Abstract
Actuator and sensor placement can be just as consequential for the performance of localized feedback flow control as controller design. Yet, effective placement is not well understood, and the use of suboptimal placements is common. This manuscript reports descriptions and characteristics of effective actuator and sensor placements for optimal flow control. We review \(\mathcal{H}_{2}\) optimal placements in the linearized Ginzburg–Landau and Orr–Sommerfeld/Squire models of fluid flow. We then analyze the feedback control of these models by relating physical observations with mathematical tools. Although these tools do not fully predict optimal placements, they do reveal patterns that most or all effective placements share. Most notably, effective actuator–sensor placements provide good authority over unstable modes and transient growth, and avoid large time lags between inputs and outputs.
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References
van de Wal, M., de Jager, B.: A review of methods for input/output selection. Automatica 37(4), 487–510 (2001)
Morris, K.: Linear-quadratic optimal actuator location. IEEE Trans. Autom. Control 56(1), 113–124 (2011)
Darivandi, N., Morris, K., Khajepour, A.: An algorithm for LQ optimal actuator location. Smart Mater. Struct. 22(3) (2013)
Hiramoto, K., Doki, H., Obinata, G.: Optimal sensor/actuator placement for active vibration control using explicit solution of algebraic Riccati equation. J. Sound Vib. 229(5), 1057–1075 (2000)
Güney, M., Eşkinat, E.: Optimal actuator and sensor placement in flexible structures using closed-loop criteria. J. Sound Vib. 312(1-2), 210–233 (2008)
Roussopoulos, K.: Feedback control of vortex shedding at low Reynolds numbers. J. Fluid Mech. 248, 267–296 (1993)
Gillies, E.A.: Multiple sensor control of vortex shedding. AIAA J. 39(4), 748–750 (2001)
Lauga, E., Bewley, T.R.: The decay of stabilizability with Reynolds number in a linear model of spatially developing flows. Proc. R. Soc. A 459(2036), 2077–2095 (2003)
Giannetti, F., Luchini, P.: Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197 (2007)
Chen, K.K., Rowley, C.W.: H 2 optimal actuator and sensor placement in the linearised complex Ginzburg–Landau system. J. Fluid Mech. 681, 241–260 (2011)
Strykowski, P.J., Sreenivasan, K.R.: On the formation and suppression of vortex ‘shedding’ at low Reynolds numbers. J. Fluid Mech. 218, 71–107 (1990)
Åkervik, E., Hœpffner, J., Ehrenstein, U., Henningson, D.S.: Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes. J. Fluid Mech. 579, 305–314 (2007)
Bagheri, S., Henningson, D.S., Hœpffner, J., Schmid, P.J.: Input-output analysis and control design applied to a linear model of spatially developing flows. Appl. Mech. Rev. 62, 020803 (2009)
Chen, K.K., Rowley, C.W.: Fluid flow control applications of \(\mathcal{H}_2\) optimal actuator and sensor placement. In: Proceedings of the American Control Conference (ACC), Portland, OR, USA. American Automatic Control Council (2014)
Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control: Analysis and Design, 2nd edn. John Wiley & Sons Ltd., West Sussex (2005)
Weideman, J.A.C., Reddy, S.C.: A MATLAB differentiation matrix suite. ACM Trans. Math. Softw. 26(4), 465–519 (2000)
Cossu, C., Chomaz, J.M.: Global measures of local convective instabilities. Phys. Rev. Lett. 78(23), 4387–4390 (1997)
Chomaz, J.M.: Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392 (2005)
Schmid, P.J., Henningson, D.S.: Stability and Transition in Shear Flows. Applied Mathematical Sciences, vol. 142. Springer, New York (2001)
Belson, B.A., Semeraro, O., Rowley, C.W., Henningson, D.S.: Feedback control of instabilities in the two-dimensional Blasius boundary layer: The role of sensors and actuators. Phys. Fluids 25, 054106 (2013)
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Chen, K.K., Rowley, C.W. (2015). Heuristics for Effective Actuator and Sensor Placement in Feedback Flow Control. In: King, R. (eds) Active Flow and Combustion Control 2014. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-319-11967-0_8
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DOI: https://doi.org/10.1007/978-3-319-11967-0_8
Publisher Name: Springer, Cham
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