Vol.7, No 1, 2008 pp. 63 - 70
UDC 532.517:681.5
NONLINEAR FLOW CONTROL USING A LOW DIMENSIONAL
GALERKIN MODEL
K. Aleksić1, R. King1, B. R. Noack2,
O. Lehmann2, M. Morzyński3,
G. Tadmor4
1Department of Measurement and Control,
Berlin University of Technology, Berlin Germany, E-Mail: Katarina.Aleksic@tu-berlin.de
2Institute of Fluid Dynamics and Technical
Acoustics, Berlin University of Technology, Berlin, Germany, E-Mail: Bernd.R.Noack@tu-berlin.de
3Institute of Combustion Engines and
Transportation, Poznań University of Technology, Poznań, Poland, E-Mail:
Marek.Morzynski@put.poznan.pl
4Department of Electrical and Computer
Engineering, Northeastern University, Boston, USA, E-Mail: Tadmor@coe.neu.edu
Abstract. We propose a nonlinear flow control strategy using a low-dimensional
Galerkin model. This control design is successfully applied to the stabilization
of the flow around a circular cylinder by a transverse local volume force.
This wake stabilization problem is a well-established flow control benchmark.
A state estimation is needed, since the information of the flow is restricted
to one or few measurement points. The state estimation is used to calculate
control laws such as input-output linearization, Lyapunov-base and backstepping
controllers. These model-based strategies of nonlinear controller design
are tested in the full plant, a direct Navier-Stokes simulation of the
wake flow.
Key Words: Galerkin model, cylinder wake, input-output linearization,
Lyapunov-base controller, backstepping controller.
NELINEARNO UPRAVLJANJE STRUJANJEM FLUIDA
POMOĆU GALERKINOG MODELA NIŽEG REDA
U ovom radu predložena je nelinearna strategija upravljanja bazirana na
Galerkinom modelu nižeg reda u cilju stabilizacije strujanja fluida iza
cilindra. Upravljanje se vrši pomoću transverzalne zapreminske sile.
Ovo je poznat benčmark problem u strujanju fluida. Kako je jedina dostupna
informacija o strujanju ograničena na par mernih tačaka neophodna je
estimacija stanja. Zakon upravljanja je formiran na osnovu ocenjenih stanja.
Sve strategije upravljanja koje se baziraju na modelu su testirane pomoću
direktnih numeričkih simulacija koje rešavaju Navier-Stoksovie jednačine
koje opisuju strujanja fluida iza cilindra.
Ključne reči: Galerkin model, ulaz-izlaz linearizacija, Ljapunova
teorija stabilnosti, backstepping kontroler
