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Circuits, Systems, and Signal Processing

, Volume 35, Issue 1, pp 101–115 | Cite as

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

  • Zhenggao HuEmail author
  • Guorong Zhao
  • Lei Zhang
  • Dawang Zhou
Article

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.

Keywords

Fault estimation Nonlinear dynamic system Super-twisting algorithm Second-order sliding mode observer  Lyapunov function 

References

  1. 1.
    H. Alwi, C. Edwards, C.P. Tan, Sliding mode estimation schemes for incipient sensor faults. Automatica 45(7), 1679–1685 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    S.P. Bhat, D.S. Bernstein, Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    M. Blanke, M. Kinnaert, J. Lunze, M. Staroswiecki, Diagnosis and Fault-Tolerant Control (Springer, Berlin, 2006)zbMATHGoogle Scholar
  5. 5.
    J. Chen, R.J. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems (Kluwer, Boston, 1999)CrossRefzbMATHGoogle Scholar
  6. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    S.X. Ding, Model-Based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools (Springer, Berlin, 2008)Google Scholar
  8. 8.
    C. Edwards, S.K. Spurgeon, On the development of discontinuous observers. Int. J. Control 59(5), 1211–1229 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    C. Edwards, S.K. Spurgeon, R.J. Patton, Sliding mode observers for fault detection and isolation. Automatica 36(4), 541–553 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 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)CrossRefzbMATHGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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)MathSciNetCrossRefGoogle Scholar
  16. 16.
    B. Jiang, M. Staroswiecki, V. Cocquempot, Fault accommodation for nonlinear dynamic systems. IEEE Trans. Autom. Control 51(9), 1578–1583 (2006)MathSciNetCrossRefGoogle Scholar
  17. 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)CrossRefGoogle Scholar
  18. 18.
    A. Levant, Sliding order and sliding accuracy in sliding mode control. Int. J. Control 58(6), 1247–1263 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 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)MathSciNetCrossRefGoogle Scholar
  20. 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. 2856–2861Google Scholar
  21. 21.
    T.G. Park, Estimation strategies for fault isolation of linear systems with disturbances. IET Control Theory Appl. 4(12), 2781–2792 (2010)MathSciNetCrossRefGoogle Scholar
  22. 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)CrossRefGoogle Scholar
  23. 23.
    J. Qiu, M. Ren, Y. Niu et al., Fault estimation for nonlinear dynamic systems. Circuits Syst. Signal Process. 31(2), 555–564 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 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)MathSciNetzbMATHGoogle Scholar
  25. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 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)CrossRefGoogle Scholar
  27. 27.
    X.G. Yan, C. Edwards, Nonlinear robust fault reconstruction and estimation using a sliding mode observer. Automatica 43(9), 1605–1614 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    S.J. Yoo, Actuator fault detection and adaptive accommodation control of flexible-joint robots. IET Control Theory Appl. 6(10), 1497–1507 (2012)MathSciNetCrossRefGoogle Scholar
  29. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 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)CrossRefGoogle Scholar
  31. 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)CrossRefGoogle Scholar
  32. 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)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Zhenggao Hu
    • 1
    Email author
  • Guorong Zhao
    • 1
  • Lei Zhang
    • 2
  • Dawang Zhou
    • 1
  1. 1.Department of Control EngineeringNaval Aeronautical and Astronautical UniversityYantaiChina
  2. 2.Department of Scientific ResearchNaval Aeronautical and Astronautical UniversityYantaiChina

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