In the present work, a simple proportional feedback control is designed to suppress the vortex-shedding instability in the wake of a prototype bluff-body flow, i.e., the flow around a square cylinder confined in a channel with an incoming Poiseuille flow. Actuation is provided by two jets localized on the cylinder surface and velocity sensors are used for feedback control. This particular configuration is a pretext to propose a more general strategy for designing a controller, which is independent of the type of actuation and sensors. The method is based on the linear stability analysis of the flow, carried out on the unstable steady solution of the equations, which is also the target flow of the control. The idea is to use sensitivity analysis to predict the displacement in the complex plane of some selected eigenvalues, found by the linear stability analysis of the flow, as a function of the control design parameters. In this paper, it is shown that the information provided by only sensitivity analysis carried out on the uncontrolled system is not sufficient to design a controller which stabilizes the flow. Therefore, the control is designed iteratively by successive linearizations. Apart from possible constraints, the position of the sensors, the direction along which velocity is measured, and the feedback coefficients are outputs of the design procedure. The proposed strategy leads to a successful control up to a Reynolds number which is at least twice as large as the critical one for the primary instability, using only one velocity sensor.
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September 2010
Research Article|
September 14 2010
Feedback control of the vortex-shedding instability based on sensitivity analysis
Simone Camarri;
Simone Camarri
a)
1Dipartimento di Ingegneria Aerospaziale,
Università di Pisa
, via G. Caruso 8, 56122 Pisa, Italy
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Angelo Iollo
Angelo Iollo
2Institut de Mathématiques de Bordeaux UMR 5251 CNRS,
Université Bordeaux 1 and INRIA Bordeaux—Sud Ouest
, Equipe-Projet MC2, 351 Cours de la Libération, 33405 Talence Cedex, France
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a)
Electronic mail: s.camarri@ing.unipi.it.
Physics of Fluids 22, 094102 (2010)
Article history
Received:
February 23 2010
Accepted:
July 14 2010
Citation
Simone Camarri, Angelo Iollo; Feedback control of the vortex-shedding instability based on sensitivity analysis. Physics of Fluids 1 September 2010; 22 (9): 094102. https://doi.org/10.1063/1.3481148
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