Feedback control of three-dimensional optimal disturbances using reduced-order models

Journal of Fluid Mechanics

Volumn 677, Issue , 2011, Pages 63-102

  Semeraro, Onofrio ^a   Bagheri, Shervin ^a   Brandt, Luca ^a   Henningson, Dan S ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

boundary layer stability; control theory; flow control

Indexed keywords

ACTUATORS; BOUNDARY LAYER FLOW; BOUNDARY LAYERS; CONTROL THEORY; FEEDBACK CONTROL; FLOW CONTROL; LINEAR CONTROL SYSTEMS; REYNOLDS NUMBER; WAVE PACKETS;

BALANCED TRUNCATION METHOD; BOUNDARY LAYER STABILITIES; LINEAR QUADRATIC GAUSSIAN CONTROLLERS; LINEARIZED NAVIER-STOKES EQUATIONS; PROPER ORTHOGONAL DECOMPOSITIONS; THREE-DIMENSIONAL SETTINGS; TOLLMIEN-SCHLICHTING WAVES; TRANSITIONAL BOUNDARY LAYERS;

CONTROLLERS;

BOUNDARY LAYER; FLOW CONTROL; GAUSSIAN METHOD; NAVIER-STOKES EQUATIONS; REYNOLDS NUMBER; THREE-DIMENSIONAL MODELING;

EID: 79959256638     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112011000620     Document Type: Article

References (62)

