While the potential for the use of synthetic jet actuators to achieve flow control has been noted for some time, most of such flow control studies have been empirical or experimental in nature. Several technical issues must be resolved to achieve rigorous, model-based, closed-loop control methodologies for this class of actuators. The goal of this paper is consequently two-fold. First, we seek to derive and evaluate model order reduction methods based on proper orthogonal decomposition that are suitable for synthetic jet actuators. Second, we seek to derive rigorously stable feedback control laws for the derived reduced order models. The realizability of the control strategies is discussed, and a numerical study of the effectiveness of the reduced order models for two-dimensional flow near the jet exit is summarized.

1.
Amitay M., Smith B. L., and Glezer A., 1998, “Aerodynamic Flow Control Using Synthetic Jet Technology,” AIAA Paper No. 98-0208, 36th Aerospace Sciences Meeting & Exhibit, Reno, NV.
2.
Smith, D., Amitay, M., Kibens, V., Parekh, D., and Glezer, A., 1998, “Modifications of Lifting Body Aerodynamics Using Synthetic Jet Actuators,” AIAA Paper No. 98-0209, 36th Aerospace Sciences Meeting & Exhibit, Reno, NV.
3.
Seifert, A. and Pack, L., 1999, “Oscillatory Excitation of Unsteady Compressible Flows over Airfoils at Flight Reynolds Number,” AIAA Paper No. 99-0925.
4.
Joshi
,
S. S.
,
Speyer
,
J. L.
, and
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
, pp.
157
184
.
5.
Gilarranz, J., Singh, K., Ko, J., Rediniotis, O. K., and Kurdila, A. J., 1997, “High Frame-Rate, High Resolution Cinematographic Particle Image Velocimetry,” AIAA Paper 97-0495.
6.
Isidori, A., 1989, Nonlinear Control Systems, Springer-Verlag.
7.
Krstic, M., Kanellakopoulos, I., Kokotovic, P., 1995, Nonlinear and Adaptive Control Design, Wiley, New York.
8.
Sheen
,
J.-J.
, and
Bishop
,
R. H.
,
1994
, “
Adaptive Nonlinear Control of Spacecraft
,”
J. Astronaut. Sci.
,
42
(
4
), pp.
451
472
.
9.
Ko, J., Kurdila, A. J., and Strganac, T. W., 1997, “Nonlinear Control of a Prototypical Wing Section with Torsional Nonlinearity,” J. Guid. Control Dyn., 20(6).
10.
Cuvelier, P., 1976, “Optimal Control of a System Governed by the Navier-Stokes Equations Coupled with the Heat Equations,” in W. Eckhaus, ed., New Developments in Differential Equations, North-Holland, Amsterdam, pp. 81–98.
11.
Gunzburger
,
M.
, and
Lee
,
H. C.
,
1994
, “
Analysis, Approximation, and Computation of a Coupled Solid/Fluid Temperature Control Problem
,”
Comput. Methods Appl. Mech. Eng.
,
118
, pp.
133
152
.
12.
Burns, J. A., and Ou, Y., 1994, “Feedback Control of the Driven Cavity Problem Using LQR Designs,” Proceedings of the 33rd Conference on Decision and Control, pp. 289–294, Lake Buena Vista, FL, Dec.
13.
Banks, H. T., and Ito, K., 1994 “Structural Actuator Control of Fluid/Structure Interactions,” Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, pp. 283–288.
14.
Desai
,
M.
, and
Ito
,
K.
,
1994
, “
Optimal Control of Navier-Stokes Equations
,”
SIAM J. Control Optim.
,
32
(
5
), pp.
1428
1446
.
15.
Ito
,
K.
, and
Kang
,
S.
,
1994
, “
A Dissipative Feedback Control Synthesis for Systems Arising in Fluid Dynamics
,”
SIAM J. Control Optim.
,
32
(
3
), pp.
831
854
.
16.
Ravindran
,
S. S.
, and
Hou
,
L. S.
,
1998
, “
A Penalized Neumann Control Approach for Solving an Optimal Dirichlet Control Problem for the Navier-Stokes Equations
,”
SIAM J. Control Optim.
