Independent Design of Multi-loop PI/PID Controllers for Multi-delay Processes

Authors: Truong Nguyen Luan Vu, Moonyong Lee

Abstract:

The interactions between input/output variables are a very common phenomenon encountered in the design of multi-loop controllers for interacting multivariable processes, which can be a serious obstacle for achieving a good overall performance of multiloop control system. To overcome this impediment, the decomposed dynamic interaction analysis is proposed by decomposing the multiloop control system into a set of n independent SISO systems with the corresponding effective open-loop transfer function (EOTF) within the dynamic interactions embedded explicitly. For each EOTF, the reduced model is independently formulated by using the proposed reduction design strategy, and then the paired multi-loop proportional-integral-derivative (PID) controller is derived quite simply and straightforwardly by using internal model control (IMC) theory. This design method can easily be implemented for various industrial processes because of its effectiveness. Several case studies are considered to demonstrate the superior of the proposed method.

Keywords: Multi-loop PID controller, internal model control(IMC), effective open-loop transfer function (EOTF)

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081119

References:

[1] H. H. Rosenbrock, Computer-aided Control System Design. New York: Academic Press, 1974.
[2] A.G. J. MacFarlanne, Frequency Response Methods in Control Systems. New York: IEEE Press, 1979.
[3] J. M. Maciejowski, Multivariable Feedback Design. New York: Addison Wesley, 1989.
[4] E. F. Camacho and C. Bordons, Model Predictive Control. New York: Springer, 1998.
[5] Q. G. Wang, Y. Zhang, and M. S. Chiu, "Non-interacting control design for multivariable industrial processes," J. Process Control, vol. 13, pp. 253-265, 2003.
[6] P. Grosdidier and M. Morari, "A computer aided methodology for the design of decentralized controllers," Comput. Chem. Eng., vol. 11, pp. 423-433, 1987.
[7] M. F. Witcher and T. J. McAvoy, "Interaction control systems: steady state and dynamic measurement of interaction," ISA Trans., vol. 16, no. 3, pp. 35-41, 1977.
[8] E. H. Bristol, "Recent results on interactions for multivariable process control," Proc. AIChE Meeting, Miami, FL, 1978.
[9] L. S. Tung and T. F. Edgar, "Analysis of control-output interactions in dynamic systems," AIChE J., vol. 27, no. 4, pp. 690-693, 1981.
[10] Y. Lee, S. Park, M. Lee, and C. Brosilow, "PID controller tuning for desired closed-loop responses for SI/SO systems," AIChE J., vol. 44, pp. 106-115, 1998.
[11] S. L. William, Control System Fundamentals. CRC Press, 1999.
[12] R. K. Wood and M. W. Berry, "Terminal composition control of a binary distillation column," Chem. Eng. Sci., vol. 28, pp. 1707-1717, 1973.
[13] W. H. Ho, T. H Lee, and O. P. Gan, "Tuning of multi-loop PID controllers based on gain and phase margin specifications," Ind. Eng. Chem. Res., vol. 36, pp. 2231-2238, 1997.
[14] A. P. Loh, C. C. Hang, C. K. Quek, and V. U. Vasnani, "Auto-tuning of multi-loop proportional-integral controllers using relay feedback," Ind. Eng. Chem. Res., vol. 32, pp. 1102-1107, 1993.
[15] W. L. Luyben, "Simple method for tuning SISO controllers in multivariable systems," Ind. Eng. Chem. Process Des. Dev., vol. 25, pp. 654-660, 1986.
[16] J. Lee, W. Cho, and T. F. Edgar, "Multi-loop PI controller tuning for interacting multivariable processes," Comp. Chem. Eng., vol. 22, pp. 1711-1723, 1998.
[17] 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, no. 7, pp. 1631-1635, 2004.