Multiobjective PI/PID Control Design Using an Iterative Linear Matrix Inequalities Algorithm

  • Bevrani, Hassan (Department of Electrical and Computer Eng., University of Kurdistan) ;
  • Hiyama, Takashi (Department of Computer Science and Electrical Eng., Kumamoto University)
  • 발행 : 2007.04.30

초록

Many real world control systems usually track several control objectives, simultaneously. At the moment, it is desirable to meet all specified goals using the controllers with simple structures like as proportional-integral (PI) and proportional-integral-derivative (PID) which are very useful in industry applications. Since in practice, these controllers are commonly tuned based on classical or trial-and-error approaches, they are incapable of obtaining good dynamical performance to capture all design objectives and specifications. This paper addresses a new method to bridge the gap between the power of optimal multiobjective control and PI/PID industrial controls. First the PI/PID control problem is reduced to a static output feedback control synthesis through the mixed $H_2/H_{\infty}$ control technique, and then the control parameters are easily carried out using an iterative linear matrix inequalities (ILMI) algorithm. Numerical examples on load-frequency control (LFC) and power system stabilizer (PSS) designs are given to illustrate the proposed methodology. The results are compared with genetic algorithm (GA) based multiobjective control and LMI based full order mixed $H_2/H_{\infty}$ control designs.

