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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 249))

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Abstract

SMOs have found wide application in the areas of fault detection, fault reconstruction and health monitoring in recent years. Their well-known advantages are robustness and insensitivity to external disturbance. Higher-order SMOs have better performance as compared to classical sliding mode based observers because their output is continuous and does not require filtering. However, insofar as we are aware, their application in FDI has remained unstudied. In this chapter, we shall develop the theoretical background of SMOs and SMO-based FDI. A bibliographical study of existing approaches in these fields will be followed by a brief presentation of some established first order and second order SMO algorithms.

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References

  1. Bacciotti, A., Rosier, L.: Liapunov Functions and Stability in Control Theory. Springer (2005)

    Google Scholar 

  2. Besançon, G.: High-gain observation with disturbance attenuation and application to robust fault detection. Automatica 39(6), 1095–1102 (2003)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. Dávila, A., Moreno, J., Fridman, L.: Optimal Lyapunov function selection for reaching time estimation of super twisting algorithm. In: Proceedings of the 48th IEEE Conference on Decision and Control, held jointly with the 28th Chinese Control Conference (CDC/CCC), pp. 8405–8410. IEEE (2009)

    Google Scholar 

  5. Davila, J., Fridman, L., Levant, A., et al.: Second-order sliding-mode observer for mechanical systems. IEEE Trans. Autom. Control. 50(11), 1785–1789 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Edwards, C., Tan, C.P.: Sensor fault tolerant control using sliding mode observers. Control. Eng. Pract. 14(8), 897–908 (2006)

    Article  Google Scholar 

  8. Filippov, A., Arscott, F.: Differential Equations with Discontinuous Righthand Sides: Control Systems, vol. 18. Springer (1988)

    Google Scholar 

  9. Floquet, T., Barbot, J.P.: Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs. Int. J. Syst. Sci. 38(10), 803–815 (2007)

    Article  MathSciNet  Google Scholar 

  10. Floquet, T., Edwards, C., Spurgeon, S.K.: On sliding mode observers for systems with unknown inputs. Int. J. Adapt. Control. Signal Process. 21(8–9), 638–656 (2007)

    Article  MathSciNet  Google Scholar 

  11. Gonzalez, T., Moreno, J.A., Fridman, L.: Variable gain super-twisting sliding mode control. IEEE Trans. Autom. Control. 57(8), 2100–2105 (2012)

    Article  MathSciNet  Google Scholar 

  12. Hong, Y., Wang, J., Xi, Z.: Stabilization of uncertain chained form systems within finite settling time. IEEE Trans. Autom. Control. 50(9), 1379–1384 (2005)

    Article  MathSciNet  Google Scholar 

  13. Hou, M., Muller, P.: Design of observers for linear systems with unknown inputs. IEEE Trans. Autom. Control. 37(6), 871–875 (1992)

    Article  MathSciNet  Google Scholar 

  14. Jiang, B., Staroswiecki, M., Cocquempot, V.: Fault estimation in nonlinear uncertain systems using robust/sliding-mode observers. IEE Proc.-Control. Theory Appl. 151(1), 29–37 (2004)

    Article  Google Scholar 

  15. Khalil, H.K.: Nonlinear Systems. Prentice Hall (2001)

    Google Scholar 

  16. Kobayashi, S., Furuta, K.: Frequency characteristics of Levant’s differentiator and adaptive sliding mode differentiator. Int. J. Syst. Sci. 38(10), 825–832 (2007)

    Article  Google Scholar 

  17. Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34(3), 379–384 (1998)

    Article  MathSciNet  Google Scholar 

  18. Liu, J., Laghrouche, S., Wack, M.: Finite time observer design for a class of nonlinear systems with unknown inputs. In: American Control Conference (ACC), pp. 286–291. IEEE (2013)

    Google Scholar 

  19. Moreno, J., Osorio, M.: Strict Lyapunov functions for the super-twisting algorithm. IEEE Trans. Autom. Control. 57(4), 1035–1040 (2012)

    Article  MathSciNet  Google Scholar 

  20. Moreno, J.A., Osorio, M.: A Lyapunov approach to second-order sliding mode controllers and observers. In: 47th IEEE Conference on Decision and Control(CDC), pp. 2856–2861. IEEE (2008)

