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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bacciotti, A., Rosier, L.: Liapunov Functions and Stability in Control Theory. Springer (2005)
Besançon, G.: High-gain observation with disturbance attenuation and application to robust fault detection. Automatica 39(6), 1095–1102 (2003)
Chen, J., Patton, R., Zhang, H.: Design of unknown input observers and robust fault detection filters. Int. J. Control. 63(1), 85–105 (1996)
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)
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)
Edwards, C., Spurgeon, S.K., Patton, R.J.: Sliding mode observers for fault detection and isolation. Automatica 36(4), 541–553 (2000)
Edwards, C., Tan, C.P.: Sensor fault tolerant control using sliding mode observers. Control. Eng. Pract. 14(8), 897–908 (2006)
Filippov, A., Arscott, F.: Differential Equations with Discontinuous Righthand Sides: Control Systems, vol. 18. Springer (1988)
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)
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)
Gonzalez, T., Moreno, J.A., Fridman, L.: Variable gain super-twisting sliding mode control. IEEE Trans. Autom. Control. 57(8), 2100–2105 (2012)
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)
Hou, M., Muller, P.: Design of observers for linear systems with unknown inputs. IEEE Trans. Autom. Control. 37(6), 871–875 (1992)
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)
Khalil, H.K.: Nonlinear Systems. Prentice Hall (2001)
Kobayashi, S., Furuta, K.: Frequency characteristics of Levant’s differentiator and adaptive sliding mode differentiator. Int. J. Syst. Sci. 38(10), 825–832 (2007)
Levant, A.: Robust exact differentiation via sliding mode technique. Automatica 34(3), 379–384 (1998)
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)
Moreno, J., Osorio, M.: Strict Lyapunov functions for the super-twisting algorithm. IEEE Trans. Autom. Control. 57(4), 1035–1040 (2012)
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)
Orlov, Y.: Finite time stability and robust control synthesis of uncertain switched systems. SIAM J. Control. Optim. 43(4), 1253–1271 (2004)
Persis, C.D., Isidori, A.: A geometric approach to nonlinear fault detection and isolation. IEEE Trans. Autom. Control. 46(6), 853–865 (2001)
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)
Rajamani, R.: Observers for Lipschitz nonlinear systems. IEEE Trans. Autom. Control. 43(3), 397–401 (1998)
Respondek, W., Pogromsky, A., Nijmeijer, H.: Time scaling for observer design with linearizable error dynamics. Automatica 40(2), 277–285 (2004)
Saif, M., Guan, Y.: A new approach to robust fault detection and identification. IEEE Trans. Aerosp. Electron. Syst. 29(3), 685–695 (1993)
Slotine, J.J., Hedrick, J., Misawa, E.: On sliding observers for nonlinear systems. In: American Control Conference, pp. 1794–1800. IEEE (1986)
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)
Spurgeon, S.K.: Sliding mode observers: a survey. Int. J. Syst. Sci. 39(8), 751–764 (2008)
Tan, C., Edwards, C.: Sliding mode observers for detection and reconstruction of sensor faults. Automatica 38(10), 1815–1821 (2002)
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)
Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, Berlin (1992)
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)
Walcott, B., Żak, S.: State observation of nonlinear uncertain dynamical systems. IEEE Trans. Autom. Control. 32(2), 166–170 (1987)
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)
Yan, X., Edwards, C.: Nonlinear robust fault reconstruction and estimation using a sliding mode observer. Automatica 43(9), 1605–1614 (2007)
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)
Yang, H., Saif, M.: Nonlinear adaptive observer design for fault detection. In: Proceedings of the American Control Conference, USA, pp. 1136–1139 (1995)
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)
Zhou, K., Doyle, J.C., Glover, K., et al.: Robust and optimal control, vol. 40. Prentice Hall, New Jersey (1996)
Zubov, V.: Methods of A.M. Lyapunov and Their Application. P. Noordhoff (1964)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-30655-7_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-30654-0
Online ISBN: 978-3-030-30655-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)