Skip to main content
SpringerLink
Log in

Fault Estimation for Nonlinear Dynamic System Based on the Second-Order Sliding Mode Observer

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

Abstract

This paper is concerned with the problem of fault estimation for a class of Lipschitz nonlinear systems. In order to settle the chattering problem caused by traditional sliding mode observer for fault estimation, a second-order sliding mode observer is proposed on the basis of the super-twisting algorithm. Firstly, linear coordinate transformations are introduced to decouple the fault signal from the system. Secondly, the Lyapunov function approach is applied to derive the criteria guaranteeing the stability of the observer error dynamic system. The obtained results eliminate the cumbersome proving process for the stability of the super-twisting algorithm by the geometric method. Thirdly, an estimation of the fault is generated by the proposed second-order sliding mode observer. Furthermore, only the output information of the system and observer is necessary for fault estimation. Finally, a robotic arm system is employed to show the effectiveness of the proposed fault estimation method.

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
Fig. 5

Similar content being viewed by others

References

  1. H. Alwi, C. Edwards, C.P. Tan, Sliding mode estimation schemes for incipient sensor faults. Automatica 45(7), 1679–1685 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. S.P. Bhat, D.S. Bernstein, Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43(5), 678–682 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. S.P. Bhat, D.S. Bernstein, Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Blanke, M. Kinnaert, J. Lunze, M. Staroswiecki, Diagnosis and Fault-Tolerant Control (Springer, Berlin, 2006)

    MATH  Google Scholar 

  5. J. Chen, R.J. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems (Kluwer, Boston, 1999)

    Book  MATH  Google Scholar 

  6. W. Chen, M. Saif, A sliding mode observer-based strategy for fault detection, isolation, and estimation in a class of Lipschitz nonlinear systems. Int. J. Syst. Sci. 38(12), 943–955 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  8. C. Edwards, S.K. Spurgeon, On the development of discontinuous observers. Int. J. Control 59(5), 1211–1229 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  9. C. Edwards, S.K. Spurgeon, R.J. Patton, Sliding mode observers for fault detection and isolation. Automatica 36(4), 541–553 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. P.M. Frank, X. Ding, Survey of robust residual generation and evaluation methods in observer-based fault detection systems. J. Process Control 7(6), 403–424 (1997)

    Article  Google Scholar 

  11. C. Gao, G. Duan, Robust adaptive fault estimation for a class of nonlinear systems subject to multiplicative faults. Circuits Syst. Signal Process. 31(6), 2035–2046 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Gao, Q. Zhao, G. Duan, Robust actuator fault diagnosis scheme for satellite attitude control systems. J. Frankl. Inst. 350(9), 2560–2580 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Z. Gao, D.H.C. Ho, Descriptor observer approaches for multivariable systems with measurement noises and application in fault detection and diagnosis. Syst. Control Lett. 55(4), 304–313 (2006)

    Article  MATH  Google Scholar 

  14. E.A. Garcia, P.M. Frank, Deterministic nonlinear observer-based approaches to fault diagnosis: a survey. Control Eng. Pract. 5(5), 663–670 (1997)

    Article  Google Scholar 

  15. I. Hwang, S. Kim, Y. Kim et al., A survey of fault detection, isolation, and reconfiguration methods. IEEE Trans. Control Syst. Technol. 18(3), 636–653 (2010)

    Article  MathSciNet  Google Scholar 

  16. 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 

  17. D. Lee, Y. Park, Y. Park, H. Robust, Sliding mode descriptor observer for fault and output disturbance estimation of uncertain systems. IEEE Trans. Autom. Control 57(11), 2928–2934 (2012)

    Article  Google Scholar 

  18. A. Levant, Sliding order and sliding accuracy in sliding mode control. Int. J. Control 58(6), 1247–1263 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  19. H.Y. Liu, Z.S. Duan, Actuator fault estimation using direct reconstruction approach for linear multivariable systems. IET Control Theory Appl. 6(1), 141–148 (2012)

    Article  MathSciNet  Google Scholar 

  20. J.A. Moreno, M. Osorio, A Lyapunov approach to second order sliding mode controllers and observers, in Proceedings of the IEEE International Conference on Decision and Control (New York, USA, 2008), pp. 2856–2861

  21. T.G. Park, Estimation strategies for fault isolation of linear systems with disturbances. IET Control Theory Appl. 4(12), 2781–2792 (2010)

    Article  MathSciNet  Google Scholar 

  22. S. Pillosu, A. Pisano, E. Usai, Unknown-input observation techniques for infiltration and water flow estimation in open-channel hydraulic systems. Control Eng. Pract. 20(12), 1374–1384 (2012)

    Article  Google Scholar 

  23. J. Qiu, M. Ren, Y. Niu et al., Fault estimation for nonlinear dynamic systems. Circuits Syst. Signal Process. 31(2), 555–564 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  24. R. Raoufi, H.J. Marquez, A.S.I. Zinober, Sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis. Int. J. Robust Nonlinear Control 20(16), 1785–1801 (2010)

    MathSciNet  MATH  Google Scholar 

  25. Z. Wang, Y. Shen, X. Zhang, Actuator fault estimation for a class of nonlinear descriptor systems. Int. J. Syst. Sci. 45(3), 487–496 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  26. X. Wei, L. Liu, L. Jia, Fault diagnosis for high order systems based on model decomposition. Int. J. Control Autom. Syst. 11(1), 75–83 (2013)

    Article  Google Scholar 

  27. 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 

  28. S.J. Yoo, Actuator fault detection and adaptive accommodation control of flexible-joint robots. IET Control Theory Appl. 6(10), 1497–1507 (2012)

    Article  MathSciNet  Google Scholar 

  29. K. Zhang, M. Staroswiecki, B. Jiang, Static output feedback based fault accommodation design for continuous-time dynamic systems. Int. J. Control 84(2), 412–423 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  30. X. Zhang, L. Tang, J. Decastro, Robust fault diagnosis of aircraft engines: a nonlinear adaptive estimation-based approach. IEEE Trans. Control Syst. Technol. 21(3), 861–868 (2013)

    Article  Google Scholar 

  31. X. Zhao, H. Liu, J. Zhang et al., Multiple-mode observer design for a class of switched linear systems. IEEE Trans. Autom. Sci. Eng. 12(1), 272–280 (2015)

    Article  Google Scholar 

  32. X. Zhao, Z. Yu, X. Yang et al., Estimator design of discrete-time switched positive linear systems with average dwell time. J. Frankl. Inst. 351(1), 579–588 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Control Engineering, Naval Aeronautical and Astronautical University, Yantai, 264001, China

    Zhenggao Hu, Guorong Zhao & Dawang Zhou

  2. Department of Scientific Research, Naval Aeronautical and Astronautical University, Yantai, 264001, China

    Lei Zhang

Authors
  1. Zhenggao Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guorong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dawang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenggao Hu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, Z., Zhao, G., Zhang, L. et al. Fault Estimation for Nonlinear Dynamic System Based on the Second-Order Sliding Mode Observer. Circuits Syst Signal Process 35, 101–115 (2016). https://doi.org/10.1007/s00034-015-0060-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-015-0060-2

Keywords

Search

Navigation