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Received March 8, 2013
Accepted August 7, 2013
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Analytical design of proportional-integral controllers for the optimal control of first-order processes with operational constraints
School of Chemical Engineering, Yeungnam University, Gyeongsan 712-749, Korea
Korean Journal of Chemical Engineering, December 2013, 30(12), 2151-2162(12), 10.1007/s11814-013-0153-1
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Abstract
A novel analytical design method of industrial proportional-integral (PI) controllers was developed for the optimal control of first-order processes with operational constraints. The control objective was to minimize a weighted sum of the controlled variable error and the rate of change in the manipulated variable under the maximum allowable limits in the controlled variable, manipulated variable and the rate of change in the manipulated variable. The constrained optimal servo control problem was converted to an unconstrained optimization to obtain an analytical tuning formula. A practical shortcut procedure for obtaining optimal PI parameters was provided based on graphical analysis of global optimality. The proposed PI controller was found to guarantee global optimum and deal explicitly with the three important operational constraints.
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References
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Zhang R, Xue A, Wang S, Chem. Eng. Sci., 66, 6002 (2001)
Javed KH, Mahmud T, Purba E, Chem. Eng. Res. Des., 84(A6), 465 (2006)
Takashi M, Toshinori F, Kazutoshi S, Kenji K, Toshiharu K, Prec. Eng., 31, 156 (2007)
Roberto H, Yunfeng L, Kenn O, Stanley K, Xinghui H, Con.Eng. Prac., 15, 291 (2007)
Lewis FL, Optimal control, New York, John Wiley and Sons (1986)
Letov AM, Automat Rem Contr., 21(4), 303 (1960)
Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mischenko EF, The 34 The Standard Regulator Problem-1 Chap. 2 Mathematical Theory of Optimal Processes, Trirogoff KN (transl.), Neustadted LW, Interscience, New York (1962)
Siebenthal CD, Aris R, Chem. Eng. Sci., 19(10), 729 (1964)
Sage AP, Optimal Systems Control. Prentice-Hall, Inc., Englewood Cliffs, N. J. (1968)
Zeng XP, Li YM, Qin J, Neurocomputing., 72(4-6), 1241 (2009)
Goldberg DE, Genetic Algorithms in Search, Optimization and machine learning, Kluwer Academic Publishers, Boston, MA (1989)
van den Bergh F, Engelbrecht AP, Inform Sciences., 176, 937 (2006)
He Q, Wang L, Eng. Appl. Artif. Intel., 20, 89 (2007)
Toscano R, Lyonnet P, IEEE Systems, Man, and Cybernetics Society., 39(5), 1231 (2009)
Kurt M, Stochastic optimization methods, 2nd Ed, Springer (2008)
Shin J, Lee J, Park S, Koo K, Lee M, Con. Eng. Prac., 16, 1391 (2008)
Lee MY, Shin JH, Chem. Eng. Commun., 196(6), 729 (2009)
Lee M, Shin J, Lee J, Hydrocarb. Process., 89(1), 71 (2010)
Lee M, Shin J, Lee J, Hydrocarb. Process., 89(2), 81 (2010)
Nguyen VH, Yamashita Y, Lee M, J. Chem. Eng. Jpn., 44(5), 345 (2011)
Vapnyarskii IB, Lagrange multipliers, In: Hazewinkel M (ed.). Encyclopedia of Mathematics, Springer, Heidelberg (2001)
Rivera DE, Morari M, Skogestad S, Ind. Eng. Chem. Proc.Des. Dev., 25, 252 (1986)
