Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 51874, 15 pages
http://dx.doi.org/10.1155/MPE/2006/51874

Constrained regulator problem for linear uncertain systems: Control of a pH process

1Constrained and Robust Regulation Research Unit, Physics Department, Faculty of Sciences, Cadi Ayyad University, B.P. 2390, Marrakesh, Morocco
2Departamento de Ingeniería de Sistemas y Automática, Universidad de Valladolid, Valladolid 47005, Spain

Received 8 November 2005; Accepted 14 February 2006

Copyright © 2006 Fouad Mesquine et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Benzaouia, “The resolution of equation XA+XBX=HX and the pole assignment problem,” IEEE Transactions on Automatic Control, vol. 39, no. 10, pp. 2091–2095, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. Benzaouia and C. Burgat, “Regulator problem for linear discrete-time systems with nonsymmetrical constrained control,” International Journal of Control, vol. 48, no. 6, pp. 2441–2451, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Benzaouia and A. Hmamed, “Regulator problem for linear continuous-time systems with nonsymmetrical constrained control,” IEEE Transactions on Automatic Control, vol. 38, no. 10, pp. 1556–1560, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. A. Benzaouia and F. Mesquine, “Regulator problem for uncertain linear discrete-time systems with constrained control,” International Journal of Robust and Nonlinear Control, vol. 4, no. 3, pp. 387–395, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. Benzaouia, F. Mesquine, M. Naib, and A. Hmamed, “Robust pole assignment in complex plane regions for linear uncertain constrained control systems,” International Journal of Systems Science, vol. 32, no. 1, pp. 83–89, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. K. K. Biasizzo, I. Skrjanc, and D. Matko, “Fuzzy predictive control of highly nonlinear pH process,” Computers & Chemical Engineering, vol. 21, no. 1-2, pp. S613–S618, 1997. View at Publisher · View at Google Scholar
  7. G. Bitsoris and E. Gravalou, “Robust linear controller under state and control constraints,” in Proceedings of Conference on Decision and Control, Arizona, 1992.
  8. F. Blanchini, “Feedback control for linear time-invariant systems with state and control bounds in the presence of disturbances,” IEEE Transactions on Automatic Control, vol. 35, no. 11, pp. 1231–1234, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. F. Blanchini, “Set invariance in control,” Automatica, vol. 35, no. 11, pp. 1747–1767, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. E. F. Camacho and C. Bordons, Model Predictive Control, Springer, London, 1999.
  11. M. A. Dahleh and I. J. Diaz-Bobillo, Control of Uncertain Systems: A Linear Programming Approach, Prentice-Hall, New Jersey, 1995.
  12. M. J. Fuente, C. Robles, O. Lobato, and F. Tadeo, “Fuzzy control of a neutralization process,” in Proceedings of IEEE Conference on Control Applications, pp. 1032–1037, Glasgow, 2002.
  13. O. Galan, J. A. Romagnoli, and A. Palazoglu, “Robust H control of nonlinear plants based on multi-linear models: an application to a bench-scale pH neutralization reactor,” Chemical Engineering Science, vol. 55, no. 20, pp. 4435–4450, 2000. View at Publisher · View at Google Scholar
  14. J. B. Gomm, S. K. Doherty, and D. Williams, “Control of pH in-line using a neural predictive strategy,” in Proceedings of IEE UKACC International Conference on Control, Rhode Island, 1996.
  15. T. F. Gustafsson and K. V. Waller, “Nonlinear and adaptive control of pH,” Industrial and Engineering Chemistry Research, vol. 24, pp. 809–817, 1992. View at Google Scholar
  16. D. Henrion, S. Tarbouriech, and V. Kučera, “Control of linear systems subject to input constraints: a polynomial approach,” Automatica, vol. 37, no. 4, pp. 597–604, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Z. Lin and A. Saberi, “Semi-global exponential stabilization of linear systems subject to “input saturation” via linear feedbacks,” Systems & Control Letters, vol. 21, no. 3, pp. 225–239, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. J. M. Maciejowski, Predictive Control with Constraints, Prentice-Hall, New Jersey, 2001.
  19. F. Mesquine, A. Benlamkadem, and F. Tadeo, “Robust constrained Regulator problem for linear uncertain continuous time systems: application to a pH process,” in Proceedings of the IEEE International Conference on Control Applications, pp. 391–396, Glasgow, 2002.
  20. F. Mesquine, A. Benlemkadem, and A. Benzaouia, “Robust constrained regulator problem for linear uncertain systems,” Journal of Dynamical and Control Systems, vol. 10, no. 4, pp. 527–544, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. F. Mesquine, F. Tadeo, and A. Benzaouia, “Regulator problem for linear systems with constraints on control and its increment or rate,” Automatica, vol. 40, no. 8, pp. 1387–1395, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. N. R. L. Narayanan, P. R. Krishnaswamy, and G. P. Rangaiah, “Use of alternate process variable for enhancing pH control performance,” Chemical Engineering Science, vol. 53, no. 17, pp. 3041–3049, 1998. View at Publisher · View at Google Scholar
  23. S. J. Norquay, A. Palazoglu, and A. Romagnoli, “Model predictive control based on Wiener models,” Chemical Engineering Science, vol. 53, no. 1, pp. 75–84, 1998. View at Publisher · View at Google Scholar
  24. R. H. Nystrom, K. V. Sandstom, T. K. Gustafsson, and H. T. Toivonen, “Multimodel robust control applied to a pH neutralization process,” Computers & Chemical Engineering, vol. 22, pp. S467–S474, 1998. View at Publisher · View at Google Scholar
  25. O. Pérez, F. Tadeo, and P. Vega, “Robust control of pH control plant,” in Proceedings of IEEE Conference on Control Applications, New York, 1995.
  26. C. H. Sing and B. Postlethwaite, “pH control: handling nonlinearity and deadtime with fuzzy relational model-based control,” IEE Proceedings—Control Theory and Applications, vol. 144, no. 3, pp. 263–268, 1997. View at Publisher · View at Google Scholar
  27. A. A. Stoorvogel, A. Saberi, and P. Sannuti, “Performance with regulation constraints,” Automatica, vol. 36, no. 10, pp. 1443–1456, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. S. W. Sung and I. B. Lee, “pH control using a simple set point change,” Industrial and Engineering Chemistry Research, vol. 34, no. 5, pp. 1730–1734, 1995. View at Publisher · View at Google Scholar
  29. F. Tadeo, A. Holohan, and P. Vega, “l1-optimal regulation of a pH control plant,” Computers & Chemical Engineering, vol. 22, pp. S459–S466, 1998. View at Publisher · View at Google Scholar
  30. F. Tadeo, O. P. Lopez, and T. Alvarez, “Control of neutralization processes by robust loop shaping,” IEEE Transactions on Control Systems Technology, vol. 8, no. 2, pp. 236–246, 2000. View at Publisher · View at Google Scholar
  31. S.-S. Yoon, T.-W. Yoon, D. R. Yang, and T.-S. Kang, “Indirect adaptive nonlinear control of a pH process,” Computers & Chemical Engineering, vol. 26, no. 9, pp. 1223–1230, 2002. View at Publisher · View at Google Scholar
  32. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, New Jersey, 1996.