Design and Performance Evaluation of Fractional Order PID Controller for Heat Flow System Using Particle Swarm Optimization

  • Rosy PradhanEmail author
  • Susmita Pradhan
  • Bibhuti Bhusan Pati
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 711)


The purpose of this paper is to apply a natured inspired algorithm called as Particle Swarm Optimization (PSO) for the design of fractional order proportional-integrator-derivative (FOPID) controller for a heat flow system. For the design of FOPID controller, the PSO algorithm is considered as a designing tool for obtaining the optimal values of the controller parameter. To obtain the optimal computation, different performance indices such as IAE (Integral Absolute Error), ISE (Integral Squared Error), ITAE (Integral Time Absolute Error), ITSE (Integral Time Squared Error) are considered for the optimization. All the simulations are carried out in Simulink/Matlab environment. The proposed method has shown better result in both in transient and frequency domain as compared to other published works.


FOPID Performance indices Time domain specification PSO 


  1. 1.
    Lin, H., Su, H., Shu, Z., Wu, Z. G., & Xu, Y. (2016). Optimal estimation in UDP-like networked control systems with intermittent inputs: stability analysis and suboptimal filter design. IEEE Transactions on Automatic Control, 61(7), 1794–1809.Google Scholar
  2. 2.
    Pradhan, R., Patra, P., & Pati, B. B. (2016, September). Comparative studies on design of fractional order proportional integral differential controller. In Advances in Computing, Communications and Informatics (ICACCI), 2016 International Conference on (pp. 424–429). IEEE.Google Scholar
  3. 3.
    Pradhan, J. K., Ghosh, A., & Bhende, C. N. (2017). Small-signal modeling and multivariable PI control design of VSC-HVDC transmission link. Electric Power Systems Research, 144, 115–126.Google Scholar
  4. 4.
    Pradhan, J. K., & Ghosh, A. (2015). Multi-input and multi-output proportional-integral-derivative controller design via linear quadratic regulator-linear matrix inequality approach. IET Control Theory & Applications, 9(14), 2140–2145.Google Scholar
  5. 5.
    Sain, D., Swain, S. K., & Mishra, S. K. (2016). TID and I-TD controller design for magnetic levitation system using genetic algorithm. Perspectives in Science, 8, 370–373.Google Scholar
  6. 6.
    Åström, K. J., & Hägglund, T. (2001). The future of PID control. Control engineering practice, 9(11), 1163–1175.Google Scholar
  7. 7.
    Ogata, Katsuhiko. “Modern control engineering.” (2002): 1.Google Scholar
  8. 8.
    Visioli, A. (2012). Research trends for PID controllers. Acta Polytechnica, 52(5).Google Scholar
  9. 9.
    Tan, W., Liu, J., Chen, T. and Marquez, H. (2006). Comparison of some well-known PID tuning formulas. Computers & Chemical Engineering, 30(9), pp. 1416–1423.Google Scholar
  10. 10.
    Hägglund, T., & Åström, K. J. (2002). Revisiting The Ziegler‐Nichols Tuning Rules For Pi Control. Asian Journal of Control, 4(4), 364–380.Google Scholar
  11. 11.
    Oustaloup, A., 1991. La commande CRONE, Commande robuste d’ordre non entier, Hermes (Traité des Nouvelles Technologies-Série Automatique), Paris. ISBN 2-86601-289-5.Google Scholar
  12. 12.
    Samko, S. G., Kilbas, A. A. and Marichev, O. I., 1993. Fractional integrals and derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.Google Scholar
  13. 13.
    Zamani, M., Karimi-Ghartemani, M., Sadati, N. and Parniani, M., 2009. Design of a fractional order PID controller for an AVR using particle swarm optimization. Control Engineering Practice, 17(12), pp. 1380–1387.CrossRefGoogle Scholar
  14. 14.
    Hamamci, S. E., 2007. An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers. IEEE Transactions on Automatic Control, 52(10), pp. 1964–1969.MathSciNetCrossRefGoogle Scholar
  15. 15.
    Tang, Y., Cui, M., Hua, C., Li, L., & Yang, Y. (2012). Optimum design of fractional order PI λ D μ controller for AVR system using chaotic ant swarm. Expert Systems with Applications, 39(8), 6887–6896.Google Scholar
  16. 16.
    Biswas, A., Das, S., Abraham, A., & Dasgupta, S. (2009). Design of fractional-order PI λ D μ controllers with an improved differential evolution. Engineering applications of artificial intelligence, 22(2), 343–350.Google Scholar
  17. 17.
    Lee, C. H., & Chang, F. K. (2010). Fractional-order PID controller optimization via improved electromagnetism-like algorithm. Expert Systems with Applications, 37(12), 8871–8878.Google Scholar
  18. 18.
    Luo, Y., & Chen, Y. (2009). Fractional order [proportional derivative] controller for a class of fractional order systems. Automatica, 45(10), 2446–2450.Google Scholar
  19. 19.
    Wang, D. J., & Gao, X. L. (2012). H∞ design with fractional-order PDμ controllers. Automatica, 48(5), 974–977.Google Scholar
  20. 20.
    Zamani, M., Karimi-Ghartemani, M., Sadati, N., & Parniani, M. (2009). Design of a fractional order PID controller for an AVR using particle swarm optimization. Control Engineering Practice, 17(12), 1380–1387.Google Scholar
  21. 21.
    Gaing, Z. L. (2004). A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE transactions on energy conversion, 19(2), 384–391.CrossRefGoogle Scholar
  22. 22.
    Panda, S., & Padhy, N. P. (2008). Optimal location and controller design of STATCOM for power system stability improvement using PSO. Journal of the Franklin Institute, 345(2), 166–181.Google Scholar
  23. 23.
    Ramezanian, H., Balochian, S., & Zare, A. (2013). Design of optimal fractional-order PID controllers using particle swarm optimization algorithm for automatic voltage regulator (AVR) system. Journal of Control, Automation and Electrical Systems, 24(5), 601–611.Google Scholar
  24. 24.
    Bingul, Z., & Karahan, O. (2011, April). Tuning of fractional PID controllers using PSO algorithm for robot trajectory control. In Mechatronics (ICM), 2011 IEEE International Conference on (pp. 955–960). IEEE.Google Scholar
  25. 25.
    Bouarroudj, N. (2015). A Hybrid Fuzzy Fractional Order PID Sliding-Mode Controller design using PSO algorithm for interconnected Nonlinear Systems. Journal of Control Engineering and Applied Informatics, 17(1), 41–51.Google Scholar
  26. 26.
    Quanser Innovative edutech. Heat flow laboratory. Ontario: Quancer Inc., 2012.Google Scholar
  27. 27.
    Quanser Innovative edutech. Heat flow experiment: User Manual. Ontario: Quanser Inc., 2009.Google Scholar
  28. 28.
    Al-Saggaf, U., Mehedi, I., Bettayeb, M., & Mansouri, R. (2016). Fractional-order controller design for a heat flow process. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 230(7), 680–691.Google Scholar
  29. 29.
    Gutiérrez, R. E., Rosário, J. M., & Tenreiro Machado, J. (2010). Fractional order calculus: basic concepts and engineering applications. Mathematical Problems in Engineering, 2010.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Rosy Pradhan
    • 1
    Email author
  • Susmita Pradhan
    • 1
  • Bibhuti Bhusan Pati
    • 1
  1. 1.Department of Electrical EngineeringVeer Surendra Sai University of TechnologyBurlaIndia

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