Design of an H PID controller using particle swarm optimization

  • Majid Zamani
  • Nasser Sadati
  • Masoud Karimi Ghartemani
Regular Papers Intelligent and Information Systems


This paper proposes a novel method to designing an H PID controller with robust stability and disturbance attenuation. This method uses particle swarm optimization algorithm to minimize a cost function subject to H -norm to design robust performance PID controller. We propose two cost functions to design of a multiple-input, multiple-output (MIMO) and single-input, single-output (SISO) robust performance PID controller. We apply this method to a SISO flexible-link manipulator and a MIMO super maneuverable F18/HARV fighter aircraft system as two challenging examples to illustrate the design procedure and to verify performance of the proposed PID controller design methodology. It is shown with the MIMO super maneuverable F18/HARV fighter system that PSO performs well for parametric optimization functions and performance of the PSO-based method without prior domain knowledge is superior to those of existing GA-based and OSA-based methods for designing H PID controllers.


Genetic algorithm H-optimal controller particle swarm optimization PID controller simulated annealing 


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  1. [1]
    M. J. Balas, “Feedback control of flexible systems,” IEEE Trans. on Automat. Contr., vol. 23, no. 4, pp. 673–679, Aug. 1978.zbMATHCrossRefGoogle Scholar
  2. [2]
    J. C. Doyle, K. Glover, P. Khargonekar, and B. A. Francis, “State space solutions to standard H 2 and H control problems,” IEEE Trans. on Automat. Contr., vol. AC-34, pp. 831–847, Aug. 1989.CrossRefMathSciNetGoogle Scholar
  3. [3]
    G. J. Balas, J. C. Doyle, K. Glover, A. Packard, and R. Smith, μ-Analysis and Synthesis ToolBox, Mathworks, Natick, MA, 1993.Google Scholar
  4. [4]
    R. S. Smith, C. C. Chu, and J. L. Fanson “The design of H controllers for an experimental noncollocated flexible structure problem,” IEEE Trans. on Control Systems Technology, vol. 2, no. 2, pp. 101–109, Mar. 1994.CrossRefGoogle Scholar
  5. [5]
    G. J. Balas and J. C. Doyle, “Robustness and performance trade-offs in control design for flexible structures,” IEEE Trans. on Control Systems Technology, vol. 2, no. 4, pp. 352–361, Dec. 1994.CrossRefGoogle Scholar
  6. [6]
    I. N. Kar, T. Miyakura, and K. Seto, “Bending and torsional vibration control of a flexible plate structure using H -based robust control law,” IEEE Trans. on Control Systems Technology, vol. 8, no. 3, pp. 545–553, May 2000.CrossRefGoogle Scholar
  7. [7]
    V. D. Blondel and J. N. Tsitsiklis, “A survey of computational complexity results in systems and control,” Automatica, vol. 36, pp. 1249–1274, Sep. 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    G. J. Silva, A. Datta, and S. P. Bhattacharyya, “New results on the synthesis of PID controllers,” IEEE Trans. on Automat. Contr., vol. 47, no. 2, pp. 241–252, Feb.2002.CrossRefMathSciNetGoogle Scholar
  9. [9]
    H. Xu, A. Datta, and S. P. Bhattacharyya, “Computation of all stabilizing PID gains for digital control systems,” IEEE Trans. on Automat. Contr., vol. 46, no. 4, pp. 647–652, Apr. 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    L. H. Keel, J. I. Rego, and S. P. Bhattacharyya, “A new approach to digital PID controller design,” IEEE Trans. on Automat. Contr., vol. 48, no. 4, pp. 687–692, Apr. 2003.CrossRefMathSciNetGoogle Scholar
  11. [11]
    M. T. Ho and C. Y. Lin, “PID controller design for robust performance,” IEEE Trans. on Automat. Contr., vol. 48, no. 8, pp. 1404–1409, Aug. 2003.CrossRefMathSciNetGoogle Scholar
  12. [12]
    F. Blanchini, A. Lepschy, S. Miani, and U. Viaro “Characterization of PID and Lead/Lag compensators satisfying given H specifications,” IEEE Trans. on Automat. Contr., vol. 49, no. 5, pp. 736–740, May 2004.CrossRefMathSciNetGoogle Scholar
