DOI QR코드

DOI QR Code

Eigenstructure Assignment Control for Linear Continuous-Time Systems with Probabilistic Uncertainties

확률적 불확실성을 갖는 선형 연속 시간 시스템의 고유구조 지정제어

  • 서영봉 (부산대학교 기계공학부 및 기계기술연구소) ;
  • 최재원 (부산대학교 기계공학부 및 기계기술연구소)
  • Published : 2004.02.01

Abstract

In this paper, an S(stochastic)-eigenvalue and its corresponding S-eigenvector concept for linear continuous-time systems with probabilistic uncertainties are proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the stochastic variable parameters in the dynamic model of a plant. An S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue/-eigenvector concept is also proposed. The proposed control design scheme based on the proposed concept is applied to a longitudinal dynamics of an open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure effects. These results explicitly characterize how S-eigenvalues in the complex plane may impose stability on the system.

Keywords

References

  1. G. P. Liu, and R. J. Patton, Eigenstructure Assignment for Control System Design, John Wiley & Sons, 1998
  2. K. M. Sobel, and E. Y. Shapiro, 'Eigenstructure assignment for design of multimode flight control systems,' IEEE Control Systems Magazine, pp. 9-15, 1985
  3. J. W. Choi, 'A simultaneous assignment methodology of right/left eigenstructures,' IEEE Transactions on Aerospace and Electronic Systems, vol, 34, no. 2, pp. 625-634, 1998 https://doi.org/10.1109/7.670342
  4. J. W. Choi, J. G. Lee, Y. Kim, and T. Kang, 'Design of an effective controller via disturbance accommodating left eigenstructure assignment,' Journal of Guidance, Control, and Dynamics, vol. 18, no. 2, pp. 347-354, 1995 https://doi.org/10.2514/3.21390
  5. S. Garg, 'Robust eigenspace assignment using singular value sensitivities,' Journal of Guidance, Control, and Dynamics, vol. 14, no. 2, pp. 416-424, 1991 https://doi.org/10.2514/3.20654
  6. P. Dorato, 'A historical review of robust control,' IEEE Control Systems Magazine, vol. 7, pp. 44-47, 1987
  7. R. R. Mohler, and W. J. Kolodziej, 'An overview of stochastic bilinear control process,' IEEE Transactions on Systems, Man and Cybernetics, vol. SMC-10, pp. 913-918, 1980
  8. B. D. O. Anderson, and J. B. Moore, Linear Optimal Control, Englewood-Cliffs, NJ: Prentice-Hall, 1971
  9. J. W. Choi, and Y. B. Seo, 'LQR design with eigenstructure assignment capability,' IEEE Transactions on Aerospace and Electronic Systems, vol. 35, no. 2, pp. 700-708, 1999 https://doi.org/10.1109/7.766949
  10. E. Yaz, 'Deterministic and stochastic robustness measures for discrete systems,' IEEE Transactions on Automatic Control, vol. 33, no. 10, pp. 952-955, 1988 https://doi.org/10.1109/9.7253
  11. R. F. Stengel, and L. R Ray, 'Stochastic robustness of linear time-invariant control systems,' IEEE Transactions on Automatic Control, vol. 36, no. 1, pp. 82-87, 1991 https://doi.org/10.1109/9.62270
  12. L. R. Ray, 'Robust linear-optimal control laws for active suspension systems,' Journal of Dynamic Systems, Measurement, and Control, vol. 114, pp. 592-597, 1992 https://doi.org/10.1115/1.2897729
  13. Y. B. Seo, J. W. Choi, and M. H. Lee, 'Eigenstructure assignment for L TI systems with stochastic parameter variations,' Proceedings of the 2000 American Control Conference (ACC'00), Chicago, IL, U.S.A., June 28-30, pp. 3812-3816, 2000 https://doi.org/10.1109/ACC.2000.876935
  14. P. S. Maybeck, Stochastic Models, Estimation, and Control, vol. 1, Mathematics in Science and Engineering, vol. 141, Academic Press, pp. 101-111, 1979
  15. S. B. John, Fundamentals of Linear State Space Systems, WCB/McGraw-Hill, pp. 147-193, 1999
  16. A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, Addison-Wesley Publishing Company, Inc., 1994