Abstract
A new fractional-order proportional-integral controller embedded in a Smith predictor is systematically proposed based on fractional calculus and Bode’s ideal transfer function. The analytical tuning rules are first derived by using the frequency domain for a first-order-plus-dead-time process model, and then are easily applied to various dynamics, including both the integer-order and fractional-order dynamic processes. The proposed method consistently affords superior closed-loop performance for both servo and regulatory problems, since the design scheme is simple, straightforward, and can be easily implemented in the process industry. A variety of examples are employed to illustrate the simplicity, flexibility, and effectiveness of the proposed SP-FOPI controller in comparison with other reported controllers in terms of minimum the integral absolute error with a constraint on the maximum sensitivity value.
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References
O. J. Smith, ISA J., 6, 28 (1959).
K. J. Åström, C. C. Hang and B. C. Lim, IEEE Transactions on Automatic Control, 39, 343 (1994).
T. Hägglund, IEEE Control System Magazine, 12, 57 (1992).
D. Lee, M.-Y. Lee, S. Sung and I. Lee, J. Process Control, 9, 79 (1999).
M. Morari and E. Zafiriou, Robust Process Control, Prentice-Hall, Englewood Cliffs, NJ (1989).
H. Q. Zhou, Q. G. Wang and L. Min, ISA Transactions, 46, 493 (2007).
A. S. Rao and M. Chidambaram, ISA Transactions, 47, 407 (2008).
K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, Wiley-Interscience (1993).
A. Oustaloup, La Commande CRONE: Commande Robuste d’Ordre Non Entier, Hermes, Paris (1991).
I. Podlubny, IEEE Transactions on Automatic Control, 44, 208 (1999).
R. S. Barbosa, T. Machado and I. M. Ferreira, Nonlinear Dynamics, 38, 305 (2004).
C. A. Monje, B. M. Vinagre, V. Feliu and Y.-Q. Chen, Control Eng. Pract., 16, 798 (2008).
T. N. L. Vu and M. Lee, ISA Transactions, 52, 583 (2013).
V. Feliu-Batlle, R. Rivas-Perez, F.G. Castillo-Garcia and L. Sanchez-Rodriguez, J. Process Control, 19, 506 (2009).
C. A. Monje, Y. Q. Chen, B.M. Vinare, D. Xue and V. Feliu, Fractional order systems and controls funamental and application, Spinger-Velag (2010).
H.W. Bode, Bell System Technical J., 19, 421 (1940).
H.W. Bode, Network analysis and feedback amplifier design, Van Nostrand, New York (1945).
F. Padula and A. Visioli, J. Process Control, 21, 69 (2011).
Y. Q. Chen, T. Bhaskaran and D. Xue, ASME J. Computational and Nonlinear Dynamics, 3, 0214031 (2008).
J. J. Gude and E. Kahoraho, IEEE International Conference on Emerging Technologies and Factory Automation (ETFA) (2009).
I. Podlubny, L. Dorcak and I. Kostial, Proceedings of the 36th IEEE CDC, San Diego (1999).
K. B. Mohamed and B. B. Naceur, Commun Nonlinear SCI Numer Simulat, 15, 1267 (2010).
A. Oustaloup, F. Levron and F. Nanot, EEE Trans Systems I: Fundamental Theory and Applications, 47, 25 (2000).
Y. Lee, S. Part, M. Lee and C. Brosilow, AIChE J., 44, 106 (1998).
D. E. Rivera, M. Morari and S. Skogestad, Ind. Eng. Chem. Proc. Des. Dev., 25, 252 (1986).
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Vu, T.N.L., Lee, M. Smith predictor based fractional-order PI control for time-delay processes. Korean J. Chem. Eng. 31, 1321–1329 (2014). https://doi.org/10.1007/s11814-014-0076-5
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DOI: https://doi.org/10.1007/s11814-014-0076-5