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Controlling fluid flows with positive polynomials

Controlling fluid flows with positive polynomials
Controlling fluid flows with positive polynomials
A novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation of
long-time averages of key flow quantities is presented. The key idea, first outlined in Ref. [1], is that the difficulties of treating
and optimising long-time averages are relaxed by shifting the analysis to upper/lower bounds for minimisation/maximisation
problems, respectively. In this setting, control design reduces to finding the polynomial-type state-feedback controller that
optimises the bound, subject to a polynomial inequality constraint involving the cost function, the nonlinear system, the controller
itself and a tunable polynomial function. A numerically tractable approach, based on Sum-of-Squares of polynomials techniques
and semidefinite programming, is proposed. As a prototypical example of control of separated flows, the mitigation of the
fluctuation kinetic energy in the unsteady two-dimensional wake past a circular cylinder at a Reynolds number equal to 100,
via controlled angular motions of the surface, is investigated. A compact control-oriented reduced-order model, resolving the
long-term behaviour of the fluid flow and the effects of actuation, is first derived using Proper Orthogonal Decomposition and
Galerkin projection. In a full-information setting, linear state-feedback controllers are then designed to reduce the long-time
average of the resolved kinetic energy associated to the limit cycle of the system. Controller performance is then assessed in
direct numerical simulations.
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
Tutty, Owen
c9ba0b98-4790-4a72-b5b7-09c1c6e20375
Chernyshenko, Sergei
0381c775-bd7f-4fb9-862d-d6d378cd9b5d
Huang, Deqing
96e466d6-59e1-4428-a6f6-4c1cecd45d00
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
Tutty, Owen
c9ba0b98-4790-4a72-b5b7-09c1c6e20375
Chernyshenko, Sergei
0381c775-bd7f-4fb9-862d-d6d378cd9b5d
Huang, Deqing
96e466d6-59e1-4428-a6f6-4c1cecd45d00

Lasagna, Davide, Tutty, Owen, Chernyshenko, Sergei and Huang, Deqing (2016) Controlling fluid flows with positive polynomials. 35th Chinese Control Conference. (In Press)

Record type: Conference or Workshop Item (Paper)

Abstract

A novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation of
long-time averages of key flow quantities is presented. The key idea, first outlined in Ref. [1], is that the difficulties of treating
and optimising long-time averages are relaxed by shifting the analysis to upper/lower bounds for minimisation/maximisation
problems, respectively. In this setting, control design reduces to finding the polynomial-type state-feedback controller that
optimises the bound, subject to a polynomial inequality constraint involving the cost function, the nonlinear system, the controller
itself and a tunable polynomial function. A numerically tractable approach, based on Sum-of-Squares of polynomials techniques
and semidefinite programming, is proposed. As a prototypical example of control of separated flows, the mitigation of the
fluctuation kinetic energy in the unsteady two-dimensional wake past a circular cylinder at a Reynolds number equal to 100,
via controlled angular motions of the surface, is investigated. A compact control-oriented reduced-order model, resolving the
long-term behaviour of the fluid flow and the effects of actuation, is first derived using Proper Orthogonal Decomposition and
Galerkin projection. In a full-information setting, linear state-feedback controllers are then designed to reduce the long-time
average of the resolved kinetic energy associated to the limit cycle of the system. Controller performance is then assessed in
direct numerical simulations.

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More information

Accepted/In Press date: 9 April 2016
Venue - Dates: 35th Chinese Control Conference, 2016-04-09
Organisations: Aeronautics, Astronautics & Comp. Eng, Faculty of Engineering and the Environment

Identifiers

Local EPrints ID: 392747
URI: https://eprints.soton.ac.uk/id/eprint/392747
PURE UUID: 33482a43-abff-4406-9133-d64e63ae8090
ORCID for Davide Lasagna: ORCID iD orcid.org/0000-0002-6501-6041

Catalogue record

Date deposited: 19 Apr 2016 15:45
Last modified: 06 Jun 2018 12:24

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Contributors

Author: Davide Lasagna ORCID iD
Author: Owen Tutty
Author: Sergei Chernyshenko
Author: Deqing Huang

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