Control of fluid flows using multivariate spline reduced order models

HJ Tol; CC de Visser; M Kotsonis

doi:10.2514/6.2016-1821

Control of fluid flows using multivariate spline reduced order models

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

This paper presents a study on control of fluid flows using multivariate spline reduced order models. A new approach is presented for model reduction of the incompressible Navier-Stokes equations using multivariate splines defined on triangulations. State space descriptions are derived that can be used for control design. This paper considers the linearised Navier-Stokes equations in velocity-pressure formulation. The pressure is elimi- nated from the equations by using a space of velocity fields which are divergence free. The divergence free condition along with the smoothness across the domain and the bound- ary conditions are imposed as a linear system of side constraints. The projection of the system on the null space of these constraints significantly reduces the dimension of the model while satisfying these constraints. The reduction method is applied to design and implement feedback controllers for stabilization of disturbances in a Poiseuille flow. It is shown that effective feedback stabilization can be achieved using low order control models.

Original language	English
Title of host publication	Proceedings of the 54th AIAA aerospace sciences meeting
Editors	s.n.
Place of Publication	Reston
Publisher	American Institute of Aeronautics and Astronautics Inc. (AIAA)
Number of pages	12
ISBN (Print)	978-1-62410-393-3
DOIs	https://doi.org/10.2514/6.2016-1821
Publication status	Published - 2016
Event	54th AIAA Aerospace Sciences Meeting - San Diego, United States Duration: 4 Jan 2016 → 8 Jan 2016 Conference number: 54 https://doi.org/10.2514/MASM16

Publication series

Name
Publisher	AIAA

Conference

Conference	54th AIAA Aerospace Sciences Meeting
Country/Territory	United States
City	San Diego
Period	4/01/16 → 8/01/16
Internet address	https://doi.org/10.2514/MASM16

Bibliographical note

harvest
AIAA 2016-1821

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10.2514/6.2016-1821

Control of fluid flows using multivariate spline reduced order models, 2016Accepted author manuscript, 723 KB

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title = "Control of fluid flows using multivariate spline reduced order models",

abstract = "This paper presents a study on control of fluid flows using multivariate spline reduced order models. A new approach is presented for model reduction of the incompressible Navier-Stokes equations using multivariate splines defined on triangulations. State space descriptions are derived that can be used for control design. This paper considers the linearised Navier-Stokes equations in velocity-pressure formulation. The pressure is elimi- nated from the equations by using a space of velocity fields which are divergence free. The divergence free condition along with the smoothness across the domain and the bound- ary conditions are imposed as a linear system of side constraints. The projection of the system on the null space of these constraints significantly reduces the dimension of the model while satisfying these constraints. The reduction method is applied to design and implement feedback controllers for stabilization of disturbances in a Poiseuille flow. It is shown that effective feedback stabilization can be achieved using low order control models. ",

author = "HJ Tol and {de Visser}, CC and M Kotsonis",

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doi = "10.2514/6.2016-1821",

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isbn = "978-1-62410-393-3",

publisher = "American Institute of Aeronautics and Astronautics Inc. (AIAA)",

editor = "s.n.",

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address = "United States",

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}

Tol, HJ, de Visser, CC & Kotsonis, M 2016, Control of fluid flows using multivariate spline reduced order models. in s.n. (ed.), Proceedings of the 54th AIAA aerospace sciences meeting. American Institute of Aeronautics and Astronautics Inc. (AIAA), Reston, 54th AIAA Aerospace Sciences Meeting, San Diego, California, United States, 4/01/16. https://doi.org/10.2514/6.2016-1821

Control of fluid flows using multivariate spline reduced order models. / Tol, HJ; de Visser, CC ; Kotsonis, M.
Proceedings of the 54th AIAA aerospace sciences meeting. ed. / s.n. Reston: American Institute of Aeronautics and Astronautics Inc. (AIAA), 2016.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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T1 - Control of fluid flows using multivariate spline reduced order models

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AU - de Visser, CC

AU - Kotsonis, M

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N2 - This paper presents a study on control of fluid flows using multivariate spline reduced order models. A new approach is presented for model reduction of the incompressible Navier-Stokes equations using multivariate splines defined on triangulations. State space descriptions are derived that can be used for control design. This paper considers the linearised Navier-Stokes equations in velocity-pressure formulation. The pressure is elimi- nated from the equations by using a space of velocity fields which are divergence free. The divergence free condition along with the smoothness across the domain and the bound- ary conditions are imposed as a linear system of side constraints. The projection of the system on the null space of these constraints significantly reduces the dimension of the model while satisfying these constraints. The reduction method is applied to design and implement feedback controllers for stabilization of disturbances in a Poiseuille flow. It is shown that effective feedback stabilization can be achieved using low order control models.

AB - This paper presents a study on control of fluid flows using multivariate spline reduced order models. A new approach is presented for model reduction of the incompressible Navier-Stokes equations using multivariate splines defined on triangulations. State space descriptions are derived that can be used for control design. This paper considers the linearised Navier-Stokes equations in velocity-pressure formulation. The pressure is elimi- nated from the equations by using a space of velocity fields which are divergence free. The divergence free condition along with the smoothness across the domain and the bound- ary conditions are imposed as a linear system of side constraints. The projection of the system on the null space of these constraints significantly reduces the dimension of the model while satisfying these constraints. The reduction method is applied to design and implement feedback controllers for stabilization of disturbances in a Poiseuille flow. It is shown that effective feedback stabilization can be achieved using low order control models.

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M3 - Conference contribution

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PB - American Institute of Aeronautics and Astronautics Inc. (AIAA)

CY - Reston

T2 - 54th AIAA Aerospace Sciences Meeting

Y2 - 4 January 2016 through 8 January 2016

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Control of fluid flows using multivariate spline reduced order models

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Finite-dimensional approximation and control of shear flows

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