# 입력관측기의 정량적 성능지표 (II) -정상상태 해석-

• 정종철 (한양대학교 대학원 정밀기계공학과) ;
• 이범석 (삼성테크원㈜) ;
• 허건수 (한양대학교 기계공학부)
• Published : 2002.10.01
• 43 4

#### Abstract

The closed-loop state and input observer is a pole-placement type observer and estimates unknown state and input variables simultaneously. Pole-placement type observers may have poor performances with respect to modeling error and sensing bias error. The effects of these ill-conditioning factors must be minimized for the robust performance in designing observers. In this paper, the steady-state performance of the closed-loop state and input observer is investigated quantitatively and is represented as the estimation error bounds. The performance indices are selected from these error bounds and are related to the robustness with respect to modeling errors and sensing bias. By considering both transient and steady-state performance, the main performance index is determined as the condition number of the eigenvector matrix based on $L_2$-norm.

#### Keywords

CSIO(Closed-loop State and Input Observer);Condition Number;Performance Index;Robustness;Steady-State;Norm

#### References

1. Golub, G. H. and Van Loan, C. F., 1989, Matrix Computations, 2nd Ed., The Johns Hopkins Univ. Press
2. Patton, R. J. and Chen, J., 1997, 'Observer-Based fault Detection and Isolation:Robustness and Applications,' Control Engineering Practice, Vol. 5, No.5, pp.671-682 https://doi.org/10.1016/S0967-0661(97)00049-X
3. 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 https://doi.org/10.1115/1.2899243
4. Fattouh, A., Sename, O. and Dion, J., 2000, 'A LMI Approach to Robust Observer Design for Linear Timedelay Systems,' Proc. of the 39th IEEE Conference on Decision and Control, pp. 1495-1500 https://doi.org/10.1109/CDC.2000.912070
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 https://doi.org/10.1115/1.2801119
6. Luenberger, D. G., 1966, 'Observers for Multivariable systems,' IEEE Trans. Autom. Control, Vol. 11, pp. 190-197 https://doi.org/10.1109/TAC.1966.1098323
7. Jung, J., Lee, B. and Huh, K., 2002, 'A Quantitative Performance Index for an Input Observer (I), -Analysis in Transient State,' Trans. of the KSME, A. Vol. 26, No. 10,pp.2060-2066
8. Park, Y. and Stein, J. L., 1988, 'Closed-Loop, State and Input Observer for Systems with Unknown Inputs,' Int. J. of Control, Vol. 48, No.3, pp. 1121-1136 https://doi.org/10.1080/00207178808906239
9. Corless, M. and Tu, J., 1998, 'State and Input Estimation for a Class of Uncertain Systems,' Automatica, Vol. 34, No.6, pp. 757-764 https://doi.org/10.1016/S0005-1098(98)00013-2
10. Xiong, Y. and Saif, M., 2000, 'Output Derivative Free Design of Unknown Input Plus State Functional Observer,' Proc. of the American Control Conference, pp.399-403 https://doi.org/10.1109/ACC.2000.878929
11. Battacharyya, S. P., 1976, 'The Structure of Robust Observers,' IEEE Transactions on Automatic Control, Vol. 21, pp. 581-588 https://doi.org/10.1109/TAC.1976.1101274
12. Junkins, L. J and Kim, Y., 1993, Introduction to Dynamics and Control of Flexible Structures, AIAA Education Series
13. Liu, G. P. and Patton, R. J., 1998, Eigenstructure Assignment for Control System Design, John Wiley & Sons Ltd
14. Seo, Y. B., Choi, J. W. and Lee, M. H., 2000, 'Eigenstructure Assignment for LTI Systems with Stochastic Parameter Variations,' Proc. of the American Control Conference, pp. 3812-3816 https://doi.org/10.1109/ACC.2000.876935