From single to many-objective PID controller design using particle swarm optimization

  • Hélio Freire
  • P. B. Moura Oliveira
  • E. J. Solteiro Pires
Regular Papers Intelligent Control and Applications


Proportional, integrative and derivative (PID) controllers are among the most used in industrial control applications. Classical PID controller design methodologies can be significantly improved by incorporating recent computational intelligence techniques. Two techniques based on particle swarm optimization (PSO) algorithms are proposed to design PI-PID controllers. Both control design methodologies are directed to optimize PI-PID controller gains using two degrees-of-freedom control configurations, subjected to frequency domain robustness constraints. The first technique proposes a single-objective PSO algorithm, to sequentially design a two degrees-of-freedom control structure, considering the optimization of load disturbance rejection followed by set-point tracking optimization. The second technique proposes a many-objective PSO algorithm, to design a two degrees-of-freedom control structure, considering simultaneously, the optimization of four different design criteria. In the many-objective case, the control engineer may select the most adequate solution among the resulting optimal Pareto set. Simulation results are presented showing the effectiveness of the proposed PI-PID design techniques, in comparison with both classic and optimization based methods.


Evolutionary algorithms many-objective optimization particle swarm optimization PID control 


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  1. [1]
    A. O’Dwyer, Handbook of PI and PID Controller Tuning Rules, 2nd Edition, Imperial College Press, 2006.CrossRefzbMATHGoogle Scholar
  2. [2]
    D. Vrančić, S. Strmčnik and Ð. Juričić, “A magnitude optimum multiple integration tuning method for filtered PID controller,” Automatica, vol. 37, no. 9, pp. 1473–1479, 2001. [click]CrossRefzbMATHGoogle Scholar
  3. [3]
    K. J. Åström and T. Hägglund, “The future of PID control,” Control Engineering Practice, vol. 9, no. 11, pp. 1163–1175, 2001.CrossRefGoogle Scholar
  4. [4]
    S. Skogestad, “Simple analytic rules for model reduction and PID controller tuning,” Modeling, Identification and Control, vol. 25, no. 2, pp. 85–120, 2004. [click]MathSciNetCrossRefGoogle Scholar
  5. [5]
    M. G. Lin, S. Lakshminarayanan, and G. P. Rangaiah, “A Comparative Study of Recent/Popular PID Tuning Rules for Stable, First-Order Plus Dead Time, Single-Input Single-Output Processes,” Industrial & Engineering Chemistry Research, vol. 47, no. 2, pp. 344–368, 2008. [click]CrossRefGoogle Scholar
  6. [6]
    W. Cho, J. Lee, and T. F. Edgar, “Simple Analytic Proportional-Integral-Derivative (PID) Controller Tuning Rules for Unstable Processes,” Industrial & Engineering Chemistry Research, vol. 53, no. 13, pp. 5048–5054, 2014. [click]CrossRefGoogle Scholar
  7. [7]
    M. Hast, K. J. Åström, B. Bernhardsson, S. Boyd, “PID design by convex-concave optimization,” Proc. of Control Conference (ECC), 2013 European, IEEE, pp. 4460–4465, July 2013.Google Scholar
  8. [8]
    C. M. Fonseca and P. J. Fleming, “Multiobjective optimal controller design with genetic algorithms,” Proc. of Control, 1994. Control’ 94. International Conference on, vol. 1, pp. 745–749, March 1994.Google Scholar
  9. [9]
    A. H. Jones and P. B. de Moura Oliveira, “Genetic autotuning of PID controllers,” Proc. of Genetic Algorithms in Engineering Systems: Innovations and Applications, 1995. GALESIA. First International Conference on (Conf. Publ. No. 414), pp. 141–145, Sheffield, September 1995.Google Scholar
  10. [10]
    A. Herreros, E. Baeyens, and J. R. Perán, “Design of PIDtype controllers using multiobjective genetic algorithms,” ISA Transactions, vol. 41, no. 4, pp. 457–472, 2002. [click]CrossRefGoogle Scholar
  11. [11]
