Table of Contents Author Guidelines Submit a Manuscript
Corrigendum

A corrigendum for this article has been published. To view the corrigendum, please click here.

Journal of Control Science and Engineering
Volume 2008 (2008), Article ID 154956, 11 pages
http://dx.doi.org/10.1155/2008/154956
Research Article

Empirical Reduced-Order Modeling for Boundary Feedback Flow Control

1Department of Electrical Engineering and Computer Science, University of Tennessee, 1508 Middle Drive, Knoxville, TN 37996, USA
2Performance Assessment and Decision Analysis Department, Carlsbad Program Group, Sandia National Laboratories, 4100 National Parks Highway MS 1395, Carlsbad, NM 88220, USA
3Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, OH 45433, USA

Received 27 December 2007; Revised 4 November 2008; Accepted 24 December 2008

Academic Editor: Onur Toker

Copyright © 2008 Seddik M. Djouadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. Willcox and J. Peraire, “Balanced model reduction via the proper orthogonal decomposition,” AIAA Journal, vol. 40, no. 11, pp. 2323–2330, 2002. View at Publisher · View at Google Scholar
  2. S. M. Djouadi, R. C. Camphouse, and J. H. Myatt, “Optimal order reduction for the the two-dimensional Burgers' equation,” in Proceedings of the 46th IEEE Conference on Decision and Control (CDC '07), pp. 3507–3512, New Orleans, La, USA, December 2007. View at Publisher · View at Google Scholar
  3. M. Ilak and C. W. Rowley, “Reduced-order modeling of channel flow using traveling POD and balanced POD,” in Proceedings of the 3rd AIAA Flow Control Conference, vol. 2, pp. 1–11, San Francisco, Calif, USA, June 2006.
  4. D. A. Lawrence, “Empirical model reduction for active closed-loop flow control,” Final Report, Faculty Summer Research Opportunity, ARL, State College, Pa, USA, 2004. View at Google Scholar
  5. F. Leibfritx and S. Volkwein, “Numerical feedback controller design for PDE systems using model reduction: techniques and case studies,” in Real-Time PDE-Constrained Optimization, SIAM, Philadelphia, Pa, USA, 2006. View at Google Scholar
  6. C. W. Rowley, T. Colonius, and R. M. Murray, “Model reduction for compressible flows using POD and Galerkin projection,” Physica D, vol. 189, no. 1-2, pp. 115–129, 2004. View at Publisher · View at Google Scholar
  7. M. N. Glauser, M. J. Young, H. Higuchi, C. E. Tinney, and H. Carlson, “POD based experimental flow control on a NACA-4412 airfoil,” in Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit, pp. 4861–4870, Reno, Nev, USA, January 2004, paper no. 2004-0575.
  8. H. A. Carlson, M. Glauser, and R. Roveda, “Models for controlling airfoil lift and drag,” in Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit, pp. 5627–5638, Reno, Nev, USA, January 2004, paper no. 2004-0579.
  9. K. Cohen, S. Siegel, T. McLaughlin, and J. Myatt, “Proper orthogonal decomposition modeling of a controlled Ginzburg-Landau cylinder wake model,” in Proceedings of the 21st International Communications Satellite Systems Conference and Exhibit, Reno, Nev, USA, January 2003, paper no. 2003-2405.
  10. R. C. Camphouse and J. H. Myactt, “Reduced order modelling and boundary feedback control of nonlinear convection,” in Proceedings of the AIAA Guidance, Navigation, and Control Conference, vol. 1, pp. 289–297, San Francisco, Calif, USA, August 2005, paper no. 2005-5844.
  11. R. C. Camphouse, S. M. Djouadi, and J. H. Myatt, “Feedback control for aerodynamics,” in Proceedings of the 45th IEEE Conference on Decision and Control (CDC '06), pp. 1–14, San-Diego, Calif, USA, December 2006.
  12. W. R. Graham, J. Peraire, and K. Y. Tang, “Optimal control of vortex shedding using low-order models—part I: open-loop model development,” International Journal for Numerical Methods in Engineering, vol. 44, no. 7, pp. 945–972, 1999. View at Publisher · View at Google Scholar
  13. H. Banks, R. Del Rosario, and R. Smith, “Reduced order model feedback control design: numerical implantation in a thin shell model,” Tech. Rep. CRSC-TR98-27, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, USA, June 1998. View at Google Scholar
  14. E. Caraballo, M. Samimy, and J. DeBonis, “Low dimensional modeling of flow for closed-loop flow control,” in Proceedings of the AIAA Aerospace Sciences Meeting, Reno, Nev, USA, January 2003, paper no. 2003-0059.
  15. W. J. Rugh, Linear System Theory, Prentice-Hall, Upper Saddle River, NJ, USA, 2nd edition, 1996.
  16. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, Upper Saddle River, NJ, USA, 1996.
  17. K. Zhou and J. C. Doyle, Essentials of Robust Control, Prentice-Hall, Upper Saddle River, NJ, USA, 1998.
  18. A. Defant and K. Floret, Tensor Norms and Operator Ideals, Elsevier Science, Amsterdam, The Netherlands, 1993.
  19. B. C. Moore, “Principal component analysis in linear systems: controllability, observability, and model reduction,” IEEE Transactions on Automatic Control, vol. 26, no. 1, pp. 17–32, 1981. View at Publisher · View at Google Scholar
  20. J. Hahn and T. F. Edgar, “Reduction of nonlinear models using balancing of empirical gramians and Galerkin projections,” in Proceedings of the American Control Conference, vol. 4, pp. 2864–2868, Chicago, Ill, USA, June 2000.
  21. M. Condon and R. Ivanov, “Empirical balanced truncation of nonlinear systems,” Journal of Nonlinear Science, vol. 14, no. 5, pp. 405–414, 2004. View at Publisher · View at Google Scholar
  22. C. A. Antoulas, Approximation of Large-Scale Dynamical Systems, Advances in Design and Control, SIAM, Philadelphia, Pa, USA, 2006.
  23. V. Sreeram, “Frequency response error bounds for time-weighted balanced truncation,” in Proceedings of the 41st IEEE Conference on Decision and Control, vol. 3, pp. 3330–3331, Las Vegas, Nev, USA, December 2002.
  24. T. J. Chung, Computational Fluid Dynamics, Cambridge University Press, Cambridge, UK, 2002.
  25. P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Cambridge, UK, 1996.
  26. J. Juang, Applied System Identification, Prentice-Hall, Upper Saddle River, NJ, USA, 1994.