Skip to main content

Advertisement

Springer Nature Link
Log in

A New Approach for Interval Type-3 Fuzzy Control of Nonlinear Plants

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This article is focused on the implementation Interval Type-3 Fuzzy Logic Systems (IT3FLSs) for control problems with the goal of analyzing their performance and efficiency in the stabilization of nonlinear plants when perturbation is considered on the models. Two control problems are presented in which IT3FLSs allow the design of efficient fuzzy controllers when compared to alternative approaches. The methodology with the implementation of the vertical slices concept is utilized for approximating the results of IT3FLSs in the control problems. Simulation results with type-1, interval type-2, and generalized type-2 are presented and analyzed in comparison with IT3FLSs. To highlight the excellent performance of IT3FLs, two types of perturbations are considered in the models, showing that IT3FLs outperform type-2 and type-1 in control. The parameters of \(\lambda ({\text{Lower}}\; {\text{Scale}}) \; {\text{and}}\;{\ell}({\text{Lower}}\; {\text{Lag}})\) that characterize an IT3FLS are changed manually with the 0.2, 0.5 and 0.9 values. Excellent results are presented with the value of 0.2. Several types of control performance metrics are presented to illustrate the results. The most relevant contribution is showing the potential of interval type-3 in the control area in outperforming alternative approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Zadeh, L.A.: Fuzzy sets. In: Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi A Zadeh (pp. 394–432) (1996).

  2. Zadeh, L.A., Klir, G.J., Yuan, B.: Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers, vol. 6. World Scientific, Singapore (1996)

    Google Scholar 

  3. Rickard, J.T., Aisbett, J., Gibbon, G., Morgenthaler, D.: Fuzzy subsethood for type-n fuzzy sets. In: NAFIPS 2008–2008 Annual Meeting of the North American Fuzzy Information Processing Society (pp. 1–6). IEEE (2008)

  4. Singh, D., Verma, N.K., Ghosh, A.K., Malagaudanavar, A.K.: An approach towards the design of interval type-3 TS fuzzy system. IEEE Trans. Fuzzy Syst. (2021)

  5. Qasem, S.N., Ahmadian, A., Mohammadzadeh, A., Rathinasamy, S., Pahlevanzadeh, B.: A type-3 logic fuzzy system: optimized by a correntropy based Kalman filter with adaptive fuzzy kernel size. Inf. Sci. 572, 424–443 (2021)

    Article  MathSciNet  Google Scholar 

  6. Wang, J.H., Tavoosi, J., Mohammadzadeh, A., Mobayen, S., Asad, J.H., Assawinchaichote, W., Skruch, P.: Non-Singleton type-3 fuzzy approach for flowmeter fault detection: experimental study in a gas industry. Sensors 21(21), 7419 (2021)

    Article  Google Scholar 

  7. Alattas, K.A., Mohammadzadeh, A., Mobayen, S., Aly, A.A., Felemban, B.F.: A new data-driven control system for MEMSs gyroscopes: dynamics estimation by type-3 fuzzy systems. Micromachines 12(11), 1390 (2021)

    Article  Google Scholar 

  8. Cao, Y., Raise, A., Mohammadzadeh, A., Rathinasamy, S., Band, S.S., Mosavi, A.: Deep learned recurrent type-3 fuzzy system: application for renewable energy modeling/prediction. Energy Rep. 7, 8115–8127 (2021)

    Article  Google Scholar 

  9. Tian, M.W., Mohammadzadeh, A., Tavoosi, J., Mobayen, S., Asad, J.H., Castillo, O., Várkonyi-Kóczy, A.R.: A deep-learned type-3 fuzzy system and its application in modeling problems. Acta Polytechnica Hungarica 19(2), 151–172 (2022)

    Article  Google Scholar 

  10. Mohammadzadeh, A., Sabzalian, M.H., Zhang, W.: An interval type-3 fuzzy system and a new online fractional-order learning algorithm: theory and practice. IEEE Trans. Fuzzy Syst. 28(9), 1940–1950 (2019)

    Article  Google Scholar 

  11. Ma, C., Mohammadzadeh, A., Turabieh, H., Mafarja, M., Band, S.S., Mosavi, A.: Optimal type-3 fuzzy system for solving singular multi-pantograph equations. IEEE Access 8, 225692–225702 (2020)

