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Sliding Mode Observer for Robust Fault Reconstruction of Time Delay Systems

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Recent Results on Nonlinear Delay Control Systems

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 4))

Abstract

A sliding mode observer in the presence of known output delay and its application to robust fault reconstruction is studied. The observer is designed using a singular perturbation method for which sufficient conditions are given in the form of linear matrix inequalities (LMIs) to guarantee ultimate boundedness of the error dynamics. Though an ideal sliding motion cannot be achieved in the observer when the outputs are delayed, ultimately bounded solutions can be obtained, provided the delay is sufficiently small. The bound on the solution is proportional to the delay and the magnitude of the switching gain. The proposed observer design is applied to the problem of fault reconstruction under delayed outputs and system uncertainties. It is shown that actuator or sensor faults can be reconstructed reliably from the output error dynamics. An example of observer design for an inverted pendulum system is used to demonstrate the merit of the proposed methodology, compared with existing sliding mode observer design approaches.

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References

  1. Ahmed-Ali, T., Cherrier, E., Lamnabhi-Lagarrigue, F.: Cascade high gain predictors for a class of nonlinear systems. IEEE Trans. Autom. Control 57(1), 224–229 (2012)

    Article  MathSciNet  Google Scholar 

  2. Ahmed-Ali, T., Karafyllis, I., Lamnabhi-Lagarrigue, F.: Global exponential sampled-data observers for nonlinear systems with delayed measurements. Syst. Control Lett. 62(7), 539–549 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, J., Patton, R., Zhang, H.: Design of unknown input observers and robust fault detection filters. Intern. J. Control 63(1), 85–105 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Choi, H., Chung, M.: Observer-based \(H_\infty \) controller design for state delayed linear systems. Automatica 32(7), 1073–1075 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  5. Darouach, M.: Linear functional observers for systems with delays in the state variables. IEEE Trans. Autom. Control 46(3), 491–497 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Edwards, C., Spurgeon, S.: On the development of discontinuous observers. Intern. J. Control 59(5), 1211–1229 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  7. Edwards, C., Spurgeon, S.: Sliding Mode Control: Theory and Applications. Taylor and Francis, Bristol, PA (1998)

    Google Scholar 

  8. Edwards, C., Spurgeon, S., Patton, P.: Sliding mode observers for fault detection and isolation. Automatica 36(4), 541–553 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Fridman, E.: A refined input delay approach to sampled-data control. Automatica 46(2), 421–427 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fridman, E., Dambrine, M.: Control under quantization, saturation and delay: a LMI approach. Automatica 45(10), 2258–2264 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Fridman, E., Seuret, A., Richard, J.-P.: Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40(8), 1441–1446 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Floquet, T., Barbot, J., Perruquetti, W., Djemai, M.: On the robust fault detection via a sliding mode disturbance observer. Intern. J. Control 77(7), 622–629 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  13. Germani, A., Manes, C., Pepe, P.: A new approach to state observation of nonlinear systems with delyed output. IEEE Trans. Autom. Control 47(1), 96–101 (2002)

    Article  MathSciNet  Google Scholar 

  14. Germani, A., Pepe, P.: A State observer for a class of nonlinear systems with multiple discrete and distributed time delays. Eur. J. Control 11(3), 196–205 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Han, X., Fridman, E., Spurgeon, S., Edwards, C.: On the design of sliding mode static output feedback controllers for systems with state delay. IEEE Trans. Ind. Electron. 56(9), 3656–3664 (2009)

    Article  Google Scholar 

  16. Han, X., Fridman, E., Spurgeon, S.: Sliding mode control in the presence of input delay: a singular perturbation approach. Automatica 48(8), 1904–1912 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  17. Han, X., Fridman, E., Spurgeon, S.: Sampled data sliding mode observer for robust fault reconstruction: a time delay approach. J. Frankl. Inst. 351(4), 2125–2142 (2013)

