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Published January 25, 2006 | Published
Journal Article Open

Linear models for control of cavity flow oscillations


Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes are limited by nonlinearities. We present experimental data which suggests that in some regimes, the oscillations may not be self-sustained, but lightly damped: oscillations are sustained by external forcing, such as boundary-layer turbulence. In these regimes, linear models suffice to describe the behaviour, and the final amplitude of oscillations depends on the characteristics of the external disturbances. These linear models are particularly appropriate for describing cavities in which feedback has been used for noise suppression, as the oscillations are small and nonlinearities are less likely to be important. It is shown that increasing the gain too much in such feedback control experiments can lead to a peak-splitting phenomenon, which is explained by the linear models. Fundamental performance limits indicate that peak splitting is likely to occur for narrow-bandwidth actuators and controllers.

Additional Information

©2006 Cambridge University Press. Reprinted with permission. Received 21 January 2004 and in revised form 19 July 2005. Published online 11 January 2006 This work was originally presented as an AIAA conference paper (AIAA 2002-0972) at the 2002 Aerospace Sciences meeting. We would like to thank Andrzej Banaszuk for many helpful comments, and for suggesting the method for distinguishing between stable and unstable noisy systems. The theoretical work was supported by AFOSR under grants F49620-98-1-0095 and F49620-03-1-0081 with program managers Dr Thomas Beutner and Dr Sharon Heise. The experimental work was supported by AFOSR under grants F49620-98-1-0276 and F49620-03-1-0074, with program managers Dr Steve Walker and Dr John Schmisseur.

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