    Article  Google Scholar 

  12. Gheisarnejad, M., Mohammadzadeh, A., Farsizadeh, H., Khooban, M.H.: Stabilization of 5G Telecom Converter-Based Deep Type-3 Fuzzy Machine Learning Control for Telecom Applications. Express Briefs, IEEE Transactions on Circuits and Systems II (2021)

    Google Scholar 

  13. Liu, Z., Mohammadzadeh, A., Turabieh, H., Mafarja, M., Band, S.S., Mosavi, A.: A new online learned interval type-3 fuzzy control system for solar energy management systems. IEEE Access 9, 10498–10508 (2021)

    Article  Google Scholar 

  14. Vafaie, R.H., Mohammadzadeh, A., Piran, M.: A new type-3 fuzzy predictive controller for MEMS gyroscopes. Nonlinear Dyn. 106(1), 381–403 (2021)

    Article  Google Scholar 

  15. Tian, M.W., Yan, S.R., Mohammadzadeh, A., Tavoosi, J., Mobayen, S., Safdar, R., Wudhichai, A., Mai, T.V., Zhilenkov, A.: Stability of interval type-3 fuzzy controllers for autonomous vehicles. Mathematics 9(21), 2742 (2021)

    Article  Google Scholar 

  16. Mohammadzadeh, A., Castillo, O., Band, S.S., Mosavi, A.: A novel fractional-order multiple-model type-3 fuzzy control for nonlinear systems with unmodeled dynamics. Int. J. Fuzzy Syst. 23, 1633–1651 (2021)

    Article  Google Scholar 

  17. Gheisarnejad, M., Mohammadzadeh, A., Khooban, M.: Model predictive control-based type-3 fuzzy estimator for voltage stabilization of DC power converters. IEEE Trans. Ind. Electron. 69, 13849–13858 (2021)

    Article  Google Scholar 

  18. Taghieh, A., Aly, A.A., Felemban, B.F., Althobaiti, A., Mohammadzadeh, A., Bartoszewicz, A.: A hybrid predictive type-3 fuzzy control for time-delay multi-agent systems. Electronics 11(1), 63 (2022)

    Article  Google Scholar 

  19. Yan, S., Aly, A.A., Felemban, B.F., Gheisarnejad, M., Tian, M., Khooban, M.H., Mohammadzadeh, A., Mobayen, S.: A new event-triggered type-3 fuzzy control system for multi-agent systems: optimal economic efficient approach for actuator activating. Electronics 10(24), 3122 (2021)

    Article  Google Scholar 

  20. Nabipour, N., Qasem, S.N., Jermsittiparsert, K.: Type-3 fuzzy voltage management in PV/hydrogen fuel cell/battery hybrid systems. Int. J. Hydrogen Energy 45(56), 32478–33249 (2020)

    Article  Google Scholar 

  21. Castillo, O., Castro, J.R., Melin, P.: Interval type-3 fuzzy logic systems (IT3FLS). In: Interval Type-3 Fuzzy Systems: Theory and Design (pp. 45–98). Springer, Cham (2022)

  22. Castillo, O., Castro, J.R., Melin, P.: A methodology for building interval type-3 fuzzy systems based on the principle of justifiable granularity. Int. J. Intell. Syst. 37, 7909–7943 (2022)

    Article  Google Scholar 

  23. Tian, M.W., Yan, S.R., Liu, J., Alattas, K.A., Mohammadzadeh, A., Vu, M.T.: A new type-3 fuzzy logic approach for chaotic systems: robust learning algorithm. Mathematics 10(15), 2594 (2022)

    Article  Google Scholar 

  24. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

  25. Liang, Q., Mendel, J.M.: Interval type-2 fuzzy logic systems: theory and design. IEEE Trans. Fuzzy Syst. 8(5), 535–550 (2000)

    Article  Google Scholar 

  26. Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14(6), 808–821 (2006)

    Article  Google Scholar 

  27. Wagner, C., Hagras, H.: Toward general type-2 fuzzy logic systems based on zSlices. IEEE Trans. Fuzzy Syst. 18(4), 637–660 (2010). https://doi.org/10.1109/TFUZZ.2010.2045386

    Article  Google Scholar 

  28. Chen, C., Wu, D., Garibaldi, J.M., John, R.I., Twycross, J., Mendel, J.M.: A Comprehensive study of the efficiency of type-reduction algorithms. IEEE Trans. Fuzzy Syst. 29(6), 1556–1566 (2021)

