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Modelling for robust feedback control of fluid flows

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Title: Modelling for robust feedback control of fluid flows
Authors: Jones, BL
Heins, PH
Kerrigan, EC
Morrison, JF
Sharma, AS
Item Type: Journal Article
Abstract: This paper addresses the problem of designing low-order and linear robust feedback controllers that provide a priori guarantees with respect to stability and performance when applied to a fluid flow. This is challenging, since whilst many flows are governed by a set of nonlinear, partial differential–algebraic equations (the Navier–Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are: firstly, linear; secondly, described by ordinary differential equations (ODEs); and thirdly, finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the H∞ loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl’s theory of sheared turbulence. To illustrate the application of these techniques, an H∞ loop-shaping controller is designed and applied to the problem of reducing perturbation wall shear stress in plane channel flow. Direct numerical simulation (DNS) results demonstrate robust attenuation of the perturbation shear stresses across a wide range of Reynolds numbers with a single linear controller.
Issue Date: 25-Apr-2015
Date of Acceptance: 3-Feb-2015
URI: http://hdl.handle.net/10044/1/23549
DOI: 10.1017/jfm.2015.84
ISSN: 0022-1120
Publisher: Cambridge University Press
Start Page: 687
End Page: 722
Journal / Book Title: Journal of Fluid Mechanics
Volume: 769
Issue: 1
Copyright Statement: © 2015 Cambridge University Press. Bryn Ll. Jones, P. H. Heins, E. C. Kerrigan, J. F. Morrison and A. S. Sharma (2015). Modelling for robust feedback control of fluid flows. Journal of Fluid Mechanics, 769, pp 687-722 doi:10.1017/jfm.2015.84. The final publication is available via Cambridge Journals Online at https://dx.doi.org/10.1017/jfm.2015.84.
Keywords: Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
control theory
drag reduction
low-dimensional models
PROPER ORTHOGONAL DECOMPOSITION
DIRECT NUMERICAL-SIMULATION
TURBULENT-BOUNDARY-LAYERS
NEAR-WALL TURBULENCE
H-INFINITY CONTROL
DRAG REDUCTION
CHANNEL FLOW
SHEAR-FLOW
PRESSURE-FLUCTUATIONS
TRANSIENT GROWTH
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
control theory
drag reduction
low-dimensional models
DIRECT NUMERICAL-SIMULATION
H-INFINITY CONTROL
PRESSURE-FLUCTUATIONS
TRANSIENT GROWTH
DRAG REDUCTION
TURBULENCE
SYSTEMS
CANCELLATION
TRANSITION
STABILITY
physics.flu-dyn
physics.flu-dyn
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Online Publication Date: 2015-03-25
Appears in Collections:Electrical and Electronic Engineering
Aeronautics
Faculty of Engineering