Control of Traveling Solutions in a Loop-Reactor

Y. Smagina; M. Sheintuch

Mathematical Modelling of Natural Phenomena (2010)

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

Abstract

top
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.

How to cite

top

Smagina, 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
  1. K. J. Astrom, P. Hagander, J. Sternby. Zeros of sampled system. Automatica, 20 (1984), No. 1, 31–38.  
  2. A. A. Barresi, M. Vanni, M. Brinkmann, G. Baldi. Control of an autothemal network of nonstationary catalytic reactors. AIChE Journal, 45 (1999), 1597–1602.  
  3. L. G. Stanton, A. A. Golovin. Global feedback control for pattern-forming systems. PRE, 76 (2007), 036210.  
  4. B. Echebarria, A. Karma. Spatiotemporal control of cardiac alternans. Chaos, 12 (2002), 923–930. 
  5. B. Echebarria, A. Karma. Amplitude equation approach to spatiotemporal dynamics of cardiac alternans. Physical Review E, 76 (2007), 051911.  
  6. M. Courtemanche, L. Glass, J. Keener. Instabilities of a propagating pulse in a ring of excitable media. PRL, 70 (1993), 2182–2185.  
  7. 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.  
  8. F. R. Gantmacher. The theory of matrices. New York, Chelsea Pull. Comp, 1977.  
  9. L. Hou, A. N. Michel. Some qualitative properties of sampled-date control systems. IEEE Transaction on Automatic control, 42 (1997), No.12, 1721–1725.  
  10. L. Hou, A. N. Michel.Some qualitative properties of multirate digital systems. IEEE Transaction on Automatic control, 44 (1999), No. 4, 765–770.  
  11. A. Madai, M. Sheintuch. Demonstration of loop reactor operation. AIChE Journal., 54 (2008), 2413–2422. 
  12. Yu. Sh.Matros. Catalytic process under unsteady-state conditions. Amsterdam, Elsevier,1989.  
  13. 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.  
  14. O. Nekhamkina, M. Sheintuch.Structure of operating domains of loop reactors. AIChE Journal, 54 (2008), 1292–1302.  
  15. K.Ogata. Modern Control Engineering. Prentice-Hall, London, Englewood Cliffs, 1990.  
  16. H. H. Rosenbrock. State-space and multivariable theory, London, Nelson, 1970.  
  17. M. Sheintuch, S. Shvartsman. Spatiotemporal patterns in catalytic reactors. AIChE Journal, 42 (1996), 1041–1067. 
  18. M. Sheintuch, O. Nekhamkina. The asymptotes of loop reactors. AIChE Journal, 51 (2005), 224–234. 
  19. 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.  
  20. Ye. Smagina, M. Sheintuch. Control of rotating pulses in a loop reactor. Journal of Process Control, 19 (2009), 954–963. 
  21. Ye. Smagina. System Zeros, , 2006.  URIhttp://arxiv.org/pdf/math.DG/0605092
  22. Z. Sun. Sampling and control of switched linear systems. Journal of Franklin Institute, 341 (2004), 657–674. 

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.