Fractional-Order PI Controller Tuning Rules for Cascade Control System

Authors: Truong Nguyen Luan Vu, Le Hieu Giang, Le Linh

Abstract:

The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.

Keywords: Fractional calculus, fractional–order proportional integral controller, cascade control system, internal model control approach.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125467

References:

[1] F. D. Jury, Fundamentals of Three-Mode Controllers. NY, USA: Fisher Controls Company-Technical Monogragh, 1973.
[2] J. O. Hougen, Measurement and Control Applications. Pittsburgh, USA: Instrument Society of America, 1979.
[3] T. F. Edgar, R. C. Heeb, and J. O. Hougen, “Computer-aided process control system design using interactive graphics,” Comput. Chem. Eng, vol. 5, no. 4, pp. 225-231, 1982.
[4] P. R. Krishnaswamy and G. P. Rangaiah, “When to use cascaded control,” Ind. Eng. Chem. Res., vol. 29, no. 1, pp. 2163-2166, 1990.
[5] Y. Lee, S. Park, and M. Lee, “PID controller tuning to obtain desired closed loop responses for cascade control systems,” Ind. Eng. Chem. Res., vol. 37, no. 4, pp. 1859-1865, 1998.
[6] K. S. Miller and B. Ross, An Introduction to the Fractional calculus and Fractional Differential Equations. NY, USA: A Wiley-Interscience Publication, 1993.
[7] I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations to methods of their solution and some of their applications. San Diego, USA: Academic Press, 1999.
[8] I. Podlubny, “Fractional-order systems and PIλDμ-controllers,” IEEE Trans Automatic Control, vol. 44, no. 1, pp. 208–14, 1999.
[9] N. L. V. Truong and M. Lee, “Analytical design of fractional-order proportional-integral controllers for time-delay processes,” ISA Trans., vol. 52, pp. 583-591, 2013.
[10] H. Bode, “Relations between attenuation and phase in feedback amplifier design,” Bell System Technical Journal, vol.19, no. 1, pp. 421–454, 1940.
[11] R. S. Barbosa, T. Machado, and I. M. Ferreira, “Tuning of PID controllers based on Bode’s ideal transfer function,” Nonlinear Dynamics, vol. 38, no. 2, pp. 305–21, 2004.
[12] A. Oustaloup and M. Benoit, La Commande CRONE: Du Calaire Au Multivariable. Paris, France: Hermès, 1999.
[13] B. M. Vinagre, C.A Monje, A. J. Calderon, and J. I. Suarez, “ Fractional PID controllers for industry application: a brief introduction,” Journal of Vibration Control, vol. 13, pp. 1419–1429, 2007.
[14] D. Valério, J. S. Da Costa, “Tuning of fractional PID controllers with Ziegler–Nichols-type rules,” Signal Process, vol. 86, no. 1, pp. 2771–2784, 2006.
[15] C. A Monje, B. M. Vinagre, V. Feliu, and Y.Q. Chen, “Tuning and auto-tuning of fractional order controllers for industry applications,” Control Engineering Practice, vol. 16, pp. 798–812, 2008.
[16] M. Morari, E. Zafiriou, Robust Process Control. NJ, USA: Prentice Hall, 1989.
[17] D. E. Seborg, T. F. Edgar, and D. A. Mellichamp, Process Dynamics and Control. New York, USA: Wiley, 1989.