1. Ahuja, S. 2009 Reduction methods for feedback stabilization of fluid flows. PhD thesis, Princeton University, New Jersey.
2. Ahuja, S. & Rowley, C. W. 2010 Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators. J. Fluid Mech. 645, 447-478.
3. Akervik, E., Ehrenstein, U., Gallaire, F. & Henningson, D. S. 2008 Global two-dimensional stability measures of the flat plate boundary-layer flow. Eur. J. Mech. B Fluids 27, 501-513.
4. Anderson, B. & Moore, J. 1990 Optimal Control: Linear Quadratic Methods. Prentice Hall.
5. Bagheri, S., ?Akervik, E., Brandt, L. & Henningson, D. S. 2009a Matrix-free methods for the stability and control of boundary layers. AIAA J. 47, 1057-1068.
6. Bagheri, S., Brandt, L. & Henningson, D. S. 2009b Input-output analysis, model reduction and control design of the flat-plate boundary layer. J. Fluid Mech. 620, 263-298.
7. Bagheri, S., Hœpffner, J., Schmid, P. J. & Henningson, D. S. 2009c Input-output analysis and control design applied to a linear model of spatially developing flows. Appl. Mech. Rev. 62 (2), 1-27.
8. Bamieh, B., Paganini, F. & Dahleh, M. 2002 Distributed control of spatially invariant systems. IEEE Trans. Autom. Control 47 (7), 1091-1107. (Pubitemid 34835332)
9. Barbagallo, A., Sipp, D. & Schmid, P. J. 2009 Closed-loop control of an open cavity flow using reduced-order models. J. Fluid Mech. 641, 1-50.
10. Bewley, T. R. 2001 Flow control: new challenges for a new renaissance. Prog. Aerosp. Sci. 37, 21-58. (Pubitemid 32875276)
11. Bewley, T. R. & Liu, S. 1998 Optimal and robust control and estimation of linear paths to transition. J. Fluid Mech. 365, 305-349. (Pubitemid 128506302)
12. Bewley, T. R., Moin, P. & Temam, R. 2001 DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms. J. Fluid Mech. 447, 179-225. (Pubitemid 33056279)
13. Butler, K. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4, 1637-1650.
14. Chevalier, M., Hœpffner, J., ?Akervik, E. & Henningson, D. S. 2007a Linear feedback control and estimation applied to instabilities in spatially developing boundary layers. J. Fluid Mech. 588, 163-187.
15. Chevalier, M., Hœpffner, J., Bewley, T. R. & Henningson, D. S. 2006 State estimation in wall-bounded flow systems. Part 2. Turbulent flows. J. Fluid Mech. 552, 167-187.
16. Chevalier, M., Schlatter, P., Lundbladh, A. & Henningson, D. S. 2007b A pseudo-spectral solver for incompressible boundary layer flows. Trita-Mek 7. KTH Mechanics, Stockholm, Sweden.
17. Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503-539.
18. Chomaz, J. M. 2005 Global instabilities in spatially developing flows: Non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357-392.
19. Cortelezzi, L., Speyer, J. L., Lee, K. H. & Kim, J. 1998 Robust reduced-order control of turbulent channel flows via distributed sensors and actuators. In IEEE 37th Conf. on Decision and Control, pp. 1906-1911.
20. Curtai n, R. & Zwa rt, H. 1995 An Introduction to Infinite-Dimensional Linear Systems Theory. Springer.
21. Doyle, J. C. 1978 Guaranteed margins for LQG regulators. IEEE Trans. Autom. Control 23, 756-757.
22. Doyle, J. C, Glover, K., Khargonekar, P. P. & Francis, B. A. 1989 State-space solutions to standard H2 and Hoo control problems. IEEE Trans. Autom. Control 34, 831-847.
23. Dullerud, E. G. & Paganini, F 1999 A Course in Robust Control Theory. A Convex Approach. Springer Verlag.
24. Glover, K. 1984 All optimal Hankel-norm approximations of linear multivariable systems and the l°°-error bounds. Intl J. Control 39, 1115-1193. (Pubitemid 14606446)
25. Green, M. & Limebeer, J. N. 1995 Linear Robust Control. Prentice Hall.
26. Grundmann, S. & Tropea, C. 2008 Active cancellation of artificially introduced Tollmien- Schlichting waves using plasma actuators. Exp. Fluids 44 (5), 795-806.
27. Hammond, E. P., Bewley, T. R. & Moin, P. 1998 Observed mechanisms for turbulence attenuation and enhancement in opposition-controlled wall-bounded flows. Phys. Fluids 10 (9), 2421-2423. (Pubitemid 128591626)
28. Ho, C. M. & Tai, Y. 1998 Micro-electro-mechanical systems MEMS and fluid flows. Annu. Rev. Fluid Mech. 30, 579-612.
29. Högberg, M. & Bewley, T. R. 2000 Spatially localized convolution kernels for feedback control of transitional flows. In IEEE 39th Conf. on Decision and Control, pp. 3278-3283. (Pubitemid 32528160)
30. Högberg, M., Bewley, T. R. & Henningson, D. S. 2003a Linear feedback control and estimation of transition in plane channel flow. J. Fluid Mech. 481, 149-175. (Pubitemid 36632354)
31. τ = 100 turbulence using gain scheduling and linear state-feedback control flow. Phys. Fluids 15, 3572-3575. (Pubitemid 37450218)
32. Holmes, P., Lumley, J. & Berkooz, G. 1996 Turbulence Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.
