Controlling fluid flows with positive polynomials
| Autor: | Sergei Chernyshenko, Owen Tutty, Deqing Huang, Davide Lasagna |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Semidefinite programming
0209 industrial biotechnology Polynomial Reynolds number 02 engineering and technology 01 natural sciences Upper and lower bounds 010305 fluids & plasmas Nonlinear system symbols.namesake 020901 industrial engineering & automation Control theory Limit cycle 0103 physical sciences Fluid dynamics symbols Galerkin method Mathematics |
| Zdroj: | 2016 35th Chinese Control Conference (CCC). |
| Popis: | A novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation oflong-time averages of key flow quantities is presented. The key idea, first outlined in Ref. [1], is that the difficulties of treatingand optimising long-time averages are relaxed by shifting the analysis to upper/lower bounds for minimisation/maximisationproblems, respectively. In this setting, control design reduces to finding the polynomial-type state-feedback controller thatoptimises the bound, subject to a polynomial inequality constraint involving the cost function, the nonlinear system, the controlleritself and a tunable polynomial function. A numerically tractable approach, based on Sum-of-Squares of polynomials techniquesand semidefinite programming, is proposed. As a prototypical example of control of separated flows, the mitigation of thefluctuation 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 thelong-term behaviour of the fluid flow and the effects of actuation, is first derived using Proper Orthogonal Decomposition andGalerkin projection. In a full-information setting, linear state-feedback controllers are then designed to reduce the long-timeaverage of the resolved kinetic energy associated to the limit cycle of the system. Controller performance is then assessed indirect numerical simulations. |
| Databáze: | OpenAIRE |
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