOBB University of Economics and Technology

, Ankara 06560, Turkeykasnakoglu@etu.edu.tr

R. Chris Camphouse

Sandia National Laboratories

, Carlsbad, NM 88220
Andrea Serrani

Department of Electrical and Computer Engineering,

The Ohio State University

, Columbus, OH 43210*J. Dyn. Sys., Meas., Control*. Jan 2009, 131(1): 011011 (12 pages)

**Published Online:**December 8, 2008

Article history

Received:

December 8, 2007

Revised:

September 8, 2008

Published:

December 8, 2008

Citation

Kasnakoğlu, C., Camphouse, R. C., and Serrani, A. (December 8, 2008). "Reduced-Order Model-Based Feedback Control of Flow Over an Obstacle Using Center Manifold Methods." ASME. *J. Dyn. Sys., Meas., Control*. January 2009; 131(1): 011011. https://doi.org/10.1115/1.3023122

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