    P. B. de Moura Oliveira, “Modern heuristics review for PID control optimization: a teaching experiment,” Proc. of Control and Automation, 2005. ICCA’ 05. International Conference on, vol. 2, pp. 828–833, June 2005.CrossRefGoogle Scholar
  12. [12]
    P. B. de Moura Oliveira, J. B. Cunha, and J. P. Coelho, “Design of PID controllers using the particle swarm algorithm,” Proc. of IASTED MIC’2002, pp. 263–268, Innsbruck, Austria, February 2002.Google Scholar
  13. [13]
    J.-Y. Cao and B.-G. Cao, “Design of fractional order controllers based on particle swarm optimization,” International Journal of Control, Automation, and Systems, vol. 4, no. 6, pp. 775–781, 2006.Google Scholar
  14. [14]
    P. B. de Moura Oliveira, E. J. Solteiro Pires, J. B. Cunha, and D. Vrančić, “Multi-Objective Particle Swarm Optimization Design of PID Controllers”, Distributed Computing, Artificial Intelligence, Bioinformatics, Soft Computing, and Ambient Assisted Living, Springer Berlin Heidelberg, vol. 5518 of the series Lecture Notes in Computer Science, editor S. Omatu and et. al., pp. 1222–1230, 2009.CrossRefGoogle Scholar
  15. [15]
    S.-Z. Zhao, M. W. Iruthayarajan, S. Baskar, and P. N. Suganthan, “Multi-objective robust {PID} controller tuning using two lbests multi-objective particle swarm optimization,” Information Sciences, vol. 181, no. 16, pp. 3323–3335, 2011. [click]CrossRefGoogle Scholar
  16. [16]
    R. Dong, “Differential evolution versus particle swarm optimization for PID controller design,” Proc. of Natural Computation, 2009. ICNC’ 09. Fifth International Conference on, vol. 3, pp. 236–240, August 2009.Google Scholar
  17. [17]
    P. B. de Moura Oliveira, E. J. Solteiro Pires, and P. Novais, “Gravitational Search Algorithm Design of Posicast PID Control Systems,” Soft Computing Models in Industrial and Environmental Applications, Springer International Publishing, vol. 188 of the series Advances in Intelligent Systems and Computing, editor V. Snášel, pp. 191–199, 2013.CrossRefGoogle Scholar
  18. [18]
    P. B. de Moura Oliveira, H. Freire, E. J. Solteiro Pires, and J. B. Cunha, “Bridging Classical Control with Nature Inspired Computation Through PID Robust Design,” Proc. of 10th International Conference on Soft Computing Models in Industrial and Environmental Applications, Springer International Publishing, vol. 368 of the series Advances in Intelligent Systems and Computing, editor A. Herreno et. al., pp. 307–316, 2015.Google Scholar
  19. [19]
    H. Freire, P. B. de Moura Oliveira, E. J. Solteiro Pires, and M. Bessa, “Many-Objective PSO PID Controller Tuning,” Controlo’2014-Proceedings of the 11th Portuguese Conference on Automatic Control, Springer International Publishing, vol. 321 of the series Lecture Notes in Electrical Engineering, editor A. P. Moureira et. al., pp. 183–192, 2015.Google Scholar
  20. [20]
    I. Chiha, N. Liouane, and P. Borne, “Tuning PID Controller Using Multiobjective Ant Colony Optimization,” Proc. of Appl. Comp. Intell. Soft Computing, vol. 2012, 2012.Google Scholar
  21. [21]
    V. Rajinikanth and K. Latha, “Tuning and retuning of PID controller unstable systems using evolutionary algorithm,” Appl. Comp. Intell. Soft Comput., vol. 2012, 2012.Google Scholar
  22. [22]
    H. Freire, P. B. de Moura Oliveira, E. J. Solteiro Pires, and M. Bessa, “Many-objective optimization with corner-based search,” Memetic Computing, Springer Berlin Heidelberg, vol. 7, no. 2, pp. 105–118, 2015.CrossRefGoogle Scholar
  23. [23]
    K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002.CrossRefGoogle Scholar
  24. [24]
    A. J. Nebro, J. J. Durillo, J. Garcia-Nieto, C. A. Coello Coello, F. Luna, and E. Alba, “SMPSO: A new PSO-based metaheuristic for multi-objective optimization,” Proc. of Computational intelligence in miulti-criteria decisionmaking, 2009. MCDM’ 09. IEEE symposium on, pp. 66–73, 2009.CrossRefGoogle Scholar
  25. [25]
    S. Kukkonen and J. Lampinen, “GDE3: the third evolution step of generalized differential evolution,” Evolutionary Computation, 2005. The 2005 IEEE Congress on, vol. 1, pp. 443–450, 2005.CrossRefGoogle Scholar
