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Tuning a Fractional Order PID Controller with Lead Compensator in Frequency Domain
Abstract:To achieve the desired specifications of gain and phase margins for plants with time-delay that stabilized with FO-PID controller a lead compensator is designed. At first the range of controlled system stability based on stability boundary criteria is determined. Using stability boundary locus method in frequency domain the fractional order controller parameters are tuned and then with drawing bode diagram in frequency domain accessing to desired gain and phase margin are shown. Numerical examples are given to illustrate the shapes of the stabilizing region and to show the design procedure.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077613Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2180
 I. Podlubny, "Fractional Differential Equations," Academic Press, 1999.
 R. Hilfer (ed.2), "Fractional Calculus in Physics," World Scientific, 2000.
 D. Xue, Y.Q. Chen. A Comparative Introduction of Four Fractional Order Controllers. Proceedings of the 4 World Congress on Intelligent Control and Automation June 10-14, 2002, Shanghai, P.R.China.
 S. Manabe, The Non-Integer Integral and its Applications to Control Systems, ETJ of Japan, vol. 6, no. 3/4, 1961, pp. 83-87.
 Monje, V. Feliu, A. J. Calderon, B.M. Vinagre. The Fractional Order Lead Compensator 0-7803-8588-8/04, 2004, IEEE
 M.S. Tavazoei, M. Haeri. Chaos control via a simple fractional-order controller. Physics Letters A 372 (2008) 798-807.
 R.S. Barbosa, J.A.T. Machado, M.F. Silva. Time domain design of fractional differintegrators using least-squares. Signal Processing 86 (2006) 2567-2581
 M. K. Bouafoura, N.B. Braiek. PIλD╬╝ controller design for integer and fractional plants using piecewise orthogonal functions. Commun Nonlinear Sci Numer Simulat 15 (2010) 1267-1278.
 A. Biswas, S. Das, A. Abraham, S. Dasgupta. Design offractional-order PIλD╬╝ controllers with an improved differential evolution. Engineering Applications of Artificial Intelligence 22 (2009) 343-350.
 C. A. Monje, B. M. Vinagre, Y.Q. Chen, V. Feliu, P. Lanusse, J. Sabatier. PROPOSALS FOR FRACTIONAL PIλD╬╝ TUNING. supported by the Spanish Research Grant 2PR02A024 (Junta de Extremadura)
 C. A. Monje, B.M. Vinagre. Y.Q. Chen. V. Feliu. On Fractional PIλ Controllers: Some Tuning Rules for Robustness to Plant Uncertainties. 2003 Kluwer Academic Publishers. Printed in the Netherlands.
 Y. Luo, H.S. Li, Y.Q. Chen. Fractional Order Proportional and Derivative Controller Synthesis for A Class of Fractional Order Systems: Tuning Rule and Hardware-in-the-loop Experiment. Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference Shanghai, P.R. China, December 16-18, 2009.
 Y. Luo, Y.Q. Chen. Fractional-order
[Proportional Derivative] Controller for Robust Motion Control: Tuning Procedure and Validation. 2009 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June 10-12, 2009
 H.S. Li, Y. Luo, Y.Q. Chen. A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments. IEEE Transactions on Control Systems Technology, VOL. 18, NO. 2, March 2010.
 Y. Luo, Y.Q. Chen, C.Y. Wang, Y.G. Pi. Tuning fractional order proportional integral controllers for fractional order systems. Journal of Process Control 20 (2010) 823-831
 S. E. Hamamci. An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using Fractional-Order PID Controllers. IEEE Transactions on Automatic Control, VOL. 52, NO. 10, October 2007.
 D.J. Wang. Synthesis of phase-lead/lag compensators with complete information on gain and phase margins. Automatica 45 (2009) 1026_1031.
 Q.G. Wang, Z. Ye, C.C. Hang. Tuning of phase-lead compensators for exact gain and phase margins. Automatica 42 (2006) 349 - 352.
 A.P. Loh, X. Cai, W.W. Tan. Auto-tuning of phase lead/lag compensators. Automatica 40 (2004) 423 - 429.
 K. S. Yeung, K. O. Chaid, T. X. Dinh, (1995). Bode design chart for continuous-time and discrete-time compensators. IEEE Transactions on Education, 38(3), 252_257.
 F.Y. Wang (2003). The exact and unique solution for phase-lead and phase-lag compensation. IEEE Transactions on Education, 46(2), 258_262.
 Q. G. Wang, Z. Ye, C. C. Hang. (2006). Tuning of phase-lead compensators for exact gain and phase margins. Automatica, 42, 349_352.
 I. Podlubny, "Fractional-order systems and PIλD╬╝ controllers," IEEE Trans. Autom. Control, vol. 44, no. 1, pp. 208-214, 1999.
 R.C. Dorf, R.H. Bishop. Modern Control Systems (10th Edition). Pearson Prentice Hall (2010).
 C. Hwang and Y.-C. Cheng, "A numerical algorithm for stability testing of fractional delay systems," Automatica, vol. 42, no. 5, pp. 825-831, 2006.
 J. I. Neimark, "D-decomposition of the space of quasi-polynomials (on the stability of linearized distributive systems)," in Amer. Math. Soc. (AMS) Transl., ser. 2. Providence, R. I.: AMS Soc., 1973, vol. 102, Ten papers in analysis, pp. 95-131.
 Y.C. Cheng , C. Hwang, "Stabilization of unstable first-order time delay systems using fractional-order PD controllers," J. Chinese Inst. Eng., vol. 29, no. 2, pp. 241-249, 2006.