Abstract
A closed loop control approach has been implemented for the case of an unstable open cavity flow. Model reduction techniques and Linear-Quadratic- Gaussian (LQG) control have been combined to stabilize the flow. A blowing/suction actuator has been placed upstream of the cavity and a skin friction sensor downstream of it. Reduced-order models based on global modes and balanced modes have been tested. We show that a reduced-order model based on the unstable global modes (to represent the unstable dynamics) and a few balanced modes (to capture the input-output dynamics of the stable sub-space between the actuator and the sensor) is optimal to stabilize the compensated system. On the other hand, it is shown that the direct and adjoint stable global modes are not appropriate to model the stable subspace due to their strong non-normality.
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References
Ahuja, S., Rowley, C.W.: Low-dimensional models for feedback stabilization of unstable steady states. AIAA 2008-553 (2008)
Akervik, E., Hoepffner, J., Ehrenstein, U., Henningson, D.S.: Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes. Journal of Fluid Mechanics 579, 305–314 (2007)
Antoulas, A.C.: Approximation of Large-Scale Dynamical Systems. SIAM publishing, Philadelphia (2005)
Bagheri, S., Brandt, L., Henningson, D.S.: Input-output analysis, model reduction and control of the flat-plate boundary layer. Journal of Fluid Mechanics 620, 263–298 (2009)
Bagheri, S., Henningson, D.S., Hoepffner, J., Schmid, P.J.: Input-output analysis and control design applied to a linear model of spatially developing flows. Applied Mechanics Reviews 62(2), 020, 803 (2009)
Barbagallo, A., Sipp, D., Schmid, P.J.: Closed-loop control of an open cavity flow using reduced-order models. Journal of Fluid Mechanics 641, 1–50 (2009)
Bergman, M., Cordier, L., Brancher, J.P.: Optimal rotary control of the cylinder wake using POD reduced-order model. Physics of Fluids 17, 305–314 (2005)
Bewley, T.R.: Flow control: new challenges for a new renaissance. Progress in Aerospace Sciences 37(1), 21–58 (2001)
Bewley, T.R., Liu, S.: Optimal and robust control and estimation of linear paths to transition. Journal of Fluid Mechanics 365, 305–349 (1998)
Burl, J.B.: Linear optimal control. \({\cal H}_2\) and \({\cal H}_\infty\) methods. Addison-Wesley, Reading (1999)
Chevalier, M., Hoepffner, J., Akervik, E., Henningson, D.S.: Linear feedback control and estimation applied to instabilities in spatially developing boundary layers. Journal of Fluid Mechanics 588, 163–187 (2007)
Henningson, D.S., Akervik, E.: The use of global modes to understand transition and perform flow control. Physics of Fluids 20(3) (2008)
Hogberg, M., Bewley, T.R., Henningson, D.S.: Linear feedback control and estimation of transition in plane channel flow. Journal of Fluid Mechanics 481, 149–175 (2003)
Hogberg, M., Henningson, D.S.: Linear optimal control applied to instabilities in spatially developing boundary layers. Journal of Fluid Mechanics 470, 151–179 (2002)
Ilak, M., Rowley, C.W.: Modeling of transitional channel flow using balanced proper orthogonal decomposition. Physics of Fluids 20, 034, 103 (2008)
Joshi, S.S., Speyer, J.L., Kim, J.: A systems theory approach to the feedback stabilization of infinitesimal and finite-amplitude disturbances in plane Poiseuille flow. Journal of Fluid Mechanics 332, 157–184 (1997)
Kim, J., Bewley, T.R.: A linear systems approach to flow control. Annual Review of Fluid Mechanics 39, 383–417 (2007)
Laub, A.J., Heath, M.T., Page, C.C., Ward, R.C.: Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms. IEEE Transactions on Automatic Control 32(2), 115–122 (1987)
Lauga, E., Bewley, T.R.: The decay of stabilizability with Reynolds number in a linear model of spatially developing flows. Proc. R. Soc. Lond. A 459, 2077–2095 (2003)
Luchtenburg, D.M., Gunther, B., Noack, B.R., King, R., Tadmor, G.: A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration. Journal of Fluid Mechanics 623, 283–316 (2009)
Lumley, J.L.: Stochastic Tools in Turbulence. Academic Press, London (1970)
Moore, B.: Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Transactions on Automatic Control 26, 17–32 (1981)
Rowley, C.W.: Model reduction for fluids using balanced proper orthogonal decomposition. International Journal of Bifurcation and Chaos 15, 997–1013 (2005)
Samimy, M., Debiasi, M., Caraballo, E., Serrani, A., Yuan, X., Little, J., Myatt, J.: Feedback control of subsonic cavity flows using reduced-order models. Journal of Fluid Mechanics 579, 315–346 (2007)
Sipp, D., Lebedev, A.: Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. Journal of Fluid Mechanics 593, 333–358 (2007)
Willcox, K., Peraire, J.: Balanced model reduction via proper orthogonal decomposition. AIAA Journal 40, 2323–2330 (2002)
Zhou, K., Doyle, C., Glover, E.: Robust and Optimal Control. Prentice Hall, New Jersey (1996)
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Sipp, D., Barbagallo, A., Schmid, P. (2010). Closed-Loop Control of an Unstable Open Cavity. In: King, R. (eds) Active Flow Control II. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11735-0_18
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DOI: https://doi.org/10.1007/978-3-642-11735-0_18
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