Skip to main content
Log in

Robust controller design for discrete unstable non-minimum-phase delayed stochastic processes

  • Regular Paper
  • Control Theory
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

Control of unstable non-minimum-phase delayed stochastic processes is a challenging problem. In this work based on the Diophantine equation and using pole-placement technique, a discrete control scheme for such processes has been proposed. Robust stability of the suggested control structure has been shown. Advantages of the proposed scheme over the existing algorithms have been shown through computer simulations. It has been shown that performance of the proposed scheme for handling model mismatch and colored noise is superior to the previous work proposed in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. O. J. M. Smith, “Closed control of loops with dead time,” Chemical Engineering Progress, vol. 53, no. 5, pp. 217–219, May 1957.

    Google Scholar 

  2. M. Morari and E. Zafiriou, Robust Process Control, Prentice Hall, Englewood Cliffs, 1989.

    Google Scholar 

  3. J. E. Normey-Rico and E. F. Camacho, Control of Dead-time Processes, Springer, Berlin, 2007.

    Google Scholar 

  4. J. E. Normey-Rico and E. F. Camacho, “Dead-time compensators: a survey,” Control Engineering Practice, Vol. 16, no. 4, pp. 407–428, April 2008.

    Article  Google Scholar 

  5. J. E. Normey-Rico and E. F. Camacho, “Robustness effects of a prefilter in a Smith predictor-based generalized predictive controller,” IEE Proc. Control Theory & Applications, vol. 146, no. 2, pp. 179–185, March 1999.

    Article  Google Scholar 

  6. T. Hagglund, “An industrial dead-time compensating pi controller,” Control Engineering Practice, vol. 4, no. 6, pp. 749–756, June 1996.

    Article  Google Scholar 

  7. T. Hagglund, “A predictive pi controller for process with long dead times,” IEEE Control Systems Magazine, vol. 12, no. 1, pp. 57–60, February 1992.

    Article  Google Scholar 

  8. A. Ingimundarson and T. Hagglund, “Performance comparison between PID and dead-time compensating controllers,” Journal of Process Control, vol. 12, no. 8, pp. 887–895, December 2002.

    Article  Google Scholar 

  9. C. Santacesaria and R. Scattolini, “Easy tuning of Smith predictor in presence of delay uncertainty,” Automatica, vol. 29, no. 6, pp. 1595–1597, November 1993.

    Article  MathSciNet  Google Scholar 

  10. T. H. Lee, Q. G. Wang, and K. K. Tan, “Robust Smith predictor controller for uncertain delay systems,” AIChE Journal, vol. 42, no. 4, pp. 1033–1040, April 1996.

    Article  Google Scholar 

  11. C. E. Garcia and M. Morari, “Internal model control 1: a unified review and some new results,” Industrial & Engineering Chemistry Process Design and Development, vol. 21, no. 2, pp. 308–316, April 1982.

    Article  Google Scholar 

  12. J. E. Normey-Rico, C. Bordons, and E. F. Camacho, “Improving the robustness of dead-time compensating PI controllers,” Control Engineering Practice, vol. 5, no. 6, pp. 801–810, June 1997.

    Article  Google Scholar 

  13. Z. J. Palmor, “Stability properties of Smith dead time compensator controller,” International Journal of Control, vol. 32, no. 6, pp. 937–949, June 1980.

    Article  MATH  Google Scholar 

  14. Z. J. Palmor and Y. Halevi, “On the design and properties of multivariable dead time compensators,” Automatica, vol. 19, no. 3, pp. 255–264, May 1983.

    Article  MATH  Google Scholar 

  15. M. R. Matausek and A. D. Micie, “A modified Smith predictor for controlling a process with an integrator and long dead-time,” IEEE Trans. on Automatic Control, vol. 41, no. 6, pp. 1199–1203, June 1996.

    Article  MATH  Google Scholar 

  16. M. R. Matausek and A. D. Micie, “On the modified Smith predictor for controlling a process with an integrator and long dead-time,” IEEE Trans. on Automatic Control, vol. 44, no. 8, pp. 1603–1606, August 1999.

    Article  MATH  Google Scholar 

  17. H. Kwak, S. Whan, and I. B. Lee, “Modified Smith predictor for integrating processes: Comparisons and proposition,” Industrial & Engineering Chemistry Research, vol. 40, no. 6, pp. 1500–1506, February 2001.

    Article  Google Scholar 

  18. I. Kaya, “Obtaining controller parameters for a new PI-PD Smith predictor using auto tuning,” Journal of Process Control, vol. 13, no. 5, pp. 465–472, August 2003.

    Article  MathSciNet  Google Scholar 

  19. I. L. Chien, S. C. Peng, and J. H. Liu, “Simple control method for integrating processes with long deadtime,” Journal of Process Control, vol. 12, no. 3, pp. 391–404, April 2002.

    Article  Google Scholar 

  20. C. C. Hang, Q. G. Wang, and X. P. Yang, “A modified Smith predictor for a process with an integrator and long dead time,” Industrial & Engineering Chemistry Research, vol. 42, no. 3, pp. 484–489, January 2003.

    Article  Google Scholar 

  21. J. E. Normey-Rico and E. F. Camacho, “A unified approach to design dead-time compensators for stable and integrative process with deadtime,” IEEE Trans. on Automatic Control, vol. 47, no. 2, pp. 299–305, February 2002.

    Article  MathSciNet  Google Scholar 

  22. Q. C. Zhong and J. Normey-Rico, “Control of integral processes with dead-time. part 1: disturbance observer-based 2 DOF control scheme,” IEE Proceedings Control Theory & Applications, vol. 149, no. 4, pp. 285–290, July 2002.

