Skip to main content
SpringerLink
Log in

A sliding mode observer for robust fault reconstruction in a class of nonlinear non-infinitely observable descriptor systems

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper presents a sliding mode observer (SMO) for robustly reconstructing faults affecting a class of nonlinear non-infinitely observable descriptor systems. Preliminary transformations are utilised to re-express the system such that the design freedom in its structure is easier to exploit. An infinitely observable system is formed by treating some states as unknown inputs. The faults are then reconstructed from measurable inputs and outputs using a SMO. The structure of the SMO bounds the nonlinear components of its estimation errors. The effect of disturbances on the fault reconstruction is minimised using linear matrix inequality techniques. A summarised design procedure for the SMO scheme is presented. Finally, a simulated example is carried out to showcase the efficacy of the 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. Zhang, J., Swain, A.K., Nguang, S.K.: Robust sliding mode observer based fault estimation for certain class of uncertain nonlinear systems. Asian J. Control. 17(4), 1296–1309 (2015)

    Article  MathSciNet  Google Scholar 

  2. Hou, Q., Ding, S., Yu, X.: Composite super-twisting sliding mode control design for PMSM speed regulation problem based on a novel disturbance observer, IEEE Trans. Energy Convers. In press (2020)

  3. Bessaoudi, T., Hmida, F.B., Hsieh, C.S.: Robust state and fault estimation for linear descriptor and nonlinear stochastic systems with disturbances. In: Boubaker, O., Zhu, Q., Mahmoud, M., Ragot, J., Karimi, H.R., Dávila, J. (eds.) New Trends in Observer-Based Control, pp. 357–405. Academic Press, Cambridge (2019)

    Chapter  Google Scholar 

  4. Sassi, A., Ali, H.S., Zasadzinski, M., Abderrahim, K.: Adaptive observer design for a class of descriptor nonlinear systems. Eur. J. Control. 44, 90–102 (2018)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. Wang, H., Han, Z., Zhang, W., Xie, Q.: Chaotic synchronization and secure communication based on descriptor observer. Nonlinear Dyn. 57, 69–73 (2009)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. Chan, J.C.L., Tan, C.P., Trinh, H.: Robust fault reconstruction for a class of infinitely unobservable descriptor systems. Int. J. Syst. Sci. 48(8), 1646–1655 (2017)

    Article  MathSciNet  Google Scholar 

  9. Zhirabok, A.N., Shumsky, A.E., Zuev, A.V.: Fault diagnosis in linear systems via sliding mode observers, Int. J. Control. In press (2019)

  10. Sun, Y., Ma, S.: Observer-based finite-time stabilization for discrete-time switched singular systems with quadratically inner-bounded nonlinearities. Int J. Robust Nonlinear Control. 29(6), 2041–2062 (2019)

    Article  MathSciNet  Google Scholar 

  11. Zhao, Y., Yang, J., Guanghui, W.: \(H_{\infty }\) control for uncertain switched nonlinear singular systems with time delay. Nonlinear Dyn. 74, 649–665 (2013)

    Article  MathSciNet  Google Scholar 

  12. Chan, J.C.L., Tan, C.P., Trinh, H., Kamal, M.A.S.: State and fault estimation for a class of non-infinitely observable descriptor systems using two sliding mode observers in cascade. J. Franklin Institut. 356(5), 3010–3029 (2019)

    Article  MathSciNet  Google Scholar 

  13. Duan, G.R.: Analysis and Design of Descriptor Linear Systems. Springer, New York (2010)

    Book  Google Scholar 

  14. Fahmy, M.M., O’Reilly, J.: Observers for descriptor systems. Int. J. Control. 49(6), 2013–2028 (1989)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  16. Yeu, T.K., Kim, H.S., Kawaji, S.: Fault detection, isolation and reconstruction for descriptor systems. Asian J. Control. 7(4), 356–367 (2005)

    Article  MathSciNet  Google Scholar 

  17. Hamaz, A., Draa, K.C., Bedouhene, F., Zemouche, A., Rajamani, R.: Observer design of descriptor nonlinear system with nonlinear outputs by using \({\cal{W}}^{1,2}\)-optimality criterion. J. Franklin Institut. 356(6), 3531–3553 (2019)

