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Stabilising Control Laws for the Incompressible Navier-Stokes Equations using Sector Stability Theory

Sharma, A. S. and Limebeer, D. J. N. and McKeon, B. J. and Morrison, J. F. (2006) Stabilising Control Laws for the Incompressible Navier-Stokes Equations using Sector Stability Theory. In: 3rd AIAA Flow Control Conference, June 5-8, 2006, San Francisco, CA. http://resolver.caltech.edu/CaltechAUTHORS:20150303-121446831

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Abstract

A method for nonlinear global stabilisation of the incompressible Navier-Stokes equations is presented and used to eliminate transient growth in linearly stable Poiseuille flow for the case of full-field actuation and sensing. In the absence of complete velocity field sensing and full actuation the controller synthesis procedure gives a controller that minimises the the attainable perturbation energy over all disturbances and thus maximises the disturbance threshold for transition to occur. The control laws are found using the theory of positive real systems, originating in the control systems community. It is found that a control law making the linearised part of the perturbed Navier-Stokes equations positive real, provides nonlinear global stability. A state-space synthesis procedure is presented that results in two game-theoretic algebraic Riccati equations.


Item Type:Conference or Workshop Item (Paper)
Related URLs:
URLURL TypeDescription
http://arc.aiaa.org/doi/abs/10.2514/6.2006-3695PublisherArticle
http://dx.doi.org/10.2514/6.2006-3695DOIArticle
ORCID:
AuthorORCID
Sharma, A. S.0000-0002-7170-1627
McKeon, B. J.0000-0003-4220-1583
Additional Information:©2006 AIAA. A. Sharma, J. Morrison and D. Limebeer thank BAE systems and the UK EPSRC for their support under the FLAVIIR project. B. McKeon thanks the Royal Society for their support under a Dorothy Hodgkin Fellowship.
Group:GALCIT
Funders:
Funding AgencyGrant Number
BAE SystemsUNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)FLAVIIR
Royal Society Dorothy Hodgkin FellowshipUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
AIAA Paper2006-3695
Record Number:CaltechAUTHORS:20150303-121446831
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150303-121446831
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55476
Collection:CaltechAUTHORS
Deposited By: Jamie Sei
Deposited On:04 Mar 2015 22:32
Last Modified:09 Oct 2017 22:47

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