키워드

참고문헌

  1. K. J. Astrom, T. Hagglund, C. C. Hang, and W. K. Ho, 'Automatic tuning and adaptation for PID controllers-a survey,' Control Eng. Practice, vol. 1, no. 4, pp. 699-714, 1993 https://doi.org/10.1016/0967-0661(93)91394-C
  2. P. Cominos and N. Munro, 'PID controllers: Recent tuning methods and design to specification,' IEE Proc. Control Theory Appl., vol. 149, no. 1, pp. 46-53, 2002 https://doi.org/10.1049/ip-cta:20020103
  3. J. G. Ziegler and N. B. Nichols, 'Optimum setting for automatic controllers,' Trans. ASME, vol. 64, no. 11, pp. 759-765, 1942
  4. W. K. Ho, C. C. Hang, and L. S. Cao, 'Tuning of PID controllers based on gain and phase margin specifications,' Automatica, vol. 31, no. 3, pp. 497-502, 1995 https://doi.org/10.1016/0005-1098(94)00130-B
  5. A. J. Isakson and S. F. Graebe, 'Analytical PID parameter expressions for higher order systems,' Automatica, vol. 35, no. 6. pp. 1121-1130, 1999 https://doi.org/10.1016/S0005-1098(99)00009-6
  6. S. Skogestad, 'Simple analytic rules for model reduction and PID controller tuning,' Journal of Process Control, vol. 13, pp. 291-309, 2003 https://doi.org/10.1016/S0959-1524(02)00062-8
  7. B. Kristiansson and B. Lennartson, 'Robust and optimal tuning of PI and PID controllers,' IEE Proc. on Control Theory and Applications, vol. 149, no. 1, pp. 17-25, 2002 https://doi.org/10.1049/ip-cta:20020088
  8. E. Grassi, K. Tsakalis, S. Dash, S. V. Gaikwad, W. Macarthur, and G. Stein, 'Integrated system identification and PID controller tuning by frequency loop-shaping,' IEEE Trans. Control Syst. Technology, vol. 9, no. 2, pp. 285-294, 2001 https://doi.org/10.1109/87.911380
  9. C. Lin, Q. G. Wang, and T. H. Lee, 'An improvement on multivariable PID controller design via iterative LMI approach,' Automatica, vol. 40, no. 3, pp. 519-525, 2004 https://doi.org/10.1016/j.automatica.2003.10.008
  10. F. Zheng, Q. G. Wang, and T. H. Lee, 'On the design of multivariable PID controllers via LMI approach,' Automatica, vol. 38, no. 3, pp. 517-526, 2002 https://doi.org/10.1016/S0005-1098(01)00237-0
  11. M. T. Ho, 'Synthesis of $H_{\infty}$ PID controllers: A parametric approach,' Automatica, vol. 39, pp. 1069-1075, 2003 https://doi.org/10.1016/S0005-1098(03)00078-5
  12. R. H. C. Takahashi, P. L. D. Peres, and P. A. V. Ferreira, 'Multiobjective $H_{2}$/$H_{\infty}$ guaranteed cost PID design,' IEEE Control Systems, vol. 17, no. 5, pp. 37-47, 1997
  13. B. S. Chen, Y. M. Cheng, and C. H. Lee, 'A genetic approach to mixed $H_{2}$/$H_{\infty}$ optimal PID control,' IEEE Control Systems, vol. 15, no. 5, pp. 51-60, 1998 https://doi.org/10.1109/37.466262
  14. C. S. Tseng and B. S. Chen, 'A mixed adaptive tracking control for constrained non-holonomic systems,' Automatica, vol. 39, no. 6, pp. 1011-1018, 2003 https://doi.org/10.1016/S0005-1098(03)00038-4
  15. H. Bevrani and T. Hiyama, 'PI/PID based multiobjective control design: An ILMI approach,' Proc. of IEEE Int. Canf. on Networking, Sensing and Control, USA, pp. 750-755, 2005
  16. F. Zheng, Q. G. Wang, and H. T. Lee, 'On the design of multivariab1e PID controllers via LMI approach,' Automatica, vol. 38, no. 3, pp. 517-526, 2002 https://doi.org/10.1016/S0005-1098(01)00237-0
  17. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, Englewood Cliffs, NJ, 1996
  18. Y. Y. Cao, J. Lam, Y. X. Sun, and W. J. Mao, 'Static output feedback stabilization: An ILMI approach,' Automatica, vol. 34, no. 12, pp. 1641-1645, 1998 https://doi.org/10.1016/S0005-1098(98)80021-6
  19. R. E. Skelton, J. Stoustrup, and T. Iwasaki, 'The $_{\infty}$ control problem using static output feedback,' Int. J of Robust and Nonlinear Control, vol. 4, pp. 449-455, 1994 https://doi.org/10.1002/rnc.4590040404
  20. I. Yaesh and U. Shaked, 'Minimum entropy static output-feedback control with an $H_{\infty}$-norm performance bound,' IEEE Trans. on Automatic Control, vol. 42, no. 6, pp. 853-858, 1997 https://doi.org/10.1109/9.587343
  21. F. Leibfritz, 'An LMI-based algorithm for designing suboptimal static $H_{2}$/$H_{\infty}$ output feedback controllers,' SIAM J Control Optim., vol. 39, no. 6, pp. 1711-1735, 2001 https://doi.org/10.1137/S0363012999349553
  22. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The MathWorks, Inc., 1995
  23. M. S. Mahmoud, Robust Control and Filtering for Time-Delay. Systems, Marcel Dekker Inc., New York, 2000
  24. D. Rerkpreedapong, A. Hasanovic, and A. Feliachi, 'Robust load frequency control using genetic algorithms and linear matrix inequalities,' IEEE Trans. on Power Systems, vol. 18, no. 2, pp. 855-861, 2003 https://doi.org/10.1109/TPWRS.2003.811005
  25. H. Bevrani, Y. Mitani, and K. Tsuji, 'Robust LFC in a deregulated environment: Multi-objective control approach,' IEEJ Trans. on Power and Energy, vol. 124-B, no. 12, pp. 1409-1416, 2004
  26. T. Mori and H. Kokame, 'Stability of x(t) = Ax(t) + Bx(t - $\tau$),' IEEE Trans. on Automatic Control, vol. 34, no. 4, pp. 460-462, 1989 https://doi.org/10.1109/9.28025
  27. H. Bevrani and T. Hiyama, 'Robust design of power system stabilizer: An LMI approach,' Proc. of IASTED Int. Conf. on Energy and Power Systems (CD ROM), Chiang Mai, Thailand, 2006
  28. E. V. Larsen and D. A. Swann, 'Applying power system stabilizers parts I-III,' IEEE Trans. on Power Apparatus and Systems, vol. 101, no. 6, pp. 3017-3046, 1981