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Control of Traveling Solutions in aLoop-Reactor

Published online by Cambridge University Press:  09 June 2010

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Abstract

We consider the stabilization of a rotating temperature pulse traveling in a continuousasymptotic model of many connected chemical reactors organized in a loop with continuouslyswitching the feed point synchronously with the motion of the pulse solution. We use theswitch velocity as control parameter and design it to follow the pulse: the switchvelocity is updated at every step on-line using the discrepancy between the temperature atthe front of the pulse and a set point. The resulting feedback controller, which can beregarded as a dynamic sampled-data controller, is designed using root-locus technique.Convergence conditions of the control law are obtained in terms of the zero structure(finite zeros, infinite zeros) of the related lumped model.

Type
Research Article
Copyright
© EDP Sciences, 2010

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References

Astrom, K. J., Hagander, P., Sternby, J.. Zeros of sampled system . Automatica, 20 (1984), No. 1, 3138. CrossRefGoogle Scholar
Barresi, A. A., Vanni, M., Brinkmann, M., Baldi, G.. Control of an autothemal network of nonstationary catalytic reactors . AIChE Journal, 45 (1999), 15971602. CrossRefGoogle Scholar
Stanton, L. G., Golovin, A. A.. Global feedback control for pattern-forming systems . PRE, 76 (2007), 036210. CrossRefGoogle ScholarPubMed
Echebarria, B., Karma, A.. Spatiotemporal control of cardiac alternans . Chaos, 12 (2002), 923930.CrossRefGoogle ScholarPubMed
Echebarria, B., Karma, A.. Amplitude equation approach to spatiotemporal dynamics of cardiac alternans . Physical Review E, 76 (2007), 051911. CrossRefGoogle ScholarPubMed
Courtemanche, M., Glass, L., Keener, J.. Instabilities of a propagating pulse in a ring of excitable media . PRL, 70 (1993), 21822185. CrossRefGoogle Scholar
Courtemanche, M., Keener, J., Glass, L.. A delay equation representation of pulse circulation on a ring in excitable media . SIAM.J. Appl. Math., 56 (1996) ,No.1, 119142. CrossRefGoogle Scholar
F. R. Gantmacher. The theory of matrices. New York, Chelsea Pull. Comp, 1977.
Hou, L., Michel, A. N.. Some qualitative properties of sampled-date control systems . IEEE Transaction on Automatic control, 42 (1997), No.12, 17211725. Google Scholar
Hou, L., Michel, A. N.. Some qualitative properties of multirate digital systems . IEEE Transaction on Automatic control, 44 (1999), No. 4, 765770. Google Scholar
Madai, A., Sheintuch, M.. Demonstration of loop reactor operation . AIChE Journal., 54 (2008), 24132422.CrossRefGoogle Scholar
Yu. Sh.Matros. Catalytic process under unsteady-state conditions. Amsterdam, Elsevier,1989.
Mori, M.. Root-locus method of pulse transfer function for sampled-date control systems . IRE Transaction on Automatic. Control, 3 (1957), No.1, 1320. CrossRefGoogle Scholar
Nekhamkina, O., Sheintuch, M.. Structure of operating domains of loop reactors . AIChE Journal, 54 (2008), 12921302. CrossRefGoogle Scholar
K.Ogata. Modern Control Engineering. Prentice-Hall, London, Englewood Cliffs, 1990.
H. H. Rosenbrock. State-space and multivariable theory, London, Nelson, 1970.
Sheintuch, M., Shvartsman, S.. Spatiotemporal patterns in catalytic reactors . AIChE Journal, 42 (1996), 10411067.CrossRefGoogle Scholar
Sheintuch, M., Nekhamkina, O.. The asymptotes of loop reactors . AIChE Journal, 51 (2005), 224234.CrossRefGoogle Scholar
L. G. Sison, E. K. P.Chong. No-reset iterative learning control. Proceedings of 35st IEEE Conference on Decision and Control, Kobe, Japan, 1996, 3062–3063.
Smagina, Ye., Sheintuch, M.. Control of rotating pulses in a loop reactor . Journal of Process Control, 19 (2009), 954963.CrossRefGoogle Scholar
Ye. Smagina. System Zeros, http://arxiv.org/pdf/math.DG/0605092, 2006.
Sun, Z.. Sampling and control of switched linear systems . Journal of Franklin Institute, 341 (2004), 657674.CrossRefGoogle Scholar