    Article  Google Scholar 

  23. Q. C. Zhong and H. X. Li, “2-Degree-of-freedom proportional-integral derivative-type controller incorporating the Smith principle for processes with dead time,” Industrial & Engineering Chemistry Research, vol. 41, no. 10, pp. 2448–2454, April 2002.

    Article  Google Scholar 

  24. K. Watanabe and M. Ito, “A process model control for linear systems with delay,” IEEE Trans. on Automatic Control, vol. 26, no. 6, pp. 1261–1268, December 1981.

    Article  MATH  Google Scholar 

  25. J. E. Normey-Rico and E. F. Camacho, “Robust tuning of dead time compensators for process with an integrator and long time delay,” IEEE Trans. on Automatic Control, vol. 44, no. 8, pp. 1597–1603, August 1999.

    Article  MathSciNet  MATH  Google Scholar 

  26. K. J. Astrom, C. C. Hang, and B. C. Lim, “A new Smith predictor for controlling a process with an integrator and long dead time,” IEEE Trans. on Automatic Control, vol. 39, no. 2, pp. 343–345, February 1994.

    Article  MathSciNet  MATH  Google Scholar 

  27. Q. C. Zhong, “Control of integral processes with dead time — part 3: deadbeat disturbance response,” IEEE Trans. on Automatic Control, vol. 48, no. 1, pp. 153–159, January 2003.

    Article  Google Scholar 

  28. T. Liu, W. Zhang, and D. Gu, “Analytical design of two degree of freedom control scheme for openloop unstable processes with delay,” Journal of Process Control, vol. 15, no. 5, pp. 559–572, August 2005.

    Article  Google Scholar 

  29. M. R. Matausek and A. I. Ribic, “Control of stable, integrating and unstable processes by the Modified Smith Predictor,” Journal of Process Control, vol. 22, no. 2, pp. 338–343, January 2012.

    Article  Google Scholar 

  30. X. Lu, Y. S. Yang, Q. G. Wang, and W. X. Zheng, “A double two-degree of- freedom control scheme for improved control of unstable delay processes,” Journal of Process Control, vol. 15, no. 5, pp. 605–614, August 2005.

    Article  Google Scholar 

  31. Y. Lee, J. Lee, and S. Park, “IMC-based control system design for unstable process,” Industrial & Engineering Chemistry Research, vol. 41, no. 17, pp. 4288–4294, July 2002.

    Article  Google Scholar 

  32. Y. Lee, J. Lee, and S. Park, “PID controllers tuning for integrating and unstable process with time delay,” Chemical Engineering Science, vol. 55, no. 17, pp. 3481–3493, September 2000.

    Article  Google Scholar 

  33. S. Majhi and D. P. Atherton, “Obtaining controller parameters for a new Smith predictor using autotuning,” Automatica, vol. 36, no. 11, pp. 1651–1658, November 2000.

    Article  MathSciNet  MATH  Google Scholar 

  34. W. Tan, H. J. Marquez, and T. Chen, “IMC design or unstable processes with time delays,” Journal of Process Control, vol. 13, no. 3, pp. 203–213, April 2003.

    Article  Google Scholar 

  35. Q. G. Wang, H. Q. Zhou, and Y. Zhang, “A comparative study on control of unstable processes with time delay,” Proc. of the 5th Asian Control Conf., Melbourne, Australia, pp. 2006–2014, 2004.

    Google Scholar 

  36. P. Garcıa, P. Albertos, and T. Hagglund, “Control of unstable non-minimum-phase delayed systems,” Journal of Process Control, vol. 16, no. 10, pp. 1099–1111, December 2006.

    Article  Google Scholar 

  37. J. E. Normey-Rico and E. F. Camacho, “Unified approach for robust dead-time compensator design,” Journal of Process Control, vol. 19, no. 1, pp. 38–47, January 2009.

    Article  Google Scholar 

  38. T. L. M. Santos, P. E. A. Botura, and J. E. Normey-Rico, “Dealing with noise in unstable dead-time process control,” Journal of Process Control, vol. 20, no. 1, pp. 840–847, August 2010.

    Article  Google Scholar 

  39. N. F. Jerome and W. H. Ray, “High performance multivariable control strategies for systems having time delays,” AIChE Journal, vol. 32, no. 6, pp. 914–931, June 1986.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohammad Shahrokhi.

Additional information

Recommended by Editorial Board member Young Ik Son under the direction of Editor Yoshito Ohta.

Sabereh Rezaei received her B.Sc. degree in Chemical Engineering from Sharif University of Technology, Iran and her M.Sc. degree in Chemical Engineering (Process Simulation and Control) from Sharif University of Technology, in 2006 and 2009, respectively. Her research interests include process control.

Mohammad Shahrokhi received his B.Sc. degree in Chemical Engineering from Sharif University of Technology and his Ph.D. degree from Wisconsin University in the same field, in 1977 and 1981, respectively. From 1981 to 1988 he worked as a faculty member of Chem. Eng. Dept. of Isfahan University of Technology and in 1988 he joined Sharif University of Technology where he is currently working as professor of Chemical Engineering at the Department of Chem. & Petrol. Engineering. His research interest is process control especially adaptive control.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rezaei, S., Shahrokhi, M. Robust controller design for discrete unstable non-minimum-phase delayed stochastic processes. Int. J. Control Autom. Syst. 11, 893–902 (2013). https://doi.org/10.1007/s12555-012-0184-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-012-0184-0

Keywords

Navigation