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.
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O. J. M. Smith, “Closed control of loops with dead time,” Chemical Engineering Progress, vol. 53, no. 5, pp. 217–219, May 1957.
M. Morari and E. Zafiriou, Robust Process Control, Prentice Hall, Englewood Cliffs, 1989.
J. E. Normey-Rico and E. F. Camacho, Control of Dead-time Processes, Springer, Berlin, 2007.
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.
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.
T. Hagglund, “An industrial dead-time compensating pi controller,” Control Engineering Practice, vol. 4, no. 6, pp. 749–756, June 1996.
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.
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.
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.
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.
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.
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.
Z. J. Palmor, “Stability properties of Smith dead time compensator controller,” International Journal of Control, vol. 32, no. 6, pp. 937–949, June 1980.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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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.
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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
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DOI: https://doi.org/10.1007/s12555-012-0184-0