33. Ilak, M., Bagheri, S., Brandt, L., Rowley, C. W. & Henningson, D. 2010 Model reduction of the nonlinear complex Ginzburg-Landau equation. SIAM J. Appl. Dyn. Syst. 9 (4), 1284-1302.
34. Ilak, M. & Rowley, C. W. 2008 Modeling of transitional channel flow using balanced proper orthogonal decomposition. Phys. Fluids 20, 034103.
35. Joshi, S. S., Speyer, J. L. & Kim, J. 1997 A systems theory approach to the feedback stabilization of infinitesimal and finite-amplitude disturbances in plane Poiseuille flow. J. Fluid Mech. 332, 157-184.
36. Kalman, R. E. 1960 A new approach to linear filtering and prediction problems. Trans. ASME D J. Basic Engng 82, 24-45.
37. Laub, A. 1991 Invariant subspace methods for the numerical solution of Riccati equations. In The Riccati Equation (ed. S. Bittaini, A. J. Laub & J. C. Willems), pp. 163-196. Springer.
38. Laub, A., Heath, M., Paige, C. & Ward, R. 1987 Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms. IEEE Trans. Autom. Control 32 (2), 115-122. (Pubitemid 17534793)
39. Lewis, F. L. & Syrmos, L. V. 1995 Optimal Control. Wiley.
40. Lundell, F. 2003 Pulse-width modulated blowing/suction as a flow control actuator. Exp. Fluids 35, 502-504. (Pubitemid 37540375)
41. Lundell, F. 2007 Reactive control of transition induced by free-stream turbulence: an experimental demonstration. J. Fluid Mech. 585, 41-71. (Pubitemid 47232964)
42. Ma, Z., Ahuja, S. & Rowley, C. W. 2009 Reduced order models for control of fluids using the eigensystem realization algorithm. Theor. Comput. Fluid Dyn. (in press).
43. Milling, W. 1981 Tollmien-Schlichting wave cancellation. Phys. Fluids 24 (5), 979-981.
44. Monokrousos, A., ?Akervik, E., Brandt, L. & Henningson, D. S. 2010a Global optimal disturbances in the Blasius boundary-layer flow using time-steppers. J. Fluid Mech. 650, 181-214.
45. Monokrousos, A., Brandt, L., Schlatter, P. & Henningson, D. S. 2008 DNS and LES of estimation and control of transition in boundary layers subject to free-stream turbulence. Intl J. Heat Fluid Flow 29 (3), 841-855.
46. Monokrousos, A., Lundell, F. & Brandt, L. 2010b Feedback control of boundary layer bypass transition: comparison of a numerical study with experiments. J. AIAA 48 (8), 1848-1851.
47. Moore, B. 1981 Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Autom. Control 26 (1), 17-32. (Pubitemid 11495780)
48. Nordström, J., Nordin, N. & Henningson, D. S. 1999 The fringe region technique and the Fourier method used in the direct numerical simulation of spatially evolving viscous flows. SIAM J. Sci. Comput. 20 (4), 1365-1393. (Pubitemid 32251222)
49. Pang, J. & Choi, K.-S. 2004 Turbulent drag reduction by Lorentz force oscillation. Phys. Fluids 16 (5), L35-L38. (Pubitemid 38672632)
50. Pernebo, L. & Silverman, L. 1982 Model reduction via balanced state space representations. IEEE Trans. Autom. Control 27, 382-387. (Pubitemid 12499635)
51. Quadrio, M. & Ricco, P. 2004 Critical assessment of turbulent drag reduction through spanwise wall oscillations. J. Fluid Mech. 521, 251-271. (Pubitemid 40107140)
52. Rempfer, D. & Fasel, H. 1994 Evolution of three-dimensional coherent structures in a flat-plate boundary layer. J. Fluid. Mech. 260, 351-375.
53. Rowley, C. W. 2005 Model reduction for fluids using balanced proper orthogonal decomposition. Intl J. Bifurcation Chaos 15 (3), 997-1013. (Pubitemid 40878395)
54. Schlichting, H. & Gersten, K. 2000 Boundary-Layer Theory. Springer.
55. Semeraro, O., Bagheri, S., Brandt, L. & Henningson, D. S. 2010 Linear control of 3D disturbances on a flat-plate. In Seventh IUTAM Symp. on Laminar-Turbulent Transition (ed. P. Schlatter & D. S. Henningson), vol. 18. Springer.
56. Skogestad, S. & Postlethwaite, I. 2005 Multivariable Feedback Control, Analysis to Design, 2nd edn. Wiley.
57. Smith, B. L. & Glezer, A. 1998 The formation and evolution of synthetic jets. Phys. Fluids 10 (9), 2281-2297. (Pubitemid 128591615)
58. Sturzebecher, D. & Nitsche, W. 2003 Active cancellation of Tollmien-Schlichting waves instabilities on a wing using multi-channel sensor actuator systems. Intl J. Heat Fluid Flow 24, 572-583. (Pubitemid 36696115)
59. Tempelmann, D., Hanifi, A. & Henningson, D. S. 2010 Optimal disturbances and receptivity in three-dimensional boundary layers. In 5th European Conf. on Computational Fluid Dynamics, Lisbon, Portugal.
60. White, E. & Saric, W. 2000 Application of variable leading-edge roughness for transition control on swept wings. In 38th AIAA Aerospace Sciences Meeting and Exhibit. AIAA Paper 2000-283. Reno, NV.
61. Zhou, K., Doyle, J. C. & Glover, K. 2002 Robust and Optimal Control. Prentice Hall.
62. Zhou, K., Salomon, G. & Wu, E. 1999 Balanced realization and model reduction for unstable systems. Intl J. Robust Nonlinear Control 9, 183-198.