,
36
(
5
), pp.
1795
1814
.
17.
Hou
,
L. S.
, and
Yan
,
Y.
,
1997
, “
Dynamics for Controlled Navier-Stokes Systems with Distributed Controls
,”
SIAM J. Control Optim.
,
35
(
2
), pp.
654
677
.
18.
Fattorini
,
H. O.
, and
Sritharan
,
S. S.
,
1992
, “
Existence of Optimal Controls for Viscous Flow Problems
,”
Proc. R. Soc. London, Ser. A
,
439
, pp.
81
102
.
19.
Fattorini
,
H. O.
, and
Sritharam
,
S. S.
,
1995
, “
Optimal Chattering Controls for Viscous Flow
,”
Nonlinear Analysis, Theory & Applications
,
25
(
8
), pp.
763
797
.
20.
Fursikov
,
A. V.
,
Gunzburger
,
M. D.
, and
Hou
,
L. S.
,
1998
, “
Boundary Value Problems and Optimal Boundary Control for the Navier-Stokes System: The Two Dimensional Case
,”
SIAM J. Control Optim.
,
36
(
3
), pp.
852
894
, May.
21.
Joslin, R. D., Gunzburger, M. D., Nicolaides, R. A., Erlehbacher, G., and Hussaini, M. Y., 1997, “Self-Contained Automated Methodology for Optimal Flow Control,” AIAA J., 35(5).
22.
Joslin, R. D., 1997, “Direct Numerical Simulation of Evolution and Control of Linear and Nonlinear Disturbances in Three Dimensional Attachment Line Boundary Layers,” NASA Technical Paper 3623.
23.
Wygnanski, I., 1997, “Boundary Layer and Flow Control by Periodic Addition of Momentum,” 4th AIAA Shear Flow Control Conference,” Snowmass Village, CO, June 29–July 2, AIAA Paper No. 97-2117.
24.
Trujillo, S. M., Bogard, D. G., and Ball, K. S., 1997, “Turbulent Boundary Layer Drag Reduction Using an Oscillating Wall,” 28th AIAA Fluid Dynamics Conference, 4th AIAA Shear Flow Control Conference, Snowmass Village, CO, June 29–July 2, AIAA Paper No. 97-1870.
25.
Bewley, T. R., Moin, P., and Temam, R., 1997, “Optimal and Robust Approaches for Linear and Nonlinear Regulation Problems in Fluid Mechanics,” 28th AIAA Fluid Dynamics Conference, 4th AIAA Shear Flow Control Conference, Snowmass Village, CO, June 29–July 2, AIAA Paper No. 97-1872.
26.
Cho, Y., Agarwal, R. K., and Nho, K., 1997, “Neural Network Approaches to Some Model Flow Control Problems,” 4th AIAA Shear Flow Conference, Snowmass Village, CO, June 29–July 2.
27.
Aubry
,
N.
,
Holmes
,
P.
,
Lumley
,
J. L.
, and
Stone
,
E.
,
1988
, “
The Dynamics of Coherent Structures in the Wall Region of a Turbulent Boundary Layer
,”
J. Fluid Mech.
,
192
, pp.
115
173
.
28.
Ly
,
H. V.
, and
Tran
,
H. T.
,
1998
, “
Proper Orthogonal Decomposition for Flow Calculations and Optimal Control in a Horizontal CVD Reactor,” Technical Report
,
Center for Research in Scientific Computation
,
North Carolina State University.
29.
Corke
,
T. C.
,
Glauser
,
M. N.
, and
Berkooz
,
G.
,
1994
, “
Utilizing Low Dimensional Dynamical Systems Models to Guide Control Experiments
,”
Appl. Mech. Rev.
,
47
(
6
), Part 2, June, pp.
132
138
.
30.
Ito
,
K.
, and
Ravindran
,
S. S.
,
1996
Reduced Basis Method for Flow Control,” Technical Report
CRSC-TR96-25
,
Center for Research in Scientific Computation
,
North Carolina State University.
