Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Direction Assignment of Left Eigenvector in Linear MIMO System

선형 다변수 입출력 시스템에서 좌 고유벡터의 방향 지정

  • Published : 2008.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we propose novel eigenstructure assignment method in full-state feedback for linear time-invariant MIMO system such that directions of some left eigenvectors are exactly assigned to the desired directions. It is required to consider the direction of left eigenvector in designing eigenstructure of closed-loop system, because the direction of left eigenvector has influence over excitation by associated input variables in time-domain response. Exact direction of a left eigenvector can be achieved by assigning proper right eigenvector set satisfying the conditions of the presented theorem based on Moore's theorem and the orthogonality of left and right eigenvector. The right eigenvector should reside in the subspace given by the desired eigenvalue, which restrict a number of designable left eigenvector. For the two cases in which desired eigenvalues are all real and contain complex number, design freedom of designable left eigenvector are given.

Keywords

References

  1. W. M. Wonham, "On pole assignment in multi-input controllable linear systems," IEEE Trans. on Automat. Contr., 12, 6, 1967
  2. B. C. Moore, "On the flexibility offered by state feedback in multivariable systems beyond closed loop eigenvalue assignment," IEEE Trans. Automat. Contr., 21, 689-692, 1976 https://doi.org/10.1109/TAC.1976.1101355
  3. K. M. Sobel, E. Y. Shapiro, and A. N. Andry, "Eigenstructure assignment," Int. J. Contr., 59, 1, 13-37, 1994 https://doi.org/10.1080/00207179408923068
  4. J. Kautsky, N. K. Nichols, and P. Van Dooren, "Robust pole assignment in linear state feedback," Int. J. Contr., 41, 5, 1129- 1155, 1985 https://doi.org/10.1080/0020718508961188
  5. J. W. Choi, "A simultaneous assignment methodology of right/left eigenstructures," IEEE Trans. On Aerospace and Electronic systems, 34, 2, 625-634, 1998 https://doi.org/10.1109/7.670342
  6. J. W. Choi, J. G. Lee, and Y. Kim, "Design of an effective controller via disturbance accommodating left eigenstructure assignment," J. of Guidance Control and Dynamics, 18, 2, 347- 354, 1995 https://doi.org/10.2514/3.21390
  7. G. Duan, "Eigenstructure assignment in descriptor systems via output feedback: a new complete parametric approach," Int. J. Contr., 72, 4, 345-364, 1999 https://doi.org/10.1080/002071799221154
  8. G. Duan, "On the solution to the Sylvester matrix equation AV+BW=EVF," IEEE. Trans. on Automat. Contr., 41, 4, 612- 614, 1996 https://doi.org/10.1109/9.489286
  9. S. P. Burrows and R. J. Patton, "Design of a low-sensitivity, minimum norm and structurally constrained control law using eigenstructure assignment," Optimal Contr. App. Methods, 12, 131-140, 1991 https://doi.org/10.1002/oca.4660120302
  10. J. E. Ensor, "Analysis on eigenmode sensitivity to structured uncertainty," Prec. of the American Contr. Conf., 2002
  11. Q, Zhang, G. L. Slater, and R. J. Allemang, "Suppression of undesired inputs of linear systems by eigenspace assignment," J. Guidance Control and Dynamics, 13, 3, 1990
  12. G. P. Liu and R. J. Patton, Eigenstructure Assignment for Control System Design, John Wiley & Sons, 1998