    Article  Google Scholar 

  18. Nguyen, C.M., Trinh, H., Nam, P.T.: Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities. IMA J. Math. Control Inf. 34(3), 919–935 (2016)

    MathSciNet  MATH  Google Scholar 

  19. Yang, C., Zhang, Q., Zhou, L.: Stability Analysis and Design for Nonlinear Singular Systems. Springer, Berlin (2012)

    Google Scholar 

  20. Zheng, G., Boutat, D., Wang, H.: A nonlinear Luenberger-like observer for nonlinear singular systems. Automatica. 86, 11–17 (2017)

    Article  MathSciNet  Google Scholar 

  21. Yu, J., Liu, Z.: Fault reconstruction based on sliding mode observer for linear descriptor systems. In: Asian Control Conference, pp. 1132–1137 (2009)

  22. Li, J., Wang, Z., Shen, Y., Rodrigues, M.: Zonotopic fault detection observer for linear parameter-varying descriptor systems. Int J. Robust Nonlinear Control. 29(11), 3426–3445 (2019)

    Article  MathSciNet  Google Scholar 

  23. Bejarano, F.J., Floquet, T., Perruquetti, W., Zheng, G.: Observability and detectability of singular linear systems with unknown inputs. Automatica. 49(3), 793–800 (2013)

    Article  MathSciNet  Google Scholar 

  24. Bejarano, F.J.: Functional unknown input reconstruction of descriptor systems: application to fault detection. Automatica. 57, 145–151 (2015)

    Article  MathSciNet  Google Scholar 

  25. Chan, J.C.L., Tan, C.P., Trinh, H., Kamal, M.A.S., Chiew, Y.S.: Robust fault reconstruction for a class of non-infinitely observable descriptor systems using two sliding mode observers in cascade. Appl. Math. Comput. 350, 78–92 (2019)

    MathSciNet  MATH  Google Scholar 

  26. Ríos-Ruiz, C., Osorio-Gordillo, G.L., Souley-Ali, H., Darouach, M., Astorga-Zaragoza, C.M.: Finite time functional observers for descriptor systems. Application to fault tolerant control. In: Mediterranean Conference on Control and Automation, pp. 165–170 (2019)

  27. Yu, J., Sun, G., Karimi, H.R.: Fault-reconstruction-based cascaded sliding mode observers for descriptor linear systems. Math. Probl. Eng. 2012, 1–20 (2012). Art. no. 623426

    MathSciNet  MATH  Google Scholar 

  28. Chang, Y.C., Yen, H.M.: Robust tracking control for a class of electrically driven flexible-joint robots without velocity measurements. Int. J. Control. 85(2), 194–212 (2012)

    Article  MathSciNet  Google Scholar 

  29. Li, R., Yang, Y.: Sliding-mode observer-based fault reconstruction for T-S fuzzy descriptor systems. IEEE Trans. Syst., Man, Cybern.: Syst. In press (2019)

  30. Long, Y., Park, J.H., Ye, D.: Finite frequency fault detection for a class of nonhomogeneous Markov jump systems with nonlinearities and sensor failures. Nonlinear Dyn. 96(1), 285–299 (2019)

    Article  Google Scholar 

  31. Lee, T.H., Lim, C.P., Nahavandi, S., Park, J.H.: Network-based synchronization of T-S fuzzy chaotic systems with asynchronous samplings. J. Franklin Institut. 355(13), 5736–5758 (2018)

    Article  MathSciNet  Google Scholar 

  32. Sharma, V., Agrawal, V., Sharma, B.B., Nath, R.: Unknown input nonlinear observer design for continuous and discrete time systems with input recovery scheme. Nonlinear Dyn. 85, 645–658 (2016)

    Article  MathSciNet  Google Scholar 

  33. Saha, S., Aldeen, M., Tan, C.P.: Unsymmetrical fault diagnosis in transmission/distribution networks. Int. J. Electr. Power Energy Syst. 45(1), 252–263 (2013)

    Article  Google Scholar 

  34. Chua, W.S., Chan, J.C.L., Tan, C.P., Chong, E.K.P., Saha, S.: Robust fault reconstruction for a class of nonlinear systems. Automatica. 113, 1–5 (2020). Art. no. 108718

