Frequency Domain Properties of EALQR with Indefinite Weighting Matrix

  • Seo, Young-Bong (School of Mechanical Engineering and Research Institute of Mechanical Technology Pusan National University) ;
  • Park, Jae-Weon (School of Mechanical Engineering and Research Institute of Mechanical Technology Pusan National University)
  • 발행 : 2003.03.01

초록

EALQR (Linear Quadratic Regulate. design with Eigenstructure Assignment capability) has the capability of exact assignment of eigenstructure with the guaranteed margins of the LQR for MIMO (Multi-Input Multi-Output) systems. However, EALQR undergoes a restriction on the state-weighting matrix Q in LQR to be indefinite with respect to the region of allowable closedloop eigenvalues. The definiteness of the weighting matrix is closely related to the robustness property of a given system. In this paper, we derive a relation between the indefinite weighting matrix Q and the robustness property for EALQR. The modified frequency domain inequality, that could be guaranteed by EQLQR with an indefinite weighting matrix, is presented.

키워드

참고문헌

  1. Al-Sumi, F. M. and Stevens, B. L., 1992, 'Negative State Weighting in the Linear Quadratic Regulator for Aircraft Control,' Journal of Guidance, Control, and Dynamics, Vol. 15, No. 5, pp. 1279-1281 https://doi.org/10.2514/3.20980
  2. Broussaord, J. R., 1982, 'A Quadratic Weight Selection Algorithm,' IEEE Transactions on Automatic Control, Vol. 27, pp. 945-947 https://doi.org/10.1109/TAC.1982.1103046
  3. Choi, J. W., Lee, J. G., Kim, Y. and Kang, T., 1995, 'Design of an Effective Controller via Disturbance Accommodating Left Eigenstructure Assignment,' Journal of Guidance, Control, and Dynamics, Vol. 18, No. 2, pp. 347-354 https://doi.org/10.2514/3.21390
  4. Choi, J. W., 1998, 'A Simultaneous Assignment Methodology of Right/Left Eigenstructures,' IEEE Transactions on Aerospace and Electronic Systems, Vol. 34, No. 2, pp. 625-634 https://doi.org/10.1109/7.670342
  5. Choi, J. W. and Seo, Y. B., 1999, 'LQR Design with Eigenstructure Assignment Capability,' IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 2, pp. 700-708 https://doi.org/10.1109/7.766949
  6. Dorato, P., Abdallah, C. and Cerone, V., 1995, Linear-Quadratic Control, Prentice Hall, Englewood Cliffs
  7. Fujii, T., 1987, 'A New Approach to the LQ Design from the Viewpoint of the Inverse Regulator Problem,' IEEE Transactions on Automatic Control, Vol. 32, No. 11, pp. 995-1003 https://doi.org/10.1109/TAC.1987.1104479
  8. Harvey, C. A. and Stein, G., 1978, 'Quadratic Weights for Asymptotic Regulator Properties,' IEEE Transactions on Automatic Control, Vol. 23, No. 3, pp. 378-387 https://doi.org/10.1109/TAC.1978.1101741
  9. Hiroe, T., Morimoto, T., Inoue, S. I. and Takamatsu, H., 1993, 'A New Method for Selecting Weighting Matrices of LQ Regulators and Its Application to an Industrial Turbine,' Proceedings of the 32nd Conference on Decision and Control, San Antonio, Texas, U.S.A., pp. 3333-3334 https://doi.org/10.1109/CDC.1993.325827
  10. Horn, R. A. and Johnson, C. R., 1985, Matrix Analysis, Cambridge University Press, pp. 423-424
  11. Innocenti, M. and Stanziola, C., 1990, 'Performance-Robustness Trade Off of Eigenstructure Assignment Applied to Rotorcraft,' Aeronautical Journal, Vol. 94, No. 934, pp. 124-131
  12. Kenji, S., 1998, 'Partial Pole Placement by LQ Regulators : An Inverse Problem Approach,' IEEE Transactions on Automatic Control, Vol. 43, No. 5, pp. 706-708 https://doi.org/10.1109/9.668841
  13. Luo, J. and Lan, C. E., 1995, ' Determination of Weighting Matrices of a Linear Quadratic Regulator,' Journal of Guidance, Control and Dynamics, Vol. 18, No. 6, pp. 1462-1463 https://doi.org/10.2514/3.21569
  14. Molinari, B. P., 1981, 'The Stable Regulator Problem and Its Inverse,' IEEE Transactions on Automatic Control, Vol. 26, No. 1, pp. 4-16 https://doi.org/10.1109/TAC.1973.1100364
  15. Ochi, Y. and Kanai, K., 1993, 'A New Way of Pole Placement in LQR and Its Application to Flight Control,' Proceedings of the AIAA Guidance, Navigation, and Control Conference, Monterey, CA, U,S,A, pp. 1295-1301
  16. Ohta, H., Kakinuma, M. and Nikiforuk, P. N., 1991, 'Use of Negative Weights in Linear Quadratic Regulator Synthesis,' Use of Negative Weights in Linear Quadratic Regulator Synthesis, Vol. 14, No. 4, pp. 791-796 https://doi.org/10.2514/3.20714
  17. Siouris, G. M., Lee, J. G. and Choi, J. W., 1995, 'Design Modern Pitch Pointing Control System,' IEEE Transactions on Aerospace and Electronic Systems, Vol. 31, No. 2, pp. 730-738 https://doi.org/10.1109/7.381920
  18. Siouris, G. M., 1996, An Engineering Approach to Optimal Control and Estimation Theory, John Wiley & Sons, Inc., New York
  19. Wilson, R. F. and Cloutier, J. R., 1990, 'Optimal Eigenstructure Achievement with Robustness Guarantees,' Proceedings of the 1990 American Control Conference, San Diego, U.S.A., pp. 952-957
  20. Proceedings of the 1990 American Control Conference Optimal Eigenstructure Achievement with Robustness Guarantees Wilson, R. F.;Cloutier, J. R.