  13. [13]
    S. J. Ho, S. Y. Ho and L. S. Shu, “OSA: orthogonal simulated annealing algorithm and its application to designing mixed H 2/H optimal controllers,” IEEE Trans. Sys. Man and Cyber., vol. 34, no. 5, pp. 588–600, Sep. 2004.CrossRefGoogle Scholar
  14. [14]
    R. A. Krohling and J. P. Rey, “Design of optimal disturbance rejection PID controllers using genetic algorithm,” IEEE Trans. Evol. Comp., vol. 5, no. 1, pp. 78–82, Feb. 2001.CrossRefGoogle Scholar
  15. [15]
    B. S. Chen and Y. M. Cheng, “A structure-specified H optimal control design for practical applications: a genetic approach,” IEEE Trans. Control Sys. Tech., vol. 6, no. 6, pp. 707–718, Nov. 1998.CrossRefGoogle Scholar
  16. [16]
    B. S. Chen, Y. M. Cheng, and C. H. Lee, “A genetic approach to mixed optimal PID control,” IEEE Control Sys. Mag., vol. 15, pp. 51–60, Oct. 1995.CrossRefGoogle Scholar
  17. [17]
    J. Kennedy, “The particle swarm: social adaptation of knowledge,” Proc. IEEE Int. Conf. Evolutionary Comput., Indianapolis, IN, pp. 303–308, 1997.Google Scholar
  18. [18]
    J. J. Liang, A. K. Qin, P. N. Suganthan, and S. Baskar, “Comprehensive learning particle swarm optimizer for global optimization of multimodal functions,” IEEE Trans. Evol. Comp., vol. 10, no. 3, pp. 281–295, June 2006.CrossRefGoogle Scholar
  19. [19]
    O. Chao and L. Weixing, “Comparison between PSO and GA for parameters optimization of PID controller,” Proc. of International Conference on Mechatronics and Automation, pp. 2471–2475, June 2006.Google Scholar
  20. [20]
    N. Sadati, M. Zamani, and H. Mahdavian, “Hybrid particle swarm-based-simulated annealing optimization techniques,” Proc. of the IEEE Inter. Conf. on Indus. Elect., Paris, France, Nov. 2006.Google Scholar
  21. [21]
    D. B. Fogel, Evolutionary Computation Toward a New Philosophy of Machine Intelligence, IEEE, New York, 1995.Google Scholar
  22. [22]
    Y. Shi and R. Eberhart, “A modified particle swarm optimizer,” Proc. IEEE Int. Conf. on Evolutionary Computation, pp. 69–73, 1998.Google Scholar
  23. [23]
    R. Eberhart and Y. Shi, “Particle swarm optimization: Developments, applications and resources,” Proc. IEEE Int. Conf. on Evolutionary Computation, pp. 81–86, 2001.Google Scholar
  24. [24]
    M. Avriel, Nonlinear Programming: Theory and Algorithms, Wiley, New York, 1979.Google Scholar
  25. [25]
    K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice Hall, Upper Saddle River, NJ, 1996.zbMATHGoogle Scholar
  26. [26]
    M. T. Ho and Y. W. Tu, “PID controller design for a flexible-link manipulator,” Proc. IEEE Conf. on Decision and Control, Spain, pp. 6841–6846, Dec. 2005.Google Scholar
  27. [27]
    H. Kwakernaak, “Minimax frequency domain performance and robustness optimization of feedback systems,” IEEE Trans. Automat. Contr., vol. 30, pp. 994–1004, 1985.zbMATHCrossRefMathSciNetGoogle Scholar
  28. [28]
    I. Kitsios, T. Pimenides, and P. Groumpos, “A genetic algorithm for designing H structured specified controllers,” Proc. IEEE Int. Conf. Contr. Applicat., Mexico, pp. 1196–1201, 2001.Google Scholar
  29. [29]
    P. Voulgaris and L. Valavani, “High performance H and H designs for supermaneuverable F18/harv fighter aircraft,” AIAA J. Guid. Cont. Dyn., vol. 14, no. 1, pp. 157–165, 1991.zbMATHCrossRefGoogle Scholar

Copyright information

© The Institute of Control, Robotics and Systems Engineers and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg GmbH 2009

Authors and Affiliations

  • Majid Zamani
    • 1
  • Nasser Sadati
    • 2
  • Masoud Karimi Ghartemani
    • 2
  1. 1.the School of Electrical EngineeringUniversity of CaliforniaLos AngelesUSA
  2. 2.the School of Electrical EngineeringSharif University of TechnologyTehranIran

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