    Article  MathSciNet  Google Scholar 

  35. Jmal, A., Naifar, O., Ben Makhlouf, A., Derbel, N., Hammami, M.A.: Sensor fault estimation for fractional-order descriptor one-sided Lipschitz systems. Nonlinear Dyn. 91, 1713–1722 (2018)

    Article  Google Scholar 

  36. Darouach, M., Boutat-Baddas, L., Zerrougui, M.: \(H_{\infty }\) observers design for a class of nonlinear singular systems. Automatica. 47(11), 2517–2525 (2011)

    Article  MathSciNet  Google Scholar 

  37. Osorio-Gordillo, G.L., Darouach, M., Astorga-Zaragoza, C.M., Boutat-Baddas, L.: Generalised dynamic observer design for Lipschitz non-linear descriptor systems. IET Control Appl. 13(14), 2270–2280 (2019)

    Article  Google Scholar 

  38. Li, J., Zhang, Q., Yan, X.G., Spurgeon, S.K.: Observer-based fuzzy integral sliding mode control for nonlinear descriptor systems. IEEE Trans. Fuzzy Syst. 26(5), 2818–2832 (2018)

    Article  Google Scholar 

  39. Arefinia, E., Talebi, H.A., Doustmohammadi, A.: A robust adaptive observer for a class of singular nonlinear uncertain systems. Int. J. Syst. Sci. 48(7), 1404–1415 (2017)

    Article  MathSciNet  Google Scholar 

  40. Gupta, M.K., Tomar, N.K., Darouach, M.: Unknown inputs observer design for descriptor systems with monotone nonlinearities. Int. J. Robust Nonlinear Control. 28(17), 5481–5494 (2018)

    Article  MathSciNet  Google Scholar 

  41. Lin, J., Jiang, G., Gao, Z., Rong, L.: State and input simultaneous estimation for discrete-time switched singular delay systems with missing measurements. Int. J. Robust Nonlinear Control. 27(16), 2749–2772 (2017)

    Article  MathSciNet  Google Scholar 

  42. Peng, J., Ding, S., Yang, Z., Xin, J.: Adaptive neural impedance control for electrically driven robotic systems based on a neuro-adaptive observer. Nonlinear Dyn. 100(2), 1359–1378 (2020)

    Article  Google Scholar 

  43. Mei, K., Ding, S.: Second-order sliding mode controller design subject to an upper-triangular structure. IEEE Trans. Syst., Man, Cybern. In press (2018)

  44. Long, Y., Park, J.H., Ye, D.: Asynchronous fault detection and isolation for Markov jump systems with actuator failures. IEEE Trans. Syst., Man, Cybern. In press (2019)

  45. Alwi, H., Edwards, C., Tan, C.P.: Fault Detection and Fault-Tolerant Control Using Sliding Modes. Springer, London (2011)

    Book  Google Scholar 

  46. Shtessel, Y., Edwards, C., Fridman, L., Levant, A.: Sliding Mode Control and Observation. Springer, New York (2014)

    Book  Google Scholar 

  47. Hautus, M.L.J.: Controllability and observability conditions of linear autonomous systems. Proc. K. Ned. Akad. van Wet. Ser. A, Math. sci. 72, 443–448 (1969)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (No. 2020R1C1C1012707).

Author information

Authors and Affiliations

  1. Division of Electronic Engineering, Jeonbuk National University, 567 Baekje-daero, Jeonju, 54896, Republic of Korea

    Joseph Chang Lun Chan & Tae H. Lee

  2. School of Engineering and Advanced Engineering Platform, Monash University Malaysia, Subang Jaya, Selangor, Malaysia

    Chee Pin Tan

Authors
  1. Joseph Chang Lun Chan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tae H. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chee Pin Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tae H. Lee.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chan, J.C.L., Lee, T.H. & Tan, C.P. A sliding mode observer for robust fault reconstruction in a class of nonlinear non-infinitely observable descriptor systems. Nonlinear Dyn 101, 1023–1036 (2020). https://doi.org/10.1007/s11071-020-05843-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-05843-9

Keywords

Search

Navigation