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Worst-Case Fault Detection Observer Design: Optimization Approach

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Abstract

This paper deals with the fault detection problem for linear systems with unknown inputs. The H ∞ norm and H − index are employed to measure the robustness to unknown inputs and the sensitivity to faults, respectively. By using the pole assignment approach, the fault detection problem is transformed to an unconstrained optimization problem. With the aid of a gradient-based optimization approach, an explicit formula for designing the desirable observer gain is derived. Furthermore, the fault sensitivity over a finite frequency range can also be solved by the proposed method. The methodology proposed is verified through numerical simulation studies performed on the fault detection observer design of a vertical takeoff and landing aircraft.

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References

  1. Wang, H.B., Wang, J.L., Lam, J.: An optimization approach for worst-case fault detection observer design. In: Proceedings of the 2004 American Control Conference, pp. 2475–2480. American Automatic Control Council, Boston (2004)

    Google Scholar 

  2. Ge, W., Fang, C.Z.: Detection of faulty components via robust observation. Int. J. Control 47, 581–599 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  3. Patton, R.J., Frank, P.M., Clark, R.N.: Fault Diagnosis in Dynamic Systems: Theory and Applications. Prentice-Hall, London (1989)

    Google Scholar 

  4. Ding, X., Frank, P.M.: Fault detection via optimally robust detection filters. In: Proceedings of the 28th IEEE Conference on Decision and Control, vol. 2, pp. 1767–1772. IEEE, Tampa (1989)

    Chapter  Google Scholar 

  5. Ding, X., Jeinsch, T., Frank, P.M., Ding, E.L.: A unified approach to the optimization of fault detection systems. Int. J. Adapt. Control Signal Process. 14, 725–745 (2000)

    Article  MATH  Google Scholar 

  6. Hou, M., Patton, R.J.: An LMI approach to H −/H ∞ fault detection observers. In: Proceedings of the 1996 UKACC International Conference on Control, pp. 305–310. UKACC, Exeter (1996)

    Chapter  Google Scholar 

  7. Wang, H.B., Lam, J.: Robust fault detection for uncertain discrete-time systems. J. Guid. Control Dyn. 25, 291–302 (2002)

    Article  Google Scholar 

  8. Wang, H.B., Lam, J., Ding, X., Zhong, M.: Iterative LMI algorithms for fault detection with unknown inputs. J. Systems Control Eng. 219, 161–172 (2005)

    Google Scholar 

  9. Wang, H.B., Lam, J., Ding, X., Zhong, M.: An LMI approach for fault detection performance enhancement. In: Proceedings of the 2002 International Conference on Control and Automation, pp. 1238–1242. IEEE, Xiamen (2002)

    Google Scholar 

  10. Zhong, M., Ding, X., Lam, J., Wang, H.B.: An LMI approach to design robust fault detection filter for uncertain LTI systems. Automatica 39, 543–550 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Tyler, M.L.: Optimal and robust design of integrated control and diagnostic modules. In: Proceedings of the 1994 American Control Conference, pp. 2060–2064. American Automatic Control Council, Baltimore (1994)

    Chapter  Google Scholar 

  12. Rank, M.L., Niemann, H.: Norm-based design of fault detectors. Int. J. Control 72, 773–783 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. Liu, J., Wang, J.L., Yang, G.H.: Worst-case fault detection observer design: an LMI approach. In: Proceedings of the 2002 International Conference on Control and Automation, pp. 1243–1247. IEEE, Xiamen (2002)

    Google Scholar 

  14. Liu, J., Wang, J.L., Yang, G.H.: An LMI approach to worst-case analysis for fault detection observers. In: Proceedings of the 2003 American Control Conference, pp. 2985–2990. American Automatic Control Council, Denver (2003)

    Google Scholar 

  15. Liu, J., Wang, J.L., Yang, G.H.: An LMI approach to minimum sensitivity analysis with application to fault detection. Automatica 41, 1995–2004 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. Wang, H.B., Wang, J.L., Liu, J., Lam, J.: Iterative LMI approach for robust fault detection observer design. In: Proceedings of the 42th IEEE Conference on Decision and Control, pp. 1974–1979. IEEE, Maui (2003)

    Google Scholar 

  17. Hu, T., Lin, Z., Lam, J.: A unified gradient approach to performance optimization under pole assignment constraint. In: Proceedings of the 2002 International Conference on Control and Automation, pp. 1368–1372. IEEE, Xiamen (2002)

    Google Scholar 

  18. Saif, M., Guan, Y.: A new approach to robust fault detection and identification. IEEE Trans. Aerosp. Electron. Systems 29, 685–695 (1993)

    Article  Google Scholar 

  19. Narendra, K., Tripathi, S.S.: Identification and optimization of aircraft dynamics. J. Aircr. 10, 193–199 (1973)

    Article  Google Scholar 

  20. Xiong, Y., Saif, M.: Robust fault isolation observer design. In: Proceedings of the 1999 American Control Conference, pp. 2077–2081. American Automatic Control Council, San Diego (1999)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Department of Control Engineering, School of Information Science and Engineering, Central South University, Changsha, People’s Republic of China

    H. B. Wang

  2. School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, 678949, Singapore

    J. L. Wang

  3. Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong

    J. Lam

Authors
  1. H. B. Wang
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  2. J. L. Wang
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  3. J. Lam
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Corresponding author

Correspondence to J. L. Wang.

Additional information

Communicated by M.J. Balas

This work was supported in part by DSO National Laboratories under Grant DSOCL-01144, by Nanyang Technological University under Grant RGM 34/01, and by HKU CRCG 10204304. Part of this work was presented in 2004 American Control Conference [1].

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Wang, H.B., Wang, J.L. & Lam, J. Worst-Case Fault Detection Observer Design: Optimization Approach. J Optim Theory Appl 132, 475–491 (2007). https://doi.org/10.1007/s10957-007-9183-3

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