Skip to main content
SpringerLink
Log in

Robust Adaptive Fault Estimation for a Class of Nonlinear Systems Subject to Multiplicative Faults

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, a fault estimation problem for a class of nonlinear systems subject to multiplicative faults and unknown disturbances is investigated. Multiplicative faults usually mixed with system states and inputs can cause additional complexity in the design of fault estimator due to parameter changes within process. Especially for the nonlinear system corrupted with unknown disturbances, it is not an easy work to distinguish the real fault factor from the mixed term. Under the nonlinear Lipschitz condition, the proposed robust adaptive fault estimation approach not only estimates the multiplicative faults and system states simultaneously, but also extracts the real effect of the faults. Meanwhile, the effect of disturbances is restricted to an L 2 gain performance criteria which can be formulated into the basic feasibility problem of a linear matrix inequality (LMI). In order to reduce the conservatism of the proposed method, a relaxing Lipschitz matrix is introduced. Finally, an illustrative example is applied to verify the efficiency of the proposed robust adaptive estimation scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. M. Blanke, M. Kinnaert, J. Lunze, M. Staroswiecki, Fault Diagnosis and Fault-Tolerant Control, 2nd edn. (Springer, Berlin, 2006)

    MATH  Google Scholar 

  2. J.D. Boskovic, S.E. Bergstrom, R.K. Mehra, Robust integrated flight control design under failures, damage, and state-dependent disturbances. J. Guid. Control Dyn. 28(5), 902–917 (2005)

    Article  Google Scholar 

  3. J. Chen, R.J. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems. (Kluwer Academic, Norwell, 1999)

    Book  MATH  Google Scholar 

  4. S.X. Ding, Model-Based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools (Springer, Berlin, 2008)

    Google Scholar 

  5. G.R. Duan, R.J. Patton, Robust fault detection using Luenberger-type unknown input observers—a parametric approach. Int. J. Syst. Sci. 32(4), 533–540 (2001)

    MathSciNet  MATH  Google Scholar 

  6. S.X. Ding, P.M. Frank, E.L. Ding, An approach to the detection of multiplicative faults in uncertain dynamic systems, in Proceedings of the 41st IEEE Conference on Decision and Control (2003), pp. 4371–4376

    Google Scholar 

  7. P.M. Frank, Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy—a survey and some new results. Automatica 26(3), 459–474 (1990)

    Article  MATH  Google Scholar 

  8. Z. Gao, S.X. Ding, Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems. Automatica 43(5), 912–920 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Hou, Estimation of sinusoidal frequencies and amplitudes using adaptive identifier and observer. IEEE Trans. Autom. Control 52(3), 493–499 (2007)

    Article  Google Scholar 

  10. R. Isermann, Model-based fault-detection and diagnosis-status and applications. Annu. Rev. Control 29(1), 71–85 (2005)

    Article  Google Scholar 

  11. R. Isermann, Fault-Diagnosis Systems (Springer, Berlin, 2006)

    Google Scholar 

  12. P.A. Ioannou, J. Sun, Robust Adaptive Control (Prentice Hall, Englewood Cliffs, 1996)

    MATH  Google Scholar 

  13. B. Jiang, M. Staroswiecki, V. Cocquempot, Fault diagnosis based on adaptive observer for a class of non-linear systems with unknown parameters. Int. J. Control 77(4), 367–383 (2004)

    Article  MathSciNet  Google Scholar 

  14. B. Jiang, M. Staroswiecki, V. Cocquempot, Fault accommodation for nonlinear dynamic systems. IEEE Trans. Autom. Control 51(9), 1578–1583 (2006)

    Article  MathSciNet  Google Scholar 

  15. C.D. Persis, A. Isidori, A geometric approach to nonlinear fault detection and isolation. IEEE Trans. Autom. Control 46(6), 853–865 (2001)

    Article  MATH  Google Scholar 

  16. G. Phanomchoeng, R. Rajamani, Observer design for Lipschitz nonlinear systems using Riccati equations, in American Control Conference (2010), pp. 6060–6065

    Google Scholar 

  17. C.P. Tan, C. Edwards, Multiplicative fault reconstruction using sliding mode observers, in 5th Asian Control Conference (2004), pp. 957–962

    Google Scholar 

  18. K. Vijayaraghavan, R. Rajamani, J. Bokor, Quantitative fault estimation for a class of non-linear systems. Int. J. Control 80(1), 64–74 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. A. Xu, Q. Zhang, Nonlinear system fault diagnosis based on adaptive estimation. Automatica 40(7), 1181–1193 (1994)

    Article  Google Scholar 

  20. X.G. Yan, C. Edwards, Nonlinear robust fault reconstruction and estimation using a sliding mode observer. Automatica 43(9), 1605–1614 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Y. Zhang, J. Jiang, Bibliographical review on reconfigurable fault-tolerant control systems. Annu. Rev. Control 32(2), 229–252 (2008)

    Article  Google Scholar 

  22. X. Zhang, M.M. Polycarpou, T. Parisini, Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation. Automatica 46(2), 290–299 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China

    Chunyan Gao & Guangren Duan

Authors
  1. Chunyan Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guangren Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunyan Gao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, C., Duan, G. Robust Adaptive Fault Estimation for a Class of Nonlinear Systems Subject to Multiplicative Faults. Circuits Syst Signal Process 31, 2035–2046 (2012). https://doi.org/10.1007/s00034-012-9434-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-012-9434-x

Keywords

Search

Navigation