International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Parametric Approaches for Eigenstructure Assignment in High-order Linear Systems

  • Duan Guang-Ren (Center for Control and Guidance Technology, Harbin Institute of Technology)
  • Published : 2005.09.01
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Abstract

This paper considers eigenstructure assignment in high-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related with a type of so-called high-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically very simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effect of the proposed approaches.

Keywords

References

  1. G. R. Duan, 'Solutions to matrix equation AV+BW=VF and their application to eigenstructure assignment in linear systems,' IEEE Trans. on Automatic Control, vol. 38, no. 2, pp. 276-280, 1993 https://doi.org/10.1109/9.250470
  2. G. R. Duan, 'Solution to matrix equation AV+BW=EVF and eigenstructure assignment for descriptor systems,' Automatica, vol. 28, no. 3, pp. 639-643, 1992 https://doi.org/10.1016/0005-1098(92)90191-H
  3. G. R. Duan, 'Eigenstructure assignment and response analysis in descriptor linear systems with state feedback control,' International Journal of Control, vol. 69, no. 5, pp. 663-694, 1998 https://doi.org/10.1080/002071798222622
  4. G. R. Duan, 'Eigenstructure assignment in descriptor linear systems via output feedback,' International Journal of Control, vol. 72, no. 4, pp. 345-364, 1999 https://doi.org/10.1080/002071799221154
  5. M. J. Balas, 'Trends in large space structurecontrol theory: Fondest hopes, wildest dreams,' IEEE Trans. on Automatic Control, vol. 27, no. 3, pp. 522-535, 1982 https://doi.org/10.1109/TAC.1982.1102953
  6. F. Rincon, Feedback Stabilisation of Secondorder Models, Ph.D. dissertation, Northern Illinois University, De Kalb, Illinois, USA, 1992
  7. B. N. Datta and F. Rincon, 'Feedback stabilization of a second-order system: A nonmodal approach,' Linear Algebra Applications, vol. 188, pp. 138-161, 1993
  8. A. Bhaya and C. Desoer, 'On the design of large flexible space structues (LFSS),' IEEE Trans. on Automatic Control, vol. 30, no. 11, pp. 1118-1120, 1985 https://doi.org/10.1109/TAC.1985.1103847
  9. J. N. Juang, K. B. Lim, and J. L. Junkins, 'Robust eigensystem assignment for flexible structures,' Journal of Guidance, Control and Dynamics, vol. 12, no. 3, pp. 381-387, 1989 https://doi.org/10.2514/3.20419
  10. J. Juang and P. G. Maghami, 'Robust eigensystem assignment for state estimators using second-order models,' Journal of Guidance, Control and Dynamics, vol. 15, no. 4, pp. 920-927, 1992 https://doi.org/10.2514/3.20925
  11. E. K. Chu and B. N. Datta, 'Numerically robust pole assignment for second-order systems,' International Journal of Control, vol. 64, no. 4, pp. 1113-1127, 1996 https://doi.org/10.1080/00207179608921677
  12. D. J. Inman and A. Kress, 'Eigenstructure assignment using inverse eigenvalue methods,' Journal of Guidance, Control and Dynamics, vol. 18, no. 3, pp. 625-627, 1995 https://doi.org/10.2514/3.21433
  13. Y. Kim and H. S. Kim, 'Eigenstructure assignment algorithm for mechanical secondorder systems,' Journal of Guidance, Control and Dynamics, vol. 22, no. 5, pp. 729-731, 1999 https://doi.org/10.2514/2.4444
  14. B. N. Datta, S. Elhay, Y. Ram, and D. Sarkissian, 'Partial eigenstructure assignment for the quadratic matrix pencil,' Journal of Sound and Vibration, vol. 230, pp. 101-110, 2000 https://doi.org/10.1006/jsvi.1999.2620
  15. N. K. Nichols and J. Kautsky, 'Robust eigenstructure assignment in quadratic matrix polynomials,' SIAM J. Matrix Anal. Appl., vol. 23, pp. 77-102, 2001 https://doi.org/10.1137/S0895479899362867
  16. G. R. Duan, and G. P. Liu, 'Complete parametric approach for eigenstructure assignment in a class of second-order linear systems,' Automatica, vol. 38, no. 4, pp. 725- 729, 2002 https://doi.org/10.1016/S0005-1098(01)00251-5
  17. G. R. Duan, 'Two parametric approaches for eigenstructure assignment in second-order linear systems,' Journal of Control Theory and Applications, vol. 1, no. 1, pp. 59-64, 2003 https://doi.org/10.1007/s11768-003-0009-z
  18. G. R. Duan, 'Parametric eigenstructure assignment in second-order descriptor linear systems,' IEEE Trans. on Automatic Control, vol. 49, no. 10, pp. 1789-1795, 2004 https://doi.org/10.1109/TAC.2004.835580
  19. G. R. Duan, 'On the solution to the Sylvester matrix equation AV+BW=EVF,' IEEE Trans. on Automatic Control, vol. 41, no. 4, pp. 612-614, 1996 https://doi.org/10.1109/9.489286
  20. A. Laub and W. F. Arnold, 'Controllability and observability criteria for multivariate linear second-order models,' IEEE Trans. on Automatic Control, vol. 29, pp. 163-165, 1984 https://doi.org/10.1109/TAC.1984.1103470
  21. N. F. Almuthairi and S. Bingulac, 'On coprime factorization and minimal-realization of transferfunction matrices using the pseudoobservability concept,' International Journal of Systems Science, vol. 25, no. 27, pp. 1819-1844, 1994 https://doi.org/10.1080/00207729408949314
  22. T. G. J. Beelen and G. W. Veltkamp, 'Numerical computation of a coprime factorization of a transfer-function matrix,' Systems & Control Letters, vol. 9, no. 4, pp. 281-288, 1987 https://doi.org/10.1016/0167-6911(87)90052-1