Robust Observer Design for Multi-Output Systems Using Eigenstructure Assignment

고유구조 지정을 이용한 다중출력 시스템의 강인한 관측기 설계

  • 허건수 (한양대학교 기계공학부) ;
  • 남준철 (한양대학교 정밀기계공학과 대학원)
  • Published : 2004.11.01


This paper proposes a design methodology for the robust observer using the eigenstructure assignment in multi-output systems so that the observer is less sensitive to the ill-conditioning factors such as unknown initial estimation error, modeling error and measurement bias in transient and steady-state observer performance. The robustness of the observer can be achieved by selecting the desired eigenvector matrix to have a small condition number that guarantees the small upper bound of the estimation error. So the left singular vectors of the unitary matrix spanned by space of the achievable eigenvectors are selected as a desired eigenvectors. Also, this paper proposes how to select the desired eigenvector based on the measure of observability and designs the observer with small gain. An example of a spindle drive system is simulated to validate the robustness to the ill-conditioning factors in the observer performance.


Robust Observer;Condition Number;Eigenstructure;Sylvester Equation;Measure of observability


  1. Bhattacharyya, S. P., 1976, 'The Structure of Robust Observers,' IEEE Trans. on Automatic Control, Vol. 21, pp. 581-588
  2. Shen, L. C. and Hsu, P. L., 1998, 'Robust Design of Fault Isolation Observers,' Automatica, Vol. 34, No. 11, pp. 1421-1429
  3. Shafai, B. and Carrol, R. L., 1985, 'Design of Proportional-Integral Observer for Linear Time-Varying Multivariable Systems,' Proc. of the IEEE Conference on Decision and Control, pp. 597-599
  4. Huh, K. and Stein, J. L., 1994, 'A Quantitative Performance Index for Observer-Based Monitoring Systems,' ASME J. of Dynamic Systems, Measurement, and Control, Vol. 116, pp. 487-497
  5. Huh, K. and Stein, J. L., 1995, 'Well-Conditioned Observer Design for Observer-Based Monitoring Systems,' ASME J. of Dynamic Systems, Measurement, and Control, Vol. 117, pp. 592-599
  6. Liu, G. P. and Patton, R. J., 1998, Eigenstructure Assignment for Control System Design, John Wiley & Sons
  7. Choi, J. W. and Seo, Y. B., 2000, 'A Survey on Eigenstucture Assignment,' J. of Control, Automation and Systems Engineering, Vol. 6, No. 10, pp. 854-870
  8. Andry, A. N. Jr., Shapiro, E. Y. and Chung, J. C., 1983, 'Eigenstructure Assignment for Linear Systems,' IEEE Trans. on Aerospace and Electronic Systems, Vol. 19, No.5, pp. 711-729
  9. Kautsky, J., Nichols, N. K. and Van Dooren, P., 1985, 'Robust Pole Assignment in Linear State Feedback,' Int. J. of Control, Vol. 41, No.5, pp, 1129-1155
  10. Mudge, S. K. and Patton, R. J., 1988, 'An Analysis of the Technique of Robust Eigenstructure Assignment with Application to Aircraft Control,' IEE Proc. D, Vol. 135, pp. 275-281
  11. Wilson, R. F., Cloutier, J. R. and Yedavalli, R. K., 1992, 'Control Design for Robust Eigenstructure Assignment in Linear Uncertain Systems,' IEEE Control Systems Magazine, Vol. 12, No.5, pp. 29-34
  12. Choi, J. W., Lee, J. G., Kim, Y. and Kang, T., 1995, 'Design for an Effective Controller via Disturbance Accommodating Left Eigenstructure Assignment,' J. of Guidance, Control, and Dynamics, Vol. 18, No.2, pp.347-354
  13. Rew, D. W., Junkins, J. L. and Juang, J. N., 1989, 'Robust Eigenstructure Assignment by a Projection Method: Applications Using Multiple Optimization Criteria,' J. of Guidance, Control and Dynamics, Vol. 12, No.3, pp. 396-403
  14. Junkins, J. L. and Kim, Y., 1993, Introduction to Dynamics and Control of Flexible Structures, AIAA Education Series
  15. Hamdan, A.M.A. and Nayfeh, A.H., 1989, 'Measures of Modal Controllability and Observability for First- and Second-Order Linear Systems,' J. of Guidance, Control, and Dynamics, Vol. 12, No.3, pp. 421-428
  16. Golub, G. H. and Van Loan, C. F., 1996, Matrix Computation, The Johns Hopkins University Press