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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)
Publication Information
International Journal of Control, Automation, and Systems / v.5, no.2, 2007 , pp. 117-127 More about this Journal
Abstract
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.
Keywords
LFC; LMI; Mixed $H_2/H_{\infty}$ control; PI; PID; robust performance; static output feedback control; time delay;
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Times Cited By Web Of Science : 4  (Related Records In Web of Science)
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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   DOI   ScienceOn
2 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   DOI   ScienceOn
3 A. J. Isakson and S. F. Graebe, 'Analytical PID parameter expressions for higher order systems,' Automatica, vol. 35, no. 6. pp. 1121-1130, 1999   DOI   ScienceOn
4 S. Skogestad, 'Simple analytic rules for model reduction and PID controller tuning,' Journal of Process Control, vol. 13, pp. 291-309, 2003   DOI   ScienceOn
5 M. T. Ho, 'Synthesis of $H_{\infty}$ PID controllers: A parametric approach,' Automatica, vol. 39, pp. 1069-1075, 2003   DOI   ScienceOn
6 K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, Englewood Cliffs, NJ, 1996
7 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   DOI   ScienceOn
8 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   DOI   ScienceOn
9 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   DOI   ScienceOn
10 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   DOI   ScienceOn
11 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
12 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   DOI   ScienceOn
13 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   DOI   ScienceOn
14 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
15 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   DOI   ScienceOn
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   DOI   ScienceOn
17 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
18 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
19 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   DOI   ScienceOn
20 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   DOI
21 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   DOI   ScienceOn
22 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   DOI   ScienceOn
23 P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The MathWorks, Inc., 1995
24 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   DOI   ScienceOn
25 J. G. Ziegler and N. B. Nichols, 'Optimum setting for automatic controllers,' Trans. ASME, vol. 64, no. 11, pp. 759-765, 1942
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   DOI   ScienceOn
27 M. S. Mahmoud, Robust Control and Filtering for Time-Delay. Systems, Marcel Dekker Inc., New York, 2000
28 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