    Article  MathSciNet  Google Scholar 

  18. Ibrir, S.: Observer-based control of a class of time-delay nonlinear systems having triangular structure. Automatica 47(2), 388–394 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  19. Jafarov, E.: Design modification of sliding mode observers for uncertain MIMO systems without and with time-delay. Asian J. Control 7(4), 380–392 (2005)

    Article  MathSciNet  Google Scholar 

  20. Kokotovic, P., Khalil, H., O’Reilly, J.: Singul. Perturbat. Methods Control: Anal. Des. Academic Press, New York (1986)

    Google Scholar 

  21. Kolmanovskii, V., Myshkis, A.: Applied Theory of Functional Differential Equations. Series Mathematics and Its Applications (Soviet Series), vol. 85. Kluwer, Dordrecht (1992)

    Google Scholar 

  22. Mikheev, Y., Sobolev, V., Fridman, E.: Asymptotic analysis of digital control systems. Autom. Remote Control 49(9), 1175–1180 (1988)

    MATH  MathSciNet  Google Scholar 

  23. Niu, Y., Lam, J., Wang, X., Ho, D.: Observer Based sliding mode control for nonlinear state-delayed systems. Intern. J. Syst. Sci. 35(2), 139–150 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  24. Nounou, M., Nounou, H., Mahmoud, M.: Robust adaptive sliding mode control for continuous time delay systems. IMA J. Math. Control Inf. 24(3), 299–313 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  25. Spurgeon, S.: Sliding mode observers—a survey. Intern. J. Syst. Sci. 39(8), 751–764 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  26. Subbarao, K., Muralidhar, P.: State observer for linear systems with piece-wise constant output delays. IET Control Theory Appl. 3(8), 1017–1022 (2009)

    Article  MathSciNet  Google Scholar 

  27. Suplin, V., Fridman, E., Shaked, U.: Sampled-data \(H_\infty \) control and filtering: nonuniform uncertain sampling. Automatica 43(6), 1072–1083 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  28. Tan, C., Edwards, C.: An LMI approach for design sliding mode observers. Intern. J. Control 74(16), 1559–1568 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  29. Tan, C., Edwards, C.: Sliding mode observers for detection and reconstruction of sensor faults. Automatica 38(10), 1815–1821 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  30. Tan, C., Edwards, C.: Sliding mode observers for robust detection and reconstruction of actuator and sensor faults. Intern. J. Robust Nonlinear Control 13(5), 443–463 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

This work was partially supported by Israel Science Foundation Grant Number 754/10.

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Authors and Affiliations

  1. Aeronautical and Automotive Engineering, Loughborough University, Loughborough, LE11 3TU, UK

    Xiaoran Han

  2. School of Electrical Engineering, Tel Aviv University, 69978, Tel Aviv, Israel

    Emilia Fridman

  3. School of Engineering and Digital Arts, University of Kent, Canterbury, CT2 7NZ, UK

    Sarah K. Spurgeon

Authors
  1. Xiaoran Han
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  2. Emilia Fridman
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  3. Sarah K. Spurgeon
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Corresponding author

Correspondence to Xiaoran Han .

Editor information

Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Iasson Karafyllis

  2. Department of Mathematics, Louisiana State University (LSU), Baton Rouge, Louisiana, USA

    Michael Malisoff

  3. CNRS-CentraleSupélec-Université Paris Sud, EPI Inria “DISCO”, Laboratory of Signals and Systems (L2S, UMR CNRS 8506), Gif-sur-Yvette, France

    Frederic Mazenc

  4. Department of Information Engineering, Computer Science, and Mathematics, University of L’Aquila, L’Aquila, Italy

    Pierdomenico Pepe

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Han, X., Fridman, E., Spurgeon, S.K. (2016). Sliding Mode Observer for Robust Fault Reconstruction of Time Delay Systems. In: Karafyllis, I., Malisoff, M., Mazenc, F., Pepe, P. (eds) Recent Results on Nonlinear Delay Control Systems. Advances in Delays and Dynamics, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-18072-4_9

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  • DOI: https://doi.org/10.1007/978-3-319-18072-4_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18071-7

  • Online ISBN: 978-3-319-18072-4

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