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Design of Adaptive Fractional-Order PID Controller to Enhance Robustness by Means of Adaptive Network Fuzzy Inference System

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Abstract

In this paper, a tuning strategy for the design of fractional-order proportional–integral–derivative (PI λ D µ) controllers is proposed. First, a PI λ D µ controller is designed with genetic algorithm in order to obtain the training data. Then, three Adaptive Network Fuzzy Inference System (ANFIS) structures, related to K p , K i and K d parameters of the PI λ D µ controller, are formed by using the training data. These ANFIS structures are used in the PI λ D µ controller instead of K p , K i and K d parameters, and they are capable of self-tuning during the simulation based on the input signal of the adaptive PI λ D µ controller (ANFIS–PI λ D µ). Finally, in order to show the control performance and robustness of the proposed parameters adjustment method with ANFIS, simulation results are obtained by using the MATLAB–Simulink program for two different systems and the results obtained from ANFIS–PI λ D µ controller are compared with the results of PI λ D µ and fuzzy logic controller.

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References

  1. Ziegler, J.G., Nichols, N.B.: Optimum settings for automatic controllers. Trans. ASME 64, 759–765 (1942)

    Google Scholar 

  2. Ǻström, K.J., Häggland, T., Hang, C.C., Ho, W.K.: Automatik tuning and adaptation for PID controllers—a survey. Control Eng. Pract. 1, 699–714 (1993)

    Article  Google Scholar 

  3. Ǻström, K.J., Häggland, T.: PID Controllers: Theory, Design, and Tuning. Instrument Society of America, USA (1995)

    Google Scholar 

  4. Zhuang, M., Atherton, D.P.: Automatic tuning of optimum PID controllers. IEE Proc. 140, 216–224 (1993)

    Article  MATH  Google Scholar 

  5. Zhao, C.N., Zhang, X.: The application of fractional-order PID controller to position servomechanism. In: Proceedings of the 7th World Congress on Intelligent Control and Automation, Chongqing, China, 25–27 June 2008

  6. Valério, D., da Costa, J.S.: Fractional-order control of a flexible robot. In: Le Mehaute, A., Tenreiro, J.A., Trigeassou, J.C., Sabatier, J. (eds.) Fractional Differentiation and Its Applications. Ubooks, Diedorf (2005)

    Google Scholar 

  7. Ferreira, F.N.M., Machado, T.J.A., Cunha, B.J.: Fractional-order position/force control. J. Adv. Comput. Intell. Intell. Inform. 9(4), 379–385 (2005)

    Article  Google Scholar 

  8. Amit, S.C., Swapnil, W.K., Junghare, A.S., Aware, M.V.: Fractional order speed controller for buck-converter fed DC motor. In: IEEE First International Conference on Control, Measurement and Instrumentation (CMI), pp. 331–335 (2016)

  9. Khubalkar, S.W., Chopade, A.S., Junghare, A.S., Aware, M.V.: Design and tuning of fractional order PID controller for speed control of permanent magnet brushless DC motor. In: IEEE First International Conference on Control, Measurement and Instrumentation (CMI), pp. 326–330 (2016)

  10. Mishra, P., Kumar, V., Rana, K.P.S.: A fractional order fuzzy PID controller for binary distillation column control. Expert Syst. Appl. 42, 8533–8549 (2015)

    Article  Google Scholar 

  11. Lazarević, M.P., Batalov, S.A., Latinović, T.S.: Fractional PID controller tuned by genetic algorithms for a three DOF’s robot system driven by DC motors. In: 6th Workshop on Fractional Differentiation and Its Applications, pp. 385–395, 4–6 February 2013

  12. Folea, S., Muresan, C.I., Keyser, R.D., Ionescu, C.M.: Theoretical analysis and experimental validation of a simplified fractional order controller for a magnetic levitation system. IEEE Trans. Control Syst. Technol. 24, 756–763 (2015)

    Google Scholar 

  13. Valério, D., Costa, J.S.: Tuning of fractional PID controllers with Zeigler–Nichols-type rules. Sig. Process. 86, 2771–2784 (2006)

    Article  MATH  Google Scholar 

  14. Caponetto, R., Fortuna, L., Porto, D.: Parameter tuning of a non integer order PID controller. In: Electronic Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems

  15. Chen, Y.Q., Moore, K.L.: Discretization schemes for fractional-order differentiators and integrators. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 49(3), 363–367 (2002)

    Article  MathSciNet  Google Scholar 

  16. Valério, D., da Costa, J.S.: Tuning-rules for fractional PID controllers. In: 2nd IFAC Workshop on Fractional Differentiation and Its Applications 06, Porto, July 2006

  17. Arpacı, H., Özgüven, Ö.F.: ANFIS and PI λ D μ controller design and comparison for overhead cranes. Indian J. Eng. Mater. Sci. 18, 191–203 (2011)

    Google Scholar 

  18. Hou, Y., Zhang, J., Zhang, Y., Chen, L.: Integrated chassis control using ANFIS. In: Proceedings of the IEEE International Conference on Automation and Logistics Qingdao, China, September 2008

  19. Bingül, Z., Karahan, O.: Fractional PID controllers tuned by evolutionary algorithms for robot trajectory control. Turk. J. Electr. Eng. Comput. Sci. 20, 1123–1136 (2012)

    Google Scholar 

  20. Li, Y., Tong, S., Li, T.: Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems. IEEE Trans. Cybern. 45(1), 138–149 (2015)

    Article  Google Scholar 

  21. Li, Y., Tong, S.: Adaptive fuzzy output-feedback control of pure-feedback uncertain nonlinear systems with unknown dead-zone. IEEE Trans. Fuzzy Syst. 22(5), 1341–1347 (2014)

