Soft Computing

, Volume 22, Issue 2, pp 607–620 | Cite as

Model-based control using interval type-2 fuzzy logic systems

  • Rómulo AntãoEmail author
  • Alexandre Mota
  • Rui Escadas Martins
Methodologies and Application


Type-2 fuzzy logic introduced new formalisms capable of overcoming the inherent uncertainties of approximating real-world processes by computational models. Yet, despite increasingly present in the nonlinear modeling literature, model-based control theory does not seem to be taking full advantage of the improvements that type-2 fuzzy logic provides. Therefore, the present work proposes the development of a new control methodology based on the generalized predictive control theory supported by interval type-2 Takagi–Sugeno fuzzy logic systems. The developed control system is based on locally linear approximations of the type-2 Takagi–Sugeno model and will be evaluated using a nonlinear process based on the yeast fermentation reaction. For comparison purposes, two additional generalized predictive control implementations based on a linear auto-regressive model with exogenous inputs and a type-1 Takagi–Sugeno fuzzy model will be used. The performance of the closed loop systems will be evaluated by subjecting the process to quick changes in the operation regime and to unmeasured external disturbances. The mean squared error, control effort and typical transient step response metrics (overshoot and settling time) will provide the benchmark criteria. The results achieved demonstrate that at the expense of a small increase in the computational effort, type-2 fuzzy logic systems improve the transient behavior of the closed loop system, presenting significant advantages when the controlled process is subject to unmodeled disturbances.


Interval type-2 fuzzy sets Generalized predictive control Nonlinear system’s control 



The authors acknowledge the support given by FCT—Foundation for Science and Technology, in the context of Ph.D. scholarship BD/71601/2010 and the IEETA Research Unit, funded by National Funds through FCT in the context of the projects UID/CEC/00127/2013 and Incentivo/EEI /UI0127/2014.

Compliance with ethical standards

Conflict of interest

The authors Rómulo Antão, Alexandre Mota and Rui Martins declare that have no conflict of interests.


