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Fuzzy Algorithms for Fractional PID Control Systems

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 923))

Abstract

This article investigates the use of fuzzy algorithms for fractional PID control systems. The tuning of the fuzzy controllers is based on the prior knowledge of integer or fractional-order control strategy. The suggested fuzzy controllers are fine tuned using a genetic algorithm (GA). The effectiveness and robustness of the proposed methodology is illustrated through its application on the control of a fractional-order plant. The simulation results show the better performance of nonlinear fuzzy algorithms of fractional-order.

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References

  1. Barbosa, R.S., Machado, J.A.T., Silva, M.F.: Time domain design of fractional differintegrators using least-squares. Signal Process. 86, 2567–2581 (2006)

    MATH  Google Scholar 

  2. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  3. Podlubny, I.: Fractional-order systems and pi\(^{\lambda }\)d\(^{\mu }\)-controllers. IEEE Trans. Autom. Control 44, 208–214 (1999)

    MathSciNet  MATH  Google Scholar 

  4. Åström, K.J., Hägglund, T.: pid Controllers: Theory, Design, and Tuning. Instrument Society of America, San Diego (1995)

    Google Scholar 

  5. Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)

    MATH  Google Scholar 

  6. Lee, C.C.: Fuzzy logic in control systems: fuzzy logic controller - Part I & II. IEEE Trans. Syst. Man Cybern. 20, 404–435 (1990)

    MATH  Google Scholar 

  7. Li, H.-H., Gatland, H.B.: Conventional fuzzy control and its enhancement. IEEE Trans. Syst. Man Cybern.-Part B: Cybern. 26, 791–797 (1996)

    Google Scholar 

  8. Mann, G.K.I., Hu, B.-G., Gosine, R.G.: Analysis of direct action fuzzy PID controller structure. IEEE Trans. Syst. Man Cybern.-Part B: Cybern. 29, 371–388 (1999)

    Google Scholar 

  9. Passino, K.M., Yurkovich, S.: Fuzzy Control. Addison-Wesley, Menlo Park (1998)

    MATH  Google Scholar 

  10. Mizumoto, M.: Realization of PID controls by fuzzy control methods. J. Fuzzy Sets Syst. 70, 171–182 (1995)

    MathSciNet  MATH  Google Scholar 

  11. Carvajal, J., Chen, G., Ogmen, H.: Fuzzy PID controller: design performance evaluation, and stability analysis. Inf. Sci. 123, 249–270 (2000)

    MathSciNet  MATH  Google Scholar 

  12. Eker, I., Torun, Y.: Fuzzy logic control to be conventional methods. J. Energy Convers. Manage. 47, 377–394 (2006)

    Google Scholar 

  13. Jesus, I.S., Barbosa, R.S.: Genetic optimization of fuzzy fractional PD+I controllers. ISA Trans. 57, 220–230 (2015)

    Google Scholar 

  14. Machado, J.A.T.: Analysis and design of fractional-order digital control systems. SAMS J. Syst. Anal. Model. Simul. 27, 107–122 (1997)

    MATH  Google Scholar 

  15. Chen, Y.Q., Vinagre, B., Podlubny, I.: Continued fraction expansion to discretize fractional order derivatives-an expository review. Nonlinear Dyn. 38, 155–170 (2004)

    MATH  Google Scholar 

  16. Jantzen, J.: Foundations of Fuzzy Control. Wiley and Sons, Chichester (2007)

    Google Scholar 

Download references

Acknowledgements

This work is supported by FEDER Funds through the “Programa Operacional Factores de Competitividade - COMPETE” program and by National Funds through FCT “Fundação para a Ciência e a Tecnologia” under the project UID/EEA/00760/2013.

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Correspondence to Ramiro S. Barbosa .

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Barbosa, R.S., Jesus, I.S. (2020). Fuzzy Algorithms for Fractional PID Control Systems. In: Madureira, A., Abraham, A., Gandhi, N., Varela, M. (eds) Hybrid Intelligent Systems. HIS 2018. Advances in Intelligent Systems and Computing, vol 923. Springer, Cham. https://doi.org/10.1007/978-3-030-14347-3_42

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