Sliding Mode Observer for Fault Diagnosis: LPV and Takagi–Sugeno Model Approaches

  • Horst SchulteEmail author
  • Florian Pöschke
Part of the Mathematical Engineering book series (MATHENGIN)


This chapter investigates recently proposed fault reconstruction methods by sliding mode observers defined by two different model classes: linear parameter varying and Takagi–Sugeno models. Both model classes are used to design the sliding mode observers. They may be considered as a polytopic extension of the canonical form restricted to uncertain linear time-invariant systems originally introduced by Edwards and Spurgeon. This approach is best suited for plants which can be thought of as predominantly linear in the characteristics or for nonlinear plants which can be modelled well (at least locally) by linear approximations. For highly nonlinear plants which are operated in a large operating range, a structure restricted to uncertain linear time-invariant systems is not ideal, as the sliding term would then have to capture both: the nonlinear plant dynamics and the influence of the faults. The chapter describes the observer design for linear parameter varying and Takagi–Sugeno models, which are illustrated by the means of the inverted pendulum and the wind turbine benchmark from the literature. Simulation results are shown to demonstrate the capability of the designed observers.


  1. 1.
    Alwi H, Edwards C (2010) Robust actuator fault reconstruction for LPV systems using sliding mode observers. In: IEEE conference on decision and control. Hilton Atlanta Hotel, AtlantaGoogle Scholar
  2. 2.
    Bianchi FD, De Battista H, Mantz RJ (2007) Wind turbine control systems - principles modelling and gain scheduling design. Springer, London Limited, LondonGoogle Scholar
  3. 3.
    Donath H, Georg S, Schulte H (2013) Takagi-Sugeno sliding mode observer for friction compensation with application to an inverted pendulum. In: IEEE international conference on fuzzy systems (FUZZ). Hyderabad, India. doi: 10.1109/FUZZ-IEEE.2013.6622558
  4. 4.
    Edwards C, Spurgeon SK (1998) Sliding mode control: theory and applications. Taylor & Francis, Boca RatonzbMATHGoogle Scholar
  5. 5.
    Gasch R, Twele J (2012) Wind power plants, 2nd edn. Springer, BerlinCrossRefGoogle Scholar
  6. 6.
    Georg S (2015) Fault diagnosis and fault-tolerant control of wind turbines nonlinear Takagi-Sugeno and sliding mode techniques. Ph.D. thesis, University of Rostock, Faculty of Mechanical Engineering and Marine TechnologyGoogle Scholar
  7. 7.
    Georg S, Schulte H, Aschemann H (2012) Control-oriented modelling of wind turbines using a Takagi-Sugeno model structure. In: IEEE international conference on fuzzy systems. Brisbane, Australia, pp. 1737–1744Google Scholar
  8. 8.
    Gerland P (2011) Klassifikationsgestützte on-line Adaption eines robusten beobachterbasierten Fehlerdiagnoseansatzes für nichtlineare Systeme. Ph.D. thesis, Universität KasselGoogle Scholar
  9. 9.
    Gerland P, Groß D, Schulte H, Kroll A (2010) Design of sliding mode observers for TS fuzzy systems with application to disturbance and actuator fault estimation. In: IEEE conference on decision and control. Hilton Atlanta Hotel, Atlanta, pp. 4373–4378Google Scholar
  10. 10.
    Gerland P, Groß D, Schulte H, Kroll A (2010) Robust adaptive fault detection using global state information and application to mobile working machines. In: Conference on control and fault-tolerant systems. Nice, France, pp. 813–818Google Scholar
  11. 11.
    Kolodziejczak B, Szulc T (1999) Convex combinations of matrices - full rank characterization. Linear Algebra Appl 287:215–222MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kroll A, Schulte H (2014) Benchmark problems for nonlinear system identification and control using soft computing methods: need and overview. Appl Soft Comput 25(12):496–513CrossRefGoogle Scholar
  13. 13.
    Mohammadpour J, Scherer CW (eds) (2012) Control of linear parameter varying systems with applications, 1st edn. Springer, New YorkGoogle Scholar
  14. 14.
    Odgaard PF, Stoustrup J, Kinnaert M (2009) Fault tolerant control of wind turbines - a benchmark model. In: IFAC symposium on fault detection, supervision and safety of technical processes. Barcelona, Spain, pp. 155–160Google Scholar
  15. 15.
    Odgaard PF, Stoustrup J, Kinnaert M (2013) Fault-tolerant control of wind turbines: a benchmark model. IEEE Trans Control Syst Technol 21(4):1168–1182CrossRefGoogle Scholar
  16. 16.
    Ohtake H, Tanaka K, Wang HO (2001) Fuzzy modeling via sector nonlinearity concept. In: Joint 9th IFSA world congress and 20th NAFIPS international conference. Vancouver, Canada, pp. 127–132Google Scholar
  17. 17.
    Pöschke F, Georg S, Schulte H (2014) Fault reconstruction using a Takagi-Sugeno sliding mode observer for the wind turbine benchmark. In: UKACC international conference on control (CONTROL). Loughborough, pp. 456–461. doi: 10.1109/CONTROL.2014.6915183
  18. 18.
    Schulte H, Gerland P (2010) Observer-based estimation of pressure signals in hydrostatic transmissions. In: IFAC symposium advances in automotive control (AAC). Munich, GermanyGoogle Scholar
  19. 19.
    Shamma JS (1988) Analysis and desgin of gain scheduled control systems. Ph.D. thesis, Massachusetts Institute of TechnologyGoogle Scholar
  20. 20.
    Sugeno M, Kang GT (1988) Structure identification of fuzzy models. Fuzzy Sets Syst 28:15–33MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132CrossRefzbMATHGoogle Scholar
  22. 22.
    Tanaka K, Sano M (1994) On the concept of fuzzy regulators and fuzzy observers. In: IEEE conference on fuzzy systems, pp. 767–772Google Scholar
  23. 23.
    Tanaka K, Sano M (1994) A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer. IEEE Trans Fuzzy Syst 2(2):119–134CrossRefGoogle Scholar
  24. 24.
    Tanaka K, Wang HO (2001) Fuzzy control systems design and analysis: a linear matrix inequality approach. Wiley, New YorkCrossRefGoogle Scholar
  25. 25.
    Utkin VI (1979) Variable structure systems with sliding mode. IEEE Trans Autom Control 22(2):212–222MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Utkin VI (1992) Sliding modes in control optimization. Springer, BerlinCrossRefzbMATHGoogle Scholar
  27. 27.
    Wang HO, Tanaka K, Griffin MF (1996) An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans Fuzzy Syst 4(1):14–23CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Engineering I, Control EngineeringHTW BerlinBerlinGermany

Personalised recommendations