International Journal of Fuzzy Systems

, Volume 20, Issue 6, pp 1756–1766 | Cite as

Takagi—Sugeno Observers as an Alternative to Nonlinear Observers for Analytical Redundancy. Application to a Steam Generator of a Thermal Power Plant

  • C.-M. Astorga-Zaragoza
  • G.-L. Osorio-Gordillo
  • J. Reyes-Martínez
  • G. Madrigal-Espinosa
  • M. Chadli


Two observer design approaches for analytical redundancy are presented in this work. The first one is based on the use of Takagi—Sugeno observers, whereas the second method is based on nonlinear high-gain observers. The objective is to conduct a comparative study between these two different approaches for a posteriori application of monitoring process and/or fault detection. In order to ensure a fair comparison, both approaches are evaluated on a common case study: the estimation of critical variables in a steam generator for thermal power plants. A well-known simplified nonlinear model for the steam generator proposed by Bell and Åstrom is used for the high-gain observer design whereas for the Takagi—Sugeno obsever design, the nonlinear model is transformed into a Takagi—Sugeno form by means of the nonlinear sector approach. The main contribution is to propose the use of Takagi—Sugeno observers for analytical redundancy purposes and to highlight their advantages over the use nonlinear high-gain observers.


Analytical redundancy High-gain observer Takagi—Sugeno observer Steam generator 



The authors acknowledge CONACYT for supporting Jesús Reyes-Martínez through a Ph.D. Scholarship.


