# Control of Traveling Solutions in a Loop-Reactor

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 6, Issue: 1, page 209-225
- ISSN: 0973-5348

## Access Full Article

top## Abstract

top## How to cite

topSmagina, Y., and Sheintuch, M.. "Control of Traveling Solutions in a Loop-Reactor." Mathematical Modelling of Natural Phenomena 6.1 (2010): 209-225. <http://eudml.org/doc/197651>.

@article{Smagina2010,

abstract = {We consider the stabilization of a rotating temperature pulse traveling in a continuous
asymptotic model of many connected chemical reactors organized in a loop with continuously
switching the feed point synchronously with the motion of the pulse solution. We use the
switch velocity as control parameter and design it to follow the pulse: the switch
velocity is updated at every step on-line using the discrepancy between the temperature at
the front of the pulse and a set point. The resulting feedback controller, which can be
regarded 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.},

author = {Smagina, Y., Sheintuch, M.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {moving pulses; network of chemical reactors; loop-reactor; distributed systems; control; root-locus method; system zeros; dynamic sampled-data controller},

language = {eng},

month = {6},

number = {1},

pages = {209-225},

publisher = {EDP Sciences},

title = {Control of Traveling Solutions in a Loop-Reactor},

url = {http://eudml.org/doc/197651},

volume = {6},

year = {2010},

}

TY - JOUR

AU - Smagina, Y.

AU - Sheintuch, M.

TI - Control of Traveling Solutions in a Loop-Reactor

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/6//

PB - EDP Sciences

VL - 6

IS - 1

SP - 209

EP - 225

AB - We consider the stabilization of a rotating temperature pulse traveling in a continuous
asymptotic model of many connected chemical reactors organized in a loop with continuously
switching the feed point synchronously with the motion of the pulse solution. We use the
switch velocity as control parameter and design it to follow the pulse: the switch
velocity is updated at every step on-line using the discrepancy between the temperature at
the front of the pulse and a set point. The resulting feedback controller, which can be
regarded 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.

LA - eng

KW - moving pulses; network of chemical reactors; loop-reactor; distributed systems; control; root-locus method; system zeros; dynamic sampled-data controller

UR - http://eudml.org/doc/197651

ER -

## References

top- K. J. Astrom, P. Hagander, J. Sternby. Zeros of sampled system. Automatica, 20 (1984), No. 1, 31–38. Zbl0542.93047
- A. A. Barresi, M. Vanni, M. Brinkmann, G. Baldi. Control of an autothemal network of nonstationary catalytic reactors. AIChE Journal, 45 (1999), 1597–1602.
- L. G. Stanton, A. A. Golovin. Global feedback control for pattern-forming systems. PRE, 76 (2007), 036210.
- B. Echebarria, A. Karma. Spatiotemporal control of cardiac alternans. Chaos, 12 (2002), 923–930.
- B. Echebarria, A. Karma. Amplitude equation approach to spatiotemporal dynamics of cardiac alternans. Physical Review E, 76 (2007), 051911.
- M. Courtemanche, L. Glass, J. Keener. Instabilities of a propagating pulse in a ring of excitable media. PRL, 70 (1993), 2182–2185.
- M. Courtemanche, J. Keener, L. Glass. A delay equation representation of pulse circulation on a ring in excitable media. SIAM.J. Appl. Math., 56 (1996) ,No.1, 119–142. Zbl0859.35052
- F. R. Gantmacher. The theory of matrices. New York, Chelsea Pull. Comp, 1977. Zbl0085.01001
- L. Hou, A. N. Michel. Some qualitative properties of sampled-date control systems. IEEE Transaction on Automatic control, 42 (1997), No.12, 1721–1725. Zbl1041.93541
- L. Hou, A. N. Michel.Some qualitative properties of multirate digital systems. IEEE Transaction on Automatic control, 44 (1999), No. 4, 765–770. Zbl0958.93062
- A. Madai, M. Sheintuch. Demonstration of loop reactor operation. AIChE Journal., 54 (2008), 2413–2422.
- Yu. Sh.Matros. Catalytic process under unsteady-state conditions. Amsterdam, Elsevier,1989.
- M. Mori. Root-locus method of pulse transfer function for sampled-date control systems. IRE Transaction on Automatic. Control, 3 (1957), No.1, 13–20.
- O. Nekhamkina, M. Sheintuch.Structure of operating domains of loop reactors. AIChE Journal, 54 (2008), 1292–1302.
- K.Ogata. Modern Control Engineering. Prentice-Hall, London, Englewood Cliffs, 1990. Zbl0756.93060
- H. H. Rosenbrock. State-space and multivariable theory, London, Nelson, 1970. Zbl0246.93010
- M. Sheintuch, S. Shvartsman. Spatiotemporal patterns in catalytic reactors. AIChE Journal, 42 (1996), 1041–1067.
- M. Sheintuch, O. Nekhamkina. The asymptotes of loop reactors. AIChE Journal, 51 (2005), 224–234.
- 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.
- Ye. Smagina, M. Sheintuch. Control of rotating pulses in a loop reactor. Journal of Process Control, 19 (2009), 954–963.
- Ye. Smagina. System Zeros, , 2006. URIhttp://arxiv.org/pdf/math.DG/0605092
- Z. Sun. Sampling and control of switched linear systems. Journal of Franklin Institute, 341 (2004), 657–674. Zbl1064.94566

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.