    Article  Google Scholar 

  29. Chen, Y., Wang, D., Ning, W.: Studies on centroid type-reduction algorithms for general type-2 fuzzy logic systems Studies on centroid type-reduction algorithms for general type-2 fuzzy logic systems. Int. J. Innovat. Comput. Inf. Control 11(6), 1987–2000 (2015)

    Google Scholar 

  30. Mendel, J.M., Liu, X.: Simplified interval type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 21(6), 1056–1069 (2013)

    Article  Google Scholar 

  31. Mendel, J.M.: General type-2 fuzzy logic systems made simple: a tutorial. IEEE Trans. Fuzzy Syst. 22(5), 1162–1182 (2013)

    Article  Google Scholar 

  32. Lucas, L.A., Centeno, T.M., & Delgado, M. R. (2007, July). General type-2 fuzzy inference systems: Analysis, design and computational aspects. In: 2007 IEEE International Fuzzy Systems Conference (pp. 1–6). IEEE.

  33. Iancu, I.: A Mamdani type fuzzy logic controller. Fuzzy Logic-Controls Concepts Theories Appl. 15(2), 325–350 (2012)

    Google Scholar 

  34. Mamdani, E.H.: Application of fuzzy algorithms for control of simple dynamic plant. In: Proceedings of the Institution of Electrical Engineers (vol. 121, No. 12, pp. 1585–1588). IET (1974)

  35. Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man Mach. Stud. 7(1), 1–13 (1975)

    Article  MATH  Google Scholar 

  36. Mamdani, E.H.: Advances in the linguistic synthesis of fuzzy controllers. Int. J. Man Mach. Stud. 8(6), 669–678 (1976)

    Article  MATH  Google Scholar 

  37. Zulfikar, W.B., Prasetyo, P.K., Ramdhani, M.A.: Implementation of mamdani fuzzy method in employee promotion system. In: IOP Conference Series: Materials Science and Engineering, vol. 288, no. 1, p. 012147. IOP Publishing (2018)

  38. Chai, Y., Jia, L., Zhang, Z.: Mamdani model based adaptive neural fuzzy inference system and its application. Int. J. Comput. Intell. 5(1), 22–29 (2009)

    Google Scholar 

  39. Karnik, N. N. and J. M. Mendel, J. M. Operations on Type-2 Fuzzy Sets, Fuzzy Sets and Systems, vol. 122, pp. 327– 348, 2001.

  40. Calcev, G.: Some remarks on the stability of Mamdani fuzzy control systems. IEEE Trans. Fuzzy Syst. 6(3), 436–442 (1998)

    Article  MathSciNet  Google Scholar 

  41. Mamdani, E.H.: Application of fuzzy logic to approximate reasoning using linguistic synthesis. IEEE Trans. Comput. 26(12), 1182–1191 (1977)

    Article  MATH  Google Scholar 

  42. King, P.J., Mamdani, E.H.: The application of fuzzy control systems to industrial processes. Automatica 13(3), 235–242 (1977)

    Article  Google Scholar 

  43. Amador-Angulo, L., & Castillo, O.: Comparative study of bio-inspired algorithms applied in the design of fuzzy controller for the water tank. In: Recent Developments and New Direction in Soft-Computing Foundations and Applications, pp. 419–438. Springer, Cham (2016)

  44. Amador-Angulo, L., Castillo, O., Peraza, C., Ochoa, P.: An efficient chicken search optimization algorithm for the optimal design of fuzzy controllers. Axioms 10(1), 30 (2021)

    Article  Google Scholar 

  45. Castillo, O., Amador-Angulo, L.: A generalized type-2 fuzzy logic approach for dynamic parameter adaptation in bee colony optimization applied to fuzzy controller design. Inf. Sci. 460, 476–496 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tijuana Institute of Technology, Calzada Tecnologico s/n, Fracc. Tomas Aquino, 22379, Tijuana, Mexico

    Leticia Amador-Angulo, Oscar Castillo & Patricia Melin

  2. UABC University, Calzada Universidad, s/n, 22379, Tijuana, Mexico

    Juan R. Castro

Authors
  1. Leticia Amador-Angulo
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Oscar Castillo
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Juan R. Castro
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Patricia Melin
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Patricia Melin.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Amador-Angulo, L., Castillo, O., Castro, J.R. et al. A New Approach for Interval Type-3 Fuzzy Control of Nonlinear Plants. Int. J. Fuzzy Syst. 25, 1624–1642 (2023). https://doi.org/10.1007/s40815-023-01470-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-023-01470-9

Keywords