  1. 1.
    Ali, J.M., Hoang, N.H., Hussain, M.A., Dochain, D.: Review and classification of recent observers applied in chemical process systems. Comput. Chem. Eng. 76, 27–41 (2015)CrossRefGoogle Scholar
  2. 2.
    Astorga, C.M., Othman, N., Othman, S., Hammouri, H., McKenna, T.F.: Nonlinear continuous-discrete observers: application to emulsion polymerization reactors. Control Eng. Pract. 10(1), 3–13 (2002)CrossRefGoogle Scholar
  3. 3.
    Åström, K.J., Eklund, K.: A simplified non-linear model of a drum boiler-turbine unit. Int. J. Control 16(1), 145–169 (1972)CrossRefGoogle Scholar
  4. 4.
    Bell, R.D., Åström, K.J.: Dynamic models for boiler-turbine-alternator units: data logs and parameter estimation for a 160 MW unit. Tech. rep., Department of Automatic Control. Lund Institute of Technology (1987)Google Scholar
  5. 5.
    Brahim, I.H., Chaabane, M., Mehdi, D.: Fault-tolerant control for T-S fuzzy descriptor systems with sensor faults: an LMI approach. Int. J. Fuzzy Syst. 19(2), 516–527 (2017)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Brahim, I.H., Mehdi, D., Mohamed, C.: Robust fault detection for uncertain T-S system with unmeasurable premise variables: descriptor approach. Int. J. Fuzzy Syst. (2017). Google Scholar
  7. 7.
    Chadli, M., Guerra, T.M.: LMI solution for robust static output feedback control of discrete Takagi-Sugeno fuzzy models. IEEE Trans. Fuzzy Syst. 20(6), 1160–1165 (2012)CrossRefGoogle Scholar
  8. 8.
    Cheres, E.: Small and medium size drum boiler models suitable for long term dynamic response. IEEE Trans. Energy Convers. 5(4), 686–692 (1990)CrossRefGoogle Scholar
  9. 9.
    Chilali, M., Gahinet, P., Apkarian, P.: Robust pole placement in LMI regions. IEEE Trans. Automat. Control 44(12), 2257–2270 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Doyle, J., Stein, G.: Robustness with observers. IEEE Trans. Automat. Control 24(4), 607–611 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Dukelow, S.G.: The Control of Boilers, 2nd edn. Instrument Society of America, Pittsburgh, PA (1991)Google Scholar
  12. 12.
    Elleuch, I., Khedher, A., Othman, K.B.: State and faults estimation based on proportional integral sliding mode observer for uncertain Takagi-Sugeno fuzzy systems and its application to a turbo-reactor. Int. J. Fuzzy Syst. (2017). MathSciNetGoogle Scholar
  13. 13.
    Escobar, R.F., Astorga-Zaragoza, C.M., Hernández, J.A., Juárez-Romero, D., García-Beltrán, C.D.: Sensor fault compensation via software sensors: application in a heat pump’s helical evaporator. Chem. Eng. Res. Des. 93, 173–482 (2015)CrossRefGoogle Scholar
  14. 14.
    Esfandiari, F., Khalil, H.K.: Output feedback stabilization of fully linearizable systems. Int. J. Control 56(5), 1007–1037 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Gao, Z., Ding, S.X.: Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems. Automatica 43(5), 912–920 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Gauthier, J.P., Hammouri, H., Othman, S.: A simple observer for nonlinear systems application to bioreactors. IEEE Trans. Automat. Control 37(6), 875–880 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    González, T., Márquez, R., Bernal, M., Guerra, T.M.: Nonquadratic controller and observer design for continuous TS models: a discrete-inspired solution. Int. J. Fuzzy Syst. 18(1), 1–14 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Habbi, H., Zelmat, M., Bouamama, B.O.: A dynamic fuzzy model for a drum-boiler-turbine system. Automatica 39, 1213–1219 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Ichalal, D., Marx, B., Mammar, S., Maquin, D., Ragot, J.: How to cope with unmeasurable premise variables in Takagi-Sugeno observer design: dynamic extension approach. Eng. Appl. Artif. Intell. 67, 430–435 (2018)CrossRefGoogle Scholar
  20. 20.
    Khalil, H.K.: High-Gain Observers in Nonlinear Feedback Control, 1st edn. SIAM, Philadelphia, PA (2017)CrossRefzbMATHGoogle Scholar
  21. 21.
    Kong, X., Liu, X., Lee, K.Y.: Nonlinear multivariable hierarchical model predictive control for boiler-turbine system. Energy 98, 309–322 (2015)CrossRefGoogle Scholar
  22. 22.
    Lendek, Z., Guerra, T.M., Babuška, R., de Schutter, B.: Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models. Springer, Berlin (2011)CrossRefzbMATHGoogle Scholar
  23. 23.
    Li, F., Shi, P., Lim, C.C., Wu, L.: Fault detection filtering for nonhomogeneous Markovian jump systems via fuzzy approach. IEEE Trans. Fuzzy Syst. (2016). Google Scholar
  24. 24.
    Li, F., Shi, P., Wu, L., Zhang, X.: Fuzzy-model-based D-stability and nonfragile control for discrete-time descriptor systems with multiple delays. IEEE Trans. Fuzzy Syst. 22(4), 1019–1025 (2014)CrossRefGoogle Scholar
  25. 25.
    de Mello, F.P.: Boiler models for system dynamic performance studies. IEEE Trans. Power Syst. 6(1), 66–74 (1991)CrossRefGoogle Scholar
  26. 26.
    Ohtake, H., Takana, K., Wang, H.O.: Fuzzy modeling via sector nonlinearity concept. Integr. Comput. Aided Eng. 10(4), 333–341 (2003)CrossRefGoogle Scholar
  27. 27.
    Pellegrinetti, G., Bentsman, J.: Nonlinear control oriented boiler modeling-a benchmark problem for controller design. IEEE Trans. Control Syst. Technol. 4(1), 57–64 (1996)CrossRefGoogle Scholar
  28. 28.
    Téllez-Anguiano, A.C., Astorga-Zaragoza, C.M., Escobar, R.F., Alcorta-García, E., Juárez-Romero, D.: Continuous-discrete observer-based fault detection and isolation system for distillation columns using a binary mixture. Revista Mexicana de Ingeniería Química 15(1), 275–290 (2016)Google Scholar
  29. 29.
    Téllez-Anguiano, A.C., Astorga-Zaragoza, C.M., Targui, B., Aguilera-González, A., Reyes-Reyes, J., Adam-Medina, M.: Experimental validation of a high-gain observer for composition estimation in an ethanol-water distillation column. Asia-Pacific J. Chem. Eng. 4(6), 942–952 (2009)CrossRefGoogle Scholar
  30. 30.
    Tsai, S.H.: Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input. Int. J. Syst. Sci. 45(3), 187–201 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Zhang, J., Peng, C.: \({H}_\infty\) filtering for networked Takagi-Sugeno fuzzy systems with asynchronous constraints. IET Signal Process 9(5), 403–411 (2015)CrossRefGoogle Scholar
  32. 32.
    Zhang, Y., Jiang, J.: Bibliographical review on reconfigurable fault-tolerant control systems. Annu. Rev. Control 32(2), 229–252 (2008)CrossRefGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Tecnológico Nacional de México/CENIDETCuernavacaMexico
  2. 2.Instituto Nacional de Electricidad y Energías Limpias (INEEL)CuernavacaMexico
  3. 3.Université Picardie Jules VerneAmiensFrance

Personalised recommendations