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

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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ℋ_/ℋ∞ Fault Detection and Isolation for Discrete-Time Delayed Systems

이산시간 상태지연 시스템을 위한 ℋ_/ℋ∞ 고장검출 및 분리

  • Jee, Sung-Chul (School of Electronic Engineering, Inha University) ;
  • Lee, Ho-Jae (School of Electronic Engineering, Inha University)
  • Received : 2011.05.03
  • Accepted : 2011.09.02
  • Published : 2011.10.01
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Abstract

In this paper, an $\mathfrak{H}$_/$\mathfrak{H}_{\infty}$ fault detection and isolation (FDI) observer design problem is investigated for discrete-time delayed systems. To that end, a bank consisting of the sensor's number of observers is introduced. Each residual should be sensitive to a certain partial group of faults, but robust against the disturbance as far as possible. We formulate this multiobjective FDI problem as $\mathfrak{H}$_/$\mathfrak{H}_{\infty}$ observers design problem. Sufficient design condition is expressed as iterative linear matrix inequalities. The fault is then detected and isolated by evaluating the residuals through an FDI decision logic. A computer simulation is provided for verification of the proposed technique.

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References

  1. H. Tianfield and R. Unland, "Towards autonomic computing systems," Engineering Applications of Artificial Intelligence, vol. 17, no. 7, pp. 689-699, 2004. https://doi.org/10.1016/j.engappai.2004.08.029
  2. P. Park, "A delay-dependent stability criterion for systems with uncertain time-invariant delays," IEEE Transactions on Automatic Control, vol. 44, no. 4, pp. 876-877, 1999. https://doi.org/10.1109/9.754838
  3. Y. S. Moon, P. Park, W. H. Kwon, and Y. S. Lee, "Delaydependent robust stabilization of uncertain state-delayed systems," International Journal of Control, vol. 74, no. 14, pp. 1447-1455, 2001. https://doi.org/10.1080/00207170110067116
  4. Y. He, Q.-G. Wang, and C. Lin, "An improved $H_{\infty}$ filter design for systems with time-varying interval delay," IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 53, no. 11, pp. 1235-1239, 2006. https://doi.org/10.1109/TCSII.2006.883209
  5. H. Gao, J. Lam, C. Wang, and Y. Wang, "Delay-dependent output-feedback stabilisation of discrete-time systems with timevarying state delay," IEE Proceedings-Control Theory and Applications, vol. 151, no. 6, pp. 691-698, Nov. 2004. https://doi.org/10.1049/ip-cta:20040822
  6. K. Zhang, B. Jiang, and A. Shumsky, "A new criterion of fault estimation for neutral delay systems using adaptive observer," Acta Automatica Sinica, vol. 35, no. 1, pp. 85-91, 2009. https://doi.org/10.3724/SP.J.1004.2009.00085
  7. L. Bai, Z. Tian, and S. Shi, "Design of $H_{\infty}$ robust fault detection filter for linear uncertain time-delay systems," ISA Trans., vol. 45, no. 4, pp. 491-502, 2006. https://doi.org/10.1016/S0019-0578(07)60227-4
  8. L. Bai, Z. Tian, and S. Shi, "Robust fault detection for a class of nonlinear time-delay systems," Journal of the Franklin Institute, vol. 344, pp. 873-888, 2007. https://doi.org/10.1016/j.jfranklin.2006.11.004
  9. H. Karimi, M. Zapateiro, and N. Luo, "A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations," Journal of the Franklin Institute, vol. 347, no. 6, pp. 957-973, 2010. https://doi.org/10.1016/j.jfranklin.2010.03.004
  10. J. Guo, X. Huang, and Y. Cui, "Design and analysis of robust fault detection filter using LMI tools," Computers & Mathematics with Applications, vol. 57, pp. 1743-1747, 2009. https://doi.org/10.1016/j.camwa.2008.10.032
  11. F. Caliskan and I. Genc, "A robust fault detection and isolation method in load frequency control loops," IEEE Transactions on Power Systems, vol. 23, pp. 1756-1767, 2008. https://doi.org/10.1109/TPWRS.2008.2004831
  12. Z. Wang, B. Huang, and H. Unbehauen, "Robust $H_{\infty}$ observer design of linear time-delay systems with parametric uncertainty," Systems & Control Letters, vol. 42, no. 4, pp. 303-312, 2001. https://doi.org/10.1016/S0167-6911(00)00100-6
  13. D. Huang and S. K. Nguang, "Robust fault estimator design for uncertain networked control systems with random time delays: An ilmi approach," Information Sciences, vol. 180, no. 3, pp. 465-480, 2010. https://doi.org/10.1016/j.ins.2009.10.002
  14. J. Liu, J. L. Wang, and G.-H. Yang, "An LMI approach to minimum sensitivity analysis with application to fault detection," Automatica, vol. 41, no. 11, pp. 1995-2004, 2005. https://doi.org/10.1016/j.automatica.2005.06.005
  15. I. M. Jaimoukha, Z. Li, and V. Papakos, "A matrix factorization solution to the H-/$H_{\infty}$ fault detection problem," Automatica, vol. 42, pp. 1907-1912, 2006. https://doi.org/10.1016/j.automatica.2006.06.002
  16. J. L. Wang, G.-H. Yang, and J. Liu, "An LMI approach to H- index and mixed H-/$H_{\infty}$ fault detection observer design," Automatica, vol. 43, pp. 1656-1665, 2007. https://doi.org/10.1016/j.automatica.2007.02.019
  17. S. C. Jee, H. J. Lee, and Y. H. Joo, "H-/$H_{\infty}$ sensor fault detection observer design for nonlinear systems in Takagi-Sugeno's form," Nonlinear Dynamics, pp. 1-9, 2011.
  18. W. H. Lee, C. G. Park, D. H. Lee, and K. H. Kim, "Improvement of the double fault detection performance of extended parity space approach," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 15, no. 10, pp. 1002-1008, 2009. https://doi.org/10.5302/J.ICROS.2009.15.10.1002
  19. H. J. Lee and D. W. Kim, "H_ fault detection observer design for large scale time-invariant systems," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 15, no. 8, pp. 818-822, 2009. https://doi.org/10.5302/J.ICROS.2009.15.8.818