    Google Scholar 

  21. Orlov, Y.: Finite time stability and robust control synthesis of uncertain switched systems. SIAM J. Control. Optim. 43(4), 1253–1271 (2004)

    Article  MathSciNet  Google Scholar 

  22. Persis, C.D., Isidori, A.: A geometric approach to nonlinear fault detection and isolation. IEEE Trans. Autom. Control. 46(6), 853–865 (2001)

    Article  MathSciNet  Google Scholar 

  23. Qiu, Z., Gertler, J.: Robust FDI systems and \(H_\infty \)-optimization-disturbances and tall fault case. In: Proceedings of the 32nd IEEE Conference on Decision and Control, USA, pp. 1710–1715 (1993)

    Google Scholar 

  24. Rajamani, R.: Observers for Lipschitz nonlinear systems. IEEE Trans. Autom. Control. 43(3), 397–401 (1998)

    Article  MathSciNet  Google Scholar 

  25. Respondek, W., Pogromsky, A., Nijmeijer, H.: Time scaling for observer design with linearizable error dynamics. Automatica 40(2), 277–285 (2004)

    Article  MathSciNet  Google Scholar 

  26. Saif, M., Guan, Y.: A new approach to robust fault detection and identification. IEEE Trans. Aerosp. Electron. Syst. 29(3), 685–695 (1993)

    Article  Google Scholar 

  27. Slotine, J.J., Hedrick, J., Misawa, E.: On sliding observers for nonlinear systems. In: American Control Conference, pp. 1794–1800. IEEE (1986)

    Google Scholar 

  28. Slotine, J.J.E., Hedrick, J.K., Misawa, E.A.: On sliding observers for nonlinear systems. ASME J. Dyn. Syst. Meas. Control. 109, 245–252 (1987)

    Article  Google Scholar 

  29. Spurgeon, S.K.: Sliding mode observers: a survey. Int. J. Syst. Sci. 39(8), 751–764 (2008)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  32. Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, Berlin (1992)

    Book  Google Scholar 

  33. Veluvolu, K.C., Defoort, M., Soh, Y.C.: High-gain observer with sliding mode for nonlinear state estimation and fault reconstruction. J. Frankl. Inst. 351(4), 1995–2014 (2014)

    Article  MathSciNet  Google Scholar 

  34. Walcott, B., Żak, S.: State observation of nonlinear uncertain dynamical systems. IEEE Trans. Autom. Control. 32(2), 166–170 (1987)

    Article  MathSciNet  Google Scholar 

  35. Wang, H., Huang, Z.J., Daley, S.: On the use of adaptive updating rules for actuator and sensor fault diagnosis. Automatica 33, 217–225 (1997)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  37. Yan, X., Edwards, C.: Adaptive sliding-mode-observer-based fault reconstruction for nonlinear systems with parametric uncertainties. IEEE Trans. Ind. Electron. 55(11), 4029–4036 (2008)

    Article  Google Scholar 

  38. Yang, H., Saif, M.: Nonlinear adaptive observer design for fault detection. In: Proceedings of the American Control Conference, USA, pp. 1136–1139 (1995)

    Google Scholar 

  39. Zhang, X., Polycarpou, M., Parisini, T.: Fault diagnosis of a class of nonlinear uncertain systems with lipschitz nonlinearities using adaptive estimation. Automatica 46(2), 290–299 (2010)

    Article  MathSciNet  Google Scholar 

  40. Zhou, K., Doyle, J.C., Glover, K., et al.: Robust and optimal control, vol. 40. Prentice Hall, New Jersey (1996)

    Google Scholar 

  41. Zubov, V.: Methods of A.M. Lyapunov and Their Application. P. Noordhoff (1964)

    Google Scholar 

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Correspondence to Jianxing Liu .

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Liu, J., Gao, Y., Yin, Y., Wang, J., Luo, W., Sun, G. (2020). Sliding Mode Observer and Its Applications. In: Sliding Mode Control Methodology in the Applications of Industrial Power Systems. Studies in Systems, Decision and Control, vol 249. Springer, Cham. https://doi.org/10.1007/978-3-030-30655-7_3

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