31.
Ito
,
K.
, and
Ravindran
,
S. S.
,
1997
A reduced basis method for control problems governed by PDEs,” Technical Report
CRSC-TR-97-1
,
Center for Research in Scientific Computation
,
North Carolina State University.
32.
Craig, R. R., 1981, Structural Dynamics, Wiley, New York.
33.
Skelton, R. E., 1988, Dynamic Systems and Control, Wiley, New York.
34.
Tang, D., Conner, M., and Dowell, E., 1997, “A Reduced Order Finite State Aerodynamic Model and Its Application to a Nonlinear Aeroelastic System,” preprint.
35.
Elezgaray, J., Berkooz, G., Dankowicz, H., Holmes, P., and Myers, M., 1997, “Local Models and Large Scale Statistics of the Kuramoto-Sivashinsky Equation,” Wavelets and Multiscale Methods for Partial Differential Equations, W. Dahmen, A. Kurdila, and P. Oswald, eds., Academic Press.
36.
Wickerhauser, M. V., Farge, M., Goirand, E., Wesfreid, E., and Cubillo, E., 1994, “Efficiency Comparison of Wavelet Packet and Adapted Local Cosine Bases for Compression of a Two Dimensional Turbulent Flow,” Wavelets: Theory, Algorithms, and Applications, Chui, C., Montefusco, L., and Puccio, L., eds., Academic Press, pp. 509–532.
37.
Ko
,
J.
,
Kurdila
,
A. J.
,
Gilarranz
,
J. L.
, and
Rediniotis
,
O. K.
,
1998
, “
Particle Image Velocimetry via Wavelet Analysis
,”
AIAA J.
,
36
(
8
), pp.
1451
1459
.
38.
Ko, J., Kurdila, A. J., and Rediniotis, O. K., 1999, “Divergence Free Bases and Multiresolution Methods for Reduced-Order Flow Modeling,” AIAA J., in review.
39.
Gunzburger, M. D., 1989, Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms, Academic Press, Boston, MA.
40.
Temam, R., 1977, Navier-Stokes Equations, North-Holland Publishing Company.
41.
Leove, M., 1945, “Functions Aleatoire de Second Ordre,” Compte Rend. Acad. Sci. (Paris).
42.
Karhunen, K., 1946, “Zur Spektral Theorie Stochasticher Prozesse,” Ann. Acad. Sci. Fennicae, Ser. A1, Math. Phys., 37.
43.
Ball
,
K. S.
,
Sirovich
,
L.
, and
Keefe
,
L. R.
,
1991
, “
Dynamical Eigenfunction Decomposition of Turbulent Channel Flow
,”
Int. J. Numer. Methods Fluids
,
12
, pp.
585
604
.
44.
Berkooz
,
G.
,
Holmes
,
P.
, and
Lumley
,
J. L.
,
1993
, “
The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
,”
Annu. Rev. Fluid Mech.
,
25
, pp.
539
575
.
45.
Greenblatt, D. and Wygnanski, I., 1998, “Dynamic Stall Control By Oscillatory Forcing,” AIAA 98-0676.
46.
Greenblatt, D., Darabi, A., Nishri, B., and Wygnanski, I., 1998, “Separation Control By Periodic Addition of Momentum with Particular Emphasis on Dynamic Stall,” Proceedings Heli Japan 98, Paper T3-4, American Helicopter Society.
47.
Reichert
,
R. S.
,
Hatay
,
F. F.
,
Biringen
,
S.
, and
Huser
,
A.
,
1994
, “
Proper Orthogonal Decomposition Applied to Turbulent Flow in a Square Duct
,”
J. Phys. Fluids
,
6
(
9
), pp.
3086
3092
.
48.
Seifert
,
A.
,
Bachat
,
T.
,
Koss
,
D.
,
Shepshelovich
,
M.
,
Wygnanski
,
I.
,
1993
, “
Oscillatory Blowing: A Tool to Delay Boundary-Layer Separation
,”
AIAA J.
,
31
(
11
), pp.
2052
2060
.
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