Design of Advanced Multi-loop PI Controller for Multi-delay Processes

다중 시간지연 공정을 위한 개선된 다중루프 PI 제어기 설계

  • 트롱부 (영남대학교 디스플레이화학공학부) ;
  • 이문용 (영남대학교 디스플레이화학공학부)
  • Published : 2010.01.01


An analytical method for robust design of the multi-loop proportional-integral (PI) controller is proposed for various types of multi-delay processes. On the basis of the direct synthesis and generalized IMC-PID approach, the analytical tuning rules of the multi-loop PI controller are firstly derived for achieving the desired closed-loop response, and the structured singular value synthesis is then utilized for the tradeoffs between the robust stability and performance by adjusting only one design parameter (i.e., the closed-loop time constant). To verify the superiority of the proposed method, the simulation studies have been conducted on a wide variety of multivariable processes. The multi-loop PI controller designed by the proposed method shows a fast, well-balanced and robust response with the minimum integral absolute error (IAE) in compared with other renowned methods.


  1. W. L. Luyben, "Simple method for tuning SISO controllers in multivariable systems," Ind. Eng. Chem. Proc. Des. Dev., vol. 25, pp. 654-660, 1986.
  2. P. Grosdidier and M. Morari, "Interaction measures for systems under decentralized control," Automatica, vol. 22, pp. 309-319, 1986.
  3. A. P. Loh, C. C. Hang, C. K. Quek, and V. N. Vasnani, "Autotuning of multivariable proportional-integral controllers using relay feedback," Ind. Eng. Chem. Res., vol. 32, pp. 1102-1107, 1993.
  4. M. Lee, K. Lee, C. Kim, and J. Lee, "Analytical design of multi-loop PID controllers for desired closed-loop responses," AIChE J., vol. 50, pp. 1631-1635, 2004.
  5. N. L. V. Truong and M. Lee, "Robust multi-loop PI controller design for multivariable processes," Korea Automatic Control Conference, Bexco, Pusan, 2009, pp. 771-776.
  6. J. G. Truxal, Automatic Feedback Control System Synthesis, McGraw-Hill, New York, 1955.
  7. D. E. Seborg, T. F. Edgar, and D. A. Mellichamp, Process Dynamics and Control, John Wiley & Sons, New York, 1989.
  8. N. L. V. Truong and M. Lee, "Multi-loop PI controllers based on the direct synthesis for interacting multi-time delay processes," ISA Trans., in press, 2009.
  9. M. Morari and Z. Zafiriou, Robust Process Control, Prentice Hall, 1989.
  10. C. E. Garcia and M. Morari, "Internal model control I. A unifying review and some new results," Ind. Eng. Chem. Proc. Process. Des. Dev., vol. 21, pp. 308-318, 1982.
  11. D. E. Rivera, M. Morari, and S. Skogestad, "Internal model control. 4. PID controller design: multi-loop design," Ind. Eng. Process Design. Dev, vol. 25, pp. 252-262, 1986.
  12. C. G. Economou and M. Morari, "Internal model control 6: multi-loop design," Ind. Eng. Chem. Proc. Process. Des. Dev., vol. 25, pp. 411-419, 1989.
  13. N. L. V. Truong, J. Lee, and M. Lee, "Design of multi-loop PID controllers based on the generalized IMC-PID method with Mp criterion," International Journal of Control, Automation, and Systems, vol. 5, pp. 212-217, 2007.
  14. S. Skogestad and I. Postlethwaithe, Multivariable Feedback Control Analysis and Design, John Wiley & Sons, 1996.
  15. J. C. Doyle, J. E. Wall, and G. Stein, "Performance and robustness analysis for structured uncertainty," Proc. of IEEE Conf. Decision Control, pp. 629-636, 1982.
  16. S. L. William, Control system fundamentals, CRC, 1999.
  17. E. H. Bristol, "Recent results on interactions in multivariable process control," In: AIChE Annual Meeting at Florida. p. 78b, 1978.
  18. J. Jung, J. Y. Choi, and J. Lee, "One-parameter method for a multi-loop control system design," Ind. Eng. Chem. Res., vol. 38, pp. 1580-1588, 1999.
  19. J. Lee, W. Cho, and T. F. Edgar, "Multi-loop PI controller tuning for interacting multivariable processes," Comput. Chem. Eng., vol. 22, pp. 1711-1723, 1998.