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Implementation of Fractional Order PID Controller for Three Interacting Tank Process Optimally Tuned Using Bee Colony Optimization

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Swarm, Evolutionary, and Memetic Computing (SEMCCO 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8297))

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Abstract

The proposed work demonstrates the application of Bee Colony Optimization (BCO) technique for the tuning of Fractional Order Proportional-Integral-Derivative (FOPID) controller for Three Interacting Tank system. FOPID controller parameters are composed of proportionality constant, integral constant, integral order, derivative constant and derivative order. Grunwald-Letnikov definition is used for the defining the derivative controller and Oustaloup’s filter technique is used for the approximation of the function. Tuning FOPID controller parameters is more complicated as it involves a five dimensional search. Tuning is effected using an evolutionary optimization technique, the bee colony optimization so as to minimize the Integral Time Absolute Error (ITAE). The proposed technique is used to control three interacting tank process. The proposed FOPID controller tuned using Bee colony optimization technique may serve as an alternative for the tuning of the fractional order controllers.

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References

  1. Gement, A.: On fractional differentials. Proc. Philosophical Magazine 25, 540–549 (1938)

    Google Scholar 

  2. Méhauté, A.L.: Fractal Geometries: Theory and Applications. Penton Press (1991)

    Google Scholar 

  3. Oustaloup, A.: La Commande CRONE: Commande Robust Order Non Intiger. Hermes (1991)

    Google Scholar 

  4. Podlubny, I.: Fractional Diferential Equations. Academic Press, San Diego (1999)

    Google Scholar 

  5. Tenreiro Machado, J.A.: System modelling and control through fractional-order algorithms. FCAA – Journal of Fractional Calculus and Ap. Analysis 4, 47–66 (2001)

    MATH  MathSciNet  Google Scholar 

  6. Torvik, P.J., Bagley, R.L.: On the appearance of the fractional derivative in the behaviour of real materials. ASME Journal of Applied Mechanics 51, 294–298 (1984)

    Article  MATH  Google Scholar 

  7. Vinagre, B.M., Petras, I., Podlubny, I., Chen, Y.Q.: Using fractional order adjustment rules and fractional order reference models in model-reference adaptive control. Nonlinear Dynamics 29, 269–279 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  8. Westerlund, S.: Dead Matter Has Memory. Causal Consulting Kalmar, Sweden (2002)

    Google Scholar 

  9. Astrom, K., Hagglund, T.: PID Controllers: Theory, Design and Tuning. Instrument Society of America, Research Triangle Park (1995)

    Google Scholar 

  10. Cao, J., Liang, J., Cao, B.: Optimization of fractional order PID controllers based on genetic algorithms. In: Proceedings of the International Conference on Machine Learning and Cybernetics, Guangzhou, August 18-21 (2005)

    Google Scholar 

  11. Caputo, M.: Linear model of dissipation whose Q is almost frequency independent—II. Geophysical Journal of the Royal Astronomical Society 13, 529–539 (1967)

    Article  Google Scholar 

  12. Caputo, M.: Elasticitae Dissipacione. Zanichelli, Bologna (1969)

    Google Scholar 

  13. Chengbin, M., Hori, Y.: The application of fractional order PID controller for robust two-inertia speed control. In: Proceedings of the 4th International Power Electronics and Motion Control Conference. Xi’an (August 2004)

    Google Scholar 

  14. Lubich, C.H.: Discretized fractional calculus. SIAM Journal on Mathematical Analysis 17(3), 704–719 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  15. Mozaffari, A., Gorji-Bandpy, M., Gorji, T.B.: Optimal design of constraint engineering systems: application of mutable smart bee algorithm. International Journal of Bio-inspired Computation 4(3), 167–180 (2012)

    Article  Google Scholar 

  16. Panda, R., Dash, M.: Fractional generalized splines and signal processing. Signal Processing 86(9), 2340–2350 (2006)

    Article  MATH  Google Scholar 

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Sabura Banu, U. (2013). Implementation of Fractional Order PID Controller for Three Interacting Tank Process Optimally Tuned Using Bee Colony Optimization. In: Panigrahi, B.K., Suganthan, P.N., Das, S., Dash, S.S. (eds) Swarm, Evolutionary, and Memetic Computing. SEMCCO 2013. Lecture Notes in Computer Science, vol 8297. Springer, Cham. https://doi.org/10.1007/978-3-319-03753-0_37

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  • DOI: https://doi.org/10.1007/978-3-319-03753-0_37

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03752-3

  • Online ISBN: 978-3-319-03753-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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