  1. Åström K, Wittenmark B (2008) Adaptive control. Dover, LondonGoogle Scholar
  2. Camacho E, Bordons C (2007) Model predictive control, advanced textbooks in control and signal processing, 2nd edn. Springer, NewYorkzbMATHGoogle Scholar
  3. Castillo O, Melin P (2014) A review on interval type-2 fuzzy logic applications in intelligent control. Inf Sci 279:615–631MathSciNetCrossRefzbMATHGoogle Scholar
  4. Cervantes L, Castillo O, Soria J (2016) Hierarchical aggregation of multiple fuzzy controllers for global complex control problems. Appl Soft Comput 38:851–859CrossRefGoogle Scholar
  5. Chia-Feng J, Yu-Wei T (2008) A self-evolving interval type-2 fuzzy neural network with online structure and parameter learning. IEEE Trans Fuzzy Syst 16(6):1411–1423CrossRefGoogle Scholar
  6. Chiu S (1994) Fuzzy model identification based on cluster estimation. J Intell Fuzzy Syst 2(3):267–278Google Scholar
  7. Clarke D, Mohtadi C, Tuffs P (1987) Generalized predictive control—part I. The basic algorithm. Automatica 23(2):137–148CrossRefzbMATHGoogle Scholar
  8. Greenfield S, Chiclana F, Coupland S, John R (2009) The collapsing method of defuzzification for discretized interval type-2 fuzzy sets. Inf Sci 179:2055–2069CrossRefzbMATHGoogle Scholar
  9. Greenfield S, Chiclana F (2013) Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set. Int J Approx Reason 54(8):1013–1033MathSciNetCrossRefzbMATHGoogle Scholar
  10. Hägglund T (1983) New estimation techniques for adaptive control, Ph.D. thesis, Department of Automatic Control, Lund Institute of Technology, SwedenGoogle Scholar
  11. Hagras H (2007) Type-2 FLC: a new generation of fuzzy controllers. IEEE Comput Intell Mag 2(1):30–43CrossRefGoogle Scholar
  12. Hu H, Wang Y, Cai Y (2012) Advantages of enhanced opposite direction searching algorithms for computing the centroid of an interval type-2 fuzzy set. Asian J Control 14(6):1–9MathSciNetzbMATHGoogle Scholar
  13. Khanesar, M, Kayacan Teshnehlab M, Kaynak O (2011) Levenberg Marquardt algorithm for training of type-2 fuzzy neuro system with a novel type-2 fuzzy membership function. IEEE Symposium on advances in type-2 fuzzy logic systems, pp 88–93Google Scholar
  14. Kulhavý R (1985) Restricted exponential forgetting in real-time identification. IFAC Symposium on identification and system parameter estimation, pp 1143–1148Google Scholar
  15. Kumbasar T, Eksin I, Guzelkaya M, Yesil E (2011a) Interval type-2 fuzzy inverse controller design in non-linear IMC structure. Eng Appl Artif Intell 24:996–1005CrossRefGoogle Scholar
  16. Kumbasar T, Eksin I, Guzelkaya M, Yesil E (2011b) Type-2 fuzzy model inverse controller design based on bb-bc optimization method. In: 18th World congress of the international federation of automatic control (IFAC)Google Scholar
  17. Kumbasar T, Hagras H (2015) A gradient descent based online tuning mechanism for pi type single input interval type-2 fuzzy logic controllers. In: Proceedings of IEEE international conference on fuzzy systemsGoogle Scholar
  18. Ławryńczuk M (2014) Computationally efficient model predictive control algorithms—a neural network approach, studies in systems, decision and control, vol 3. Springer, BerlinzbMATHGoogle Scholar
  19. Lin Y, Liao S, Chang J, Lin C (2014) Simplified interval type-2 fuzzy neural networks. IEEE Trans Neural Netw Learn Syst 25(5):959–969CrossRefGoogle Scholar
  20. Ljung L (1998) System identification: theory for the user. Pearson Education, NewYorkCrossRefzbMATHGoogle Scholar
  21. Luyben W (2007) Chemical reactor design and control. Wiley, NewYorkCrossRefGoogle Scholar
  22. Mahfouf M, Linkens D, Abbod M (2000) Adaptive fuzzy TSK model-based predictive control using a CARIMA model structure. Chem Eng Res Des Process Control 78(4):590–596Google Scholar
  23. Maldonado Y, Castillo O, Mellin P (2014) A multi-objective optimization of type-2 fuzzy control speed in FPGA. Appl Soft Comput 24:1164–1174CrossRefGoogle Scholar
  24. Martinez-Soto R, Castillo O, Castro J (2014) Genetic algorithm optimization for type-2 non-singleton fuzzy logic controllers. Recent Adv Hybrid Approach Des Intell Syst 547:3–18CrossRefGoogle Scholar
  25. Martínez-Soto R, Castillo O, Aguilar L (2014) Type-1 and type-2 fuzzy logic controller design using a hybrid PSO-GA optimization method. Processing and mining complex data streams. Inf Sci 285:35–49CrossRefzbMATHGoogle Scholar
  26. Melin P, Castillo O (2014) A review on type-2 fuzzy logic applications in clustering, classification and pattern recognition, applied soft computing, vol 21. Elsevier, AmsterdamGoogle Scholar
  27. Mendel J (2001) Uncertain rule-based fuzzy logic systems: introduction and new directions. Prentice-Hall, Upper Saddle RiverzbMATHGoogle Scholar
  28. Mendel J (2004) Computing derivatives in interval type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 12(1):84–98MathSciNetCrossRefGoogle Scholar
  29. Mendes J, Araujo R, Souza F (2013) Adaptive fuzzy identification and predictive control for industrial processes. Expert Syst Appl 40:6964–6975CrossRefGoogle Scholar
  30. Nagy Z (2007) Model-based control of a yeast fermentation bioreactor using optimally designed artificial neural networks. Chem Eng J 127:95–109CrossRefGoogle Scholar
  31. Nguyen T, Khosravi A, Creighton D, Nahavandi S (2015) Medical data classification using interval type-2 fuzzy logic system and wavelets. Appl Soft Comput 30:812–822CrossRefGoogle Scholar
  32. Rossiter J (2004) Model-based predictive control: a practical approach, control series. CRC Press, Boca RatonGoogle Scholar
  33. Rubio-Solis A, Panoutsos G (2015) Interval type-2 radial basis function neural network: a modeling framework. IEEE Trans Fuzzy Syst 23(2):457–473CrossRefGoogle Scholar
  34. Su M, Rhinehart R (2010) A generalized TSK model with a novel rule antecedent structure: structure identification and parameter estimation. Comput Chem Eng 34(8):1199–1219CrossRefGoogle Scholar
  35. Ureña R, Chiclana F, Morente-Molinera J, Herrera-Viedma E (2015) Managing incomplete preference relations in decision making: a review and future trends. Inf Sci 302:14–32MathSciNetCrossRefzbMATHGoogle Scholar
  36. Wellstead P, Zarrop M (1991) Self-tuning systems, control and signal processing. Wiley, HobokenzbMATHGoogle Scholar
  37. Wu D (2012) On the fundamental differences between interval type-2 and type-1 fuzzy logic controllers. IEEE Trans Fuzzy Syst 20(5):832–848CrossRefGoogle Scholar
  38. Wu D (2013) Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons. IEEE Trans Fuzzy Syst 21(1):80–99CrossRefGoogle Scholar
  39. Wu D, Tan W (2005) Type-2 FLC modeling capability analysis. In: Proceeding of the 2005 IEEE international conference on fuzzy systems, pp 242–247Google Scholar
  40. Wu D, Tan W (2006) A simplified type-2 fuzzy logic controller for real-time control. ISA Trans 45(4):503–516CrossRefGoogle Scholar
  41. Yen J, Wang L, Gillespie C (1998) Improving the interpretability of TSK fuzzy models by combining global learning and local learning. IEEE Trans Fuzzy Syst 6(4):530–537CrossRefGoogle Scholar
  42. Zadeh L (1965) Fuzzy sets. Inf Control 8:338–353CrossRefzbMATHGoogle Scholar
  43. Zadeh L (1973) Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans Syst Man Cybern 3:28–44MathSciNetCrossRefzbMATHGoogle Scholar
  44. Zadeh L (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8:199–249MathSciNetCrossRefzbMATHGoogle Scholar
  45. Zhao L (2010) Direct-inverse modeling control based on interval type-2 fuzzy neural network. In: Proceedings of the 29th Chinese control conference, pp 2630–2635Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Rómulo Antão
    • 1
    Email author
  • Alexandre Mota
    • 1
  • Rui Escadas Martins
    • 1
  1. 1.Departamento of Eletrónica, Telecomunicações e InformáticaUniversidade de AveiroAveiroPortugal

Personalised recommendations