Receding Horizon Control of Cocurrent First Order Hyperbolic Partial Differential Equation Systems

Jinhoon Choi; Kwang Soon Lee

Korean Journal of Chemical Engineering, Vol.21, No.2, 345-351, March, 2004

DOI10.1007/BF02705418 Export Citation

Receding Horizon Control of Cocurrent First Order Hyperbolic Partial Differential Equation Systems

Jinhoon Choi^†, and Kwang Soon Lee

Department of Chemical & Biomolecular Engineering, Sogang University, 1 Sinsoo-Dong, Mapo-Koo, Seoul 121-742, Korea

E-mail:

Cocurrent first order hyperbolic partial differential equations (PDE’s) have finite impulse response (FIR) characteristics. A finite difference scheme that preserve these nice dynamic characteristics is recently developed [Choi, submitted]. Employing the resulting genuine FIR model, the design of receding horizon control is easier. In this paper, a receding horizon control scheme for cocurrent first order hyperbolic PDE systems is proposed using the FIR model and is elucidated with a tubular reactor example.

Keywords:First Order Hyperbolic PDE’s;Receding Horizon Control;Reaction-convection Processes

[References]

Balas MJ, Int. J. Control, 29, 1523 (1979)
Balas MJ, J. Math. Anal. Appl., 114, 17 (1986)
Choi J, "FIR Property Preserving Finite Difference Scheme for Cocurrent Reaction-Advection Processes," SIAM J. Num. Anal., submitted
Choi J, Kwon WH, SIAM J. Contr. Opt., 42, 839 (2003)
Choi J, Seo BJ, Lee KS, Korean J. Chem. Eng., 18(5), 606 (2001)
Christofides PD, Daoutidis P, AIChE J., 42(11), 3063 (1996)
Christofides PD, Daoutidis P, J. Math. Anal. Appl., 216, 398 (1997)
Cutler CR, Ramaker BL, "Dynamic Matrix Control - A Computer Control Algorithm," Proc. Joint Auto. Contr. Conf. (1980)
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Kwon WH, Pearson AE, IEEE Trans. Autom. Control, 22, 838 (1977)
Lapidus L, Pinder GF, "Numerical Solutions of Partial Differential Equations in Science and Engineering," Wiley (1982)
Lewis FL, Syrmos VL, "Optimal Control," Interscience (1995)
Lo CT, Int. J. Control, 18, 273 (1973)
Rawlings JB, Muske KR, IEEE Trans. Autom. Control, 38, 1512 (1993)
Ray WH, "Advanced Process Control," McGraw-Hill (1981)
Rhee HK, Aris R, Amundson NR, "First Order Partial Differential Equations: Vol. 1 and Vol. II," Prentice-Hall (1986)
Russel DL, SIAM Rev., 20, 639 (1978)
Ruthven DM, Sircar S, "Design of Membrane and PSA Processes for Bulk Gas Separation," Proc. 4th Inter. Conf. on Foundation of Computer-aided Process Design, 29 (1994)
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Wang PKC, Int. J. Control, 3, 255 (1966)

[Related Articles]

[1] Balas MJ, Int. J. Control, 29, 1523 (1979)

[2] Balas MJ, J. Math. Anal. Appl., 114, 17 (1986)

[3] Choi J, "FIR Property Preserving Finite Difference Scheme for Cocurrent Reaction-Advection Processes," SIAM J. Num. Anal., submitted

[4] Choi J, Kwon WH, SIAM J. Contr. Opt., 42, 839 (2003)

[5] Choi J, Seo BJ, Lee KS, Korean J. Chem. Eng., 18(5), 606 (2001)

[6] Christofides PD, Daoutidis P, AIChE J., 42(11), 3063 (1996)

[7] Christofides PD, Daoutidis P, J. Math. Anal. Appl., 216, 398 (1997)

[8] Cutler CR, Ramaker BL, "Dynamic Matrix Control - A Computer Control Algorithm," Proc. Joint Auto. Contr. Conf. (1980)

[9] Friedman A, "Partial Differential Equations," Holt, Rinerhart & Winston (1976)

[10] Kwon WH, Pearson AE, IEEE Trans. Autom. Control, 22, 838 (1977)

[11] Lapidus L, Pinder GF, "Numerical Solutions of Partial Differential Equations in Science and Engineering," Wiley (1982)

[12] Lewis FL, Syrmos VL, "Optimal Control," Interscience (1995)

[13] Lo CT, Int. J. Control, 18, 273 (1973)

[14] Rawlings JB, Muske KR, IEEE Trans. Autom. Control, 38, 1512 (1993)

[15] Ray WH, "Advanced Process Control," McGraw-Hill (1981)

[16] Rhee HK, Aris R, Amundson NR, "First Order Partial Differential Equations: Vol. 1 and Vol. II," Prentice-Hall (1986)

[17] Russel DL, SIAM Rev., 20, 639 (1978)

[18] Ruthven DM, Sircar S, "Design of Membrane and PSA Processes for Bulk Gas Separation," Proc. 4th Inter. Conf. on Foundation of Computer-aided Process Design, 29 (1994)

[19] Stangeland BE, Foss AS, Ind. Eng. Chem. Res., 38, 38 (1970)

[20] Wang PKC, Int. J. Control, 3, 255 (1966)