Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30075
Robust Fractional-Order PI Controller with Ziegler-Nichols Rules

Authors: Mazidah Tajjudin, Mohd Hezri Fazalul Rahiman, Norhashim Mohd Arshad, Ramli Adnan

Abstract:

In process control applications, above 90% of the controllers are of PID type. This paper proposed a robust PI controller with fractional-order integrator. The PI parameters were obtained using classical Ziegler-Nichols rules but enhanced with the application of error filter cascaded to the fractional-order PI. The controller was applied on steam temperature process that was described by FOPDT transfer function. The process can be classified as lag dominating process with very small relative dead-time. The proposed control scheme was compared with other PI controller tuned using Ziegler-Nichols and AMIGO rules. Other PI controller with fractional-order integrator known as F-MIGO was also considered. All the controllers were subjected to set point change and load disturbance tests. The performance was measured using Integral of Squared Error (ISE) and Integral of Control Signal (ICO). The proposed controller produced best performance for all the tests with the least ISE index.

Keywords: PID controller, fractional-order PID controller, PI control tuning, steam temperature control, Ziegler-Nichols tuning.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1087426

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2831

References:


[1] K. J. Åström and T. Hägglund, “The future of PID control,” Control Engineering Practice, vol. 9, no. 11, pp. 1163–1175, Nov. 2001.
[2] K. J. Astrom, “Toward Intelligent Control,” in American Control Conference, 1988.
[3] K. Astrom and T. Hagglund, “Revisiting the Ziegler-Nichols step response method for PID control,” Journal of Process Control, vol. 14, no. 6, pp. 635–650, Sep. 2004.
[4] K. J. Astrom and T. Hagglund, Advanced PID Control. Instrumentation, Systems, and Automation Society (ISA), 2006, p. 158.
[5] K. J. Åström and T. Hägglund, “Revisiting the Ziegler–Nichols step response method for PID control,” Journal of Process Control, vol. 14, no. 6, pp. 635–650, Sep. 2004.
[6] A. O. Dwyer, “A summary of PI and PID controller tuning rules for processes with time delay . Part 1: PI controller tuning rules,” pp. 175– 180, 2000.
[7] I. Podlubny, “Fractional-order Systems and PIλDD,” IEEE Transaction on Automatic Control, vol. 44, no. 1, pp. 208–214, 1999.
[8] A. Ruszewski and A. Sobolewski, “Comparative studies of control systems with fractional controllers,” Electrical Review, vol. 88, no. 4b, pp. 204–208, 2012.
[9] Y. Q. Chen and K. L. Moore, “Discretization schemes for fractionalorder differentiators and integrators,” IEEE Transactions on Circuits and Systems- I: Fundamental Theory and Applications, vol. 49, no. 3, pp. 363–367, Mar. 2002.
[10] C. Ma and Y. Hori, “Fractional Order Control: Theory and Applications in Motion Control,” Industrial Electronics Magazine, IEEE, no. 1, pp. 6–16, 2007.
[11] S. Manabe, “The non-integer Integral and its Application to Control Systems,” vol. 6, no. 3, pp. 84–87, 1961.
[12] M. Axtell and M. E. Bise, “Fractional Calculus Applications in Control Systems,” in IEEE 1990 Nat. Aerospace and Electronics Conference, 1990, pp. 563–566.
[13] A. Oustaloup, X. Moreau, and M. Nouillant, “The crone suspension,” Control Engineering Practice, vol. 4, no. 8, pp. 1101–1108, 1996.
[14] A. Oustaloup, J. Sabatier, and P. Lanusse, “From fractal robustness to the CRONE,” 2000.
[15] Y. Chen, H. Dou, B. M. Vinagre, and C. A. Monje, “A Robust Tuning Method For Fractional Order PI Controllers,” in Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications, 2006.
[16] J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of fractional calculus,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1140–1153, Mar. 2011.
[17] B. M. Vinagre, I. Podlubny, A. Hernandez, and V. Feliu, “Some Approximations of Fractional Order Operators Used in Control Theory and Applications,” Fractional calculus and applied analysis, vol. 3, no. 3, pp. 231–248, 2000.
[18] C. A. Monje, B. M. Vinagre, V. Feliu, and Y. Chen, “Tuning and autotuning of fractional order controllers for industry applications,” Control Engineering Practice, vol. 16, no. 7, pp. 798–812, Jul. 2008.
[19] C. A. Monje, B. M. Vinagre, Y. Q. Chen, V. Feliu, P. Lanusse, and J. Sabatier, “Proposals for Fractional PID Tuning,” 2005, vol. 024, pp. 2– 7.
[20] A. Narang, S. L. Shah, and T. Chen, “Tuning of fractional PI controllers for fractional order system models with and without time delays,” in American Control Conference, 2010, pp. 6674–6679.
[21] V. Feliu-Batlle, R. R. Pérez, and L. S. Rodríguez, “Fractional robust control of main irrigation canals with variable dynamic parameters,” Control Engineering Practice, vol. 15, no. 6, pp. 673–686, Jun. 2007.
[22] C. Wang and Y. Chen, “Fractional order proportional integral (FOPI) and
[proportional integral] (FO
[PI]) controller designs for first order plus time delay (FOPTD) systems,” 2009 Chinese Control and Decision Conference, vol. 2, no. 3, pp. 329–334, Jun. 2009.
[23] R. Barbosa, J. A. T. Machado, and I. S. Jesus, “On the Fractional PID Control of a Laboratory Servo System,” in Proceedings of the 17th World Congress The International Federation of Automatic Control (IFAC), 2008, pp. 15273–15279.
[24] J. J. Gude and E. Kahoraho, “Modified Ziegler-Nichols method for fractional PI controllers,” in Conference on Emerging Technologies & Factory Automation, 2010, no. 2, pp. 1–5.
[25] Y. Chen, T. Bhaskaran, and D. Xue, “Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers,” Journal of Computational and Nonlinear Dynamics, vol. 3, no. 2, p. 021403, 2008.
[26] F. Merrikh-Bayat, “Rules for selecting the parameters of Oustaloup recursive approximation for the simulation of linear feedback systems containing PIλDμ controller,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1852–1861, Apr. 2012.
[27] D. Valério and J. S. da Costa, “Tuning of fractional PID controllers with Ziegler–Nichols-type rules,” Signal Processing, vol. 86, no. 10, pp. 2771–2784, Oct. 2006.
[28] I. Podlubny, L. Dorcak, and I. Kostial, “On Fractional Derivatives, Fractional-Orlder Dynamic Systems and PIλ Dμ Controllers,” in Proceedings of the 36th Conference on Decision & Control, 1997, no. December, pp. 4985–4990.
[29] F. Merrikh-Bayat, “Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers.” ISA transactions, vol. 50, no. 2, pp. 170–6, Apr. 2011.
[30] K. J. Astrom and T. Hagglund, Advanced PID Control. Instrumentation, Systems, and Automation Society (ISA), 2006, p. 158.
[31] T. Hagglund and K. J. Astrom, “Revisiting the Ziegler-Nichols Tuning Rules for PI Control,” Asian Journal of Control, vol. 4, no. 4, pp. 364– 380, 2002.