  26. [26]
    V. R. Segovia, Vanessa, T. Hägglund, and K. J. Åström, “Noise filtering in PI and PID Control,” 2013 American Control Conference, IEEE, pp. 1763–1770, 2013.CrossRefGoogle Scholar
  27. [27]
    Hägglund, T., “Signal Filtering in PID Control,” IFAC Conf. Advances in PID Control, vol. 12, 2012.Google Scholar
  28. [28]
    M. Araki and H. Taguchi, H., “Two-Degree-of-Freedom PID Controllers,” International Journal of Control, Automation, and Systems, vol. 1, no. 4, pp. 401–411, 2003.Google Scholar
  29. [29]
    K. J. Åström and T. Hägglund, “PID Control,” The Control Handbook, Edit. Levine W. S., CRC-IEE Press, pp. 198–208, 1996.Google Scholar
  30. [30]
    O. Smith, Feedback Control Systems, McGraw-Hill, pp. 198–208, 1958.Google Scholar
  31. [31]
    G. F. Franklin, D. J. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, Prentice Hall PTR, 4th edition, 2001.zbMATHGoogle Scholar
  32. [32]
    J. Kennedy and R. Eberhart, “Particle swarm optimization,” Neural Networks, 1995. Proceedings., IEEE International Conference on, IEEE, Australia, vol. 4, pp. 1942–1948, 1995.Google Scholar
  33. [33]
    X. Chen and Y. M. Li, “On convergence and parameter selection of an improved particle swarm optimization,” International Journal of Control Automation and Systems, vol. 6, no. 4, pp. 559–570, 2008.Google Scholar
  34. [34]
    G. Shahgholian, A. Movahedi, and J. Faiz, “Coordinated design of TCSC and PSS controllers using VURPSO and Genetic algorithms for multi-machine power system stability,” International Journal of Control, Automation and Systems, vol. 13, no. 2, pp. 398–409, 2014. [click]CrossRefGoogle Scholar
  35. [35]
    J. C. Bansal, P. K. Singh, M. Saraswat, A. Verma, S. S. Jadon, and A. Abraham, “Inertia weight strategies in particle swarm optimization,” Proc. of Nature and Biologically Inspired Computing (NaBIC), 2011 Third World Congress on, pp. 633–640, 2011.CrossRefGoogle Scholar
  36. [36]
    C. A. Coello Coello, G. L. Lamont, and D. A. van Veldhuizen, Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edition, Springer, series of the Genetic and Evolutionary Computation, 2007.zbMATHGoogle Scholar
  37. [37]
    E. J. Solteiro Pires, P. B. de Moura Oliveira, and J. A. Tenreiro Machado, “Multi-objective MaxiMin Sorting Scheme,” Evolutionary Multi-Criterion Optimization, series of the Lecture Notes in Computer Science, Springer Berlin Heidelberg, editors C. A. Coello Coello et. al., vol. 3410, pp. 165–175, 2005.CrossRefGoogle Scholar
  38. [38]
    K. Deb, Multi-Objective Optimization using Evolutionary Algorithms, John Wiley & Sons, UK, 2001.zbMATHGoogle Scholar
  39. [39]
    C. C. Coello, G. B. Lamont, and D. A. Van Veldhuizen, Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation), Springer-Verlag New York, Inc., USA, 2006.zbMATHGoogle Scholar
  40. [40]
    G. Cohen and G. Coon, “Theoretical consideration of retarded control,” Trans. of American society of Mechanical Engineers, ASME 75, pp. 827–834, 1953.Google Scholar
  41. [41]
    P. W. Murrill, “Automatic Control of Processes,” International Textbooks in Chemical Engineering, International Textbook Company, 1967.Google Scholar
  42. [42]
    D. Vrančić, S. Strmčnik, J. Kocijan, and P. B. de Moura Oliveira, “Improving disturbance rejection of PID controllers by means of the magnitude optimum method,” ISA Transactions, vol. 49, no. 1, pp. 47–56, 2010.CrossRefGoogle Scholar
  43. [43]
    K. R. Sundaresan and P. R. Krishnaswamy, “Estimation of time delay time constant parameters in time, frequency, and laplace domains,” The Canadian Journal of Chemical Engineering, Wiley Subscription Services, Inc., A Wiley Company, vol. 56, no. 2, pp. 257–262, 1978.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Hélio Freire
    • 1
  • P. B. Moura Oliveira
    • 1
  • E. J. Solteiro Pires
    • 1
  1. 1.School of Sciences and Technology, INESC-TEC - UTAD poleUTAD UniversityVila RealPortugal

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