Fault diagnosis for high order systems based on model decomposition

Regular Paper Control Applications


Fault detection observer and fault estimation filter are the main tools for the model based fault diagnosis approach. The dimension of the observer gain normally depends on the system order and the system output dimension. The fault estimation filter traditionally has the same order as the monitored system. For high order systems, these methods have the potential problems such as parameter optimization and the real time implementation on-board for applications. In this paper, the system dynamical model is first decomposed into two subsystems. The first subsystem has a low order which is the same as the fault dimension. The other subsystem is not affected by the fault directly. With the new model structure, a fault detection approach is proposed where only the residual of the first subsystem is designed to be sensitive to the faults. The residual of the second subsystem is totally decoupled from the faults. Moreover, a lower order fault estimation filter (with the same dimension of the fault) design algorithm is investigated. In addition, the design of a static fault estimation matrix is presented for further improving the fault estimation precision. The effectiveness of the proposed method is demonstrated by a simulation example.


Fault diagnosis filter high order model decomposition observer 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Chen and R. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, London, Great Britain, 1999.MATHCrossRefGoogle Scholar
  2. [2]
    B. Jiang, J. Wang, and Y. C. Soh, “Robust fault diagnosis for a class of linear systems with uncertainty,” Proc. of the American Control Conference, Taipei, Taiwan, pp. 1900–1904, 1999.Google Scholar
  3. [3]
    X. Zhang, M. M. Polycarpou, and T. Parisini, “A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems,” IEEE Trans. on Automatic and Control, vol. 47, no. 4, pp. 576–593, 2002.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    M. Y. Zhong, S. X. Ding, J. Lam, and H. Wang, “An LMI approach to design robust fault detection filter for uncertain LTI system,” Automatica, vol. 39, no. 3, pp. 543–550, 2003.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    B. Jiang, M. Staroswiechi, and V. Cocquempot, “Fault diagnosis based on adaptive observer for a class of nonlinear systems with unknown parameters,” International Journal of Control, vol. 77, no. 4, pp. 415–426, 2004.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    B. Jiang and F. N. Chowdhury, “Fault estimation and accommodation for linear MIMO discrete-time systems,” IEEE Trans. on Control System Technology, vol. 13, no. 3, pp. 493–499, 2005.CrossRefGoogle Scholar
  7. [7]
    X. Zhang, T. Parisini, and M. M. Polycarpou, “Sensor bias fault isolation in a class of nonlinear systems,” IEEE Trans. on Automatic and Control, vol. 50, no. 3, pp. 370–376, 2005.MathSciNetCrossRefGoogle Scholar
  8. [8]
    J. L. Wang, G. H. Yang, and J. Liu, “An LMI approach H_ index and mixed H_/H fault detection observer,” Automatica, vol. 43, no. 9, pp. 1656–1665, 2007.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    S. X. Ding, Model-Based Fault Diagnosis Tehniques-Design Schemes, Algorithms and Tools, Springer-Verlag, Berlin Heidelberg, 2008.Google Scholar
  10. [10]
    X. Wei and M. Verhaegen, “Robust fault detection observer design for linear uncertain systems,” International Journal of Control, vol. 84, no. 1, pp. 197–215, 2011.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    X. Wei and M. Verhaegen, “LMI solutions to the mixed H_/H infinity fault detection observer design for linear parameter varying systems,” International Journal of Adaptive Control and Signal Processing, vol. 25, no. 5, pp. 114–136, 2011.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    X. Zhang, “Sensor bias fault detection and isolation in a class of nonlinear uncertain systems using adaptive estimation,” IEEE Trans. on Automatic and Control, vol. 56, no. 5, pp. 1220–1226, 2011.CrossRefGoogle Scholar
  13. [13]
    N. Liu and K. Zhou, “Optimal robust fault detection for linear discrete time-systems,” Journal of Control Science and Engineering, vol. 2008, pp. 1–16, 2008.MATHCrossRefGoogle Scholar
  14. [14]
    H. Wang and G.-H. Yang, “Fault detection observer design in low frequency domain,” Proc. of the 16th IEEE International Conference on Control Application, pp. 976–981, 2007.Google Scholar
  15. [15]
    M. Corless and J. Tu, “State and input estimation for a class of uncertain system,” Automatica, vol. 34, no. 6, pp. 757–764, 1998.MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    C. Edwards and S. K. Spurgeon, Sliding Mode Control-Theory and Applications, Taylor and Francis, London, UK, 1998.Google Scholar
  17. [17]
    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.MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    T. Iwasaki and S. Hara, “Dynamic output feedback synthesis with general frequency domain specification,” Proc. of IFAC World Congress, Prague, Czech Republic, 2005.Google Scholar
  19. [19]
    T. Iwasaki and S. Hara, “Robust control synthesis with general frequency domain specifications: static gain feedback case,” Proc. of American Control Conference, Massachusetts, USA, pp. 4613–4618, 2004.Google Scholar
  20. [20]
    R. E. Skelton, T. Iwasaki, and K. M. Grigoriadis, A Unified Algebraic Approach to Linear Control Design, Taylor and Francis, London, UK, 1998.Google Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Xiukun Wei and Limin Jia are with State Key Laboratory of Rail Traffic Control and SafetyBeijing Jiaotong UniversityBeijingChina
  2. 2.Institute of AutomationBeijing Information Science and Technology UniversityBeijingChina

Personalised recommendations