    Article  Google Scholar 

  22. Mann, G.K.I., Hu, B.G., Gosine, R.G.: Analysis of direct action fuzzy PID controller structures. IEEE Trans. Syst. Man Cybern. Part B 29(3), 371–388 (1999)

    Article  Google Scholar 

  23. Akbıyık, B., Eksin, İ., Güzelkaya, M., Yeşil, E.: Evaluation of the performance of various fuzzy PID controller structures on benchmark systems. In: ELECO ‘2005, 4th International Conference on Electrical and Electronics Engineering, Bursa, Turkey (2005)

  24. Chang, L.Y., Chen, H.C.: Tuning of fractional PID controllers using adaptive genetic algorithm for active magnetic bearing system. WSEAS Trans. Syst. 8, 226–236 (2009)

    Google Scholar 

  25. Xue, D., Zhao, C., Chen,Y.Q.: A modified approximation method of fractional order system. In: Proceedings of the 2006 IEEE International Conference on Mechatronics and Automation, Luoyang, China, 25–28 June 2006

  26. Das, S.: Functional Fractional Calculus for System Identification and Controls. Springer, Berlin (2008)

    MATH  Google Scholar 

  27. Vinagre, B.M., Chen, Y.Q., Petras, I.: Two direct tustin discretization methods for fractional-order differentiator/integrator. J. Franklin Inst. 340, 349–362 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  28. Cao, J.Y, Liang, J., Cao, B.G.: Optimization of fractional order PID controllers based on generic algorithm. In: 2005 International Conference on Machine Learning and Cybernetics, vol. 9, pp. 5686–5689, 18–21 Aug 2005

  29. Podlubny, I.: Fractional-order systems and PI λ D μ controllers. IEEE Trans. Autom. Control 44, 208–214 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  30. Petras, I.: Control quality enhancement by fractional-order controllers. Acta Montan. Slovaca 3(2), 143–148 (1998)

    MathSciNet  Google Scholar 

  31. Monje, C.A., Calderon, A.J., Vinegre, B.M., Chen, Y., Feliu, V.: On fractional PI λ controllers: some tuning rules for robustness to plant uncertainties. Nonlinear Dyn. 38(1–2), 369–381 (2004)

    Article  MATH  Google Scholar 

  32. Buckley, J.J., Hayashi, Y.: Fuzzy neural networks: a survey. Fuzzy Sets Syst. 66, 1–13 (1994)

    Article  MathSciNet  Google Scholar 

  33. Buckley, J.J., Hayashi, Y.: Neural networks for fuzzy systems. Fuzzy Sets Syst. 71, 265–276 (1995)

    Article  Google Scholar 

  34. Nauck, D., Klawonn, F., Kruse, R.: Foundations of neuro-fuzzy systems. Wiley, Chichester (1997)

    MATH  Google Scholar 

  35. Nauck, D., Kruse, R.: Designing neuro-fuzzy systems through backpropagation. In: Pedrycz, W. (ed.) Fuzzy Modelling: Paradigms and Practice, pp. 203–228. Kluwer, Boston (1996)

    Chapter  Google Scholar 

  36. Lee, C.C.: Fuzzy logic in control systems: fuzzy logic controller, Part 1–2. IEEE Trans. Syst. Man Cybern. 20(2), 404–435 (1990)

    Article  MATH  Google Scholar 

  37. Takagi, T., Sugeno, M.: Derivation of fuzzy control rules from human operator’s control actions. In: Proceedings IFAC Symposium on Fuzzy Information, Knowledge Representation and Decision Analysis, pp. 55–60, July 1983

  38. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. SMC-15, 116–132 (1985)

    Article  MATH  Google Scholar 

  39. Jang, J.-S.R.: ANFIS: adaptive-network-based fuzzy inference systems. IEEE Trans. Syst. Man Cybern. 23, 665–685 (1993)

    Article  Google Scholar 

  40. Zhang, Y., Li., J.: Fractional-order PID controller tuning based on genetic algorithm. In: 2011 International Conference on Business Management and Electronic Information (BMEI), vol. 3, pp. 764–767, 13–15 May 2011

  41. http://ctms.engin.umich.edu/CTMS/index.php?example=MotorSpeed&section=SystemModeling. Accessed in 2016

  42. http://www.mathworks.com/matlabcentral/fileexchange/36508-fuzzy-controller-based-speed-control-of-dc-motor/all_files. Accessed in 2016

  43. Huang, J.J., DeBra, D.B.: Liquid temperature control for a hydraulic turning machine. IEEE Control Syst. 17(4), 55–63 (1997)

    Article  Google Scholar 

  44. Duka, A.V., Oltean, S.E.: Fuzzy control of a heat exchanger. In: 2012 IEEE International Conference on Automation Quality and Testing Robotics (AQTR), pp. 135–139, 24–27 May 2012

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Authors and Affiliations

  1. Department of Computer and Instructional Technology, Inonu University, Malatya, Turkey

    Huseyin Arpaci

  2. Department of Biomedical Engineering, Inonu University, Malatya, Turkey

    Omerul Faruk Ozguven

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  1. Huseyin Arpaci
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  2. Omerul Faruk Ozguven
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Correspondence to Huseyin Arpaci.

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Arpaci, H., Ozguven, O.F. Design of Adaptive Fractional-Order PID Controller to Enhance Robustness by Means of Adaptive Network Fuzzy Inference System. Int. J. Fuzzy Syst. 19, 1118–1131 (2017). https://doi.org/10.1007/s40815-016-0283-9

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  • DOI: https://doi.org/10.1007/s40815-016-0283-9

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