Multi-Objective Optimal Fuzzy Fractional-Order PID Controller Design

Amir Hajiloo; Wen-Fang Xie

doi:10.20965/jaciii.2014.p0262

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JACIII Vol.18 No.3 pp. 262-270

doi: 10.20965/jaciii.2014.p0262

(2014)

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Multi-Objective Optimal Fuzzy Fractional-Order PID Controller Design

Amir Hajiloo and Wen-Fang Xie

Department of Mechanical and Industrial Engineering, Concordia University, 1455 de Maisonneuve W., Montreal, QC, H3G 1M8, Canada

Received:

November 1, 2013

Accepted:

February 21, 2014

Published:

May 20, 2014

Keywords:

fractional-order calculus, PID controller, fuzzy logic, Pareto

Abstract

The design of the optimal fuzzy fractional-order PID controller is addressed in this work. A multi-objective genetic algorithm is proposed to design rule base and membership functions of the fuzzy logic systems. Three conflicting objective functions in both time and frequency domains have been used in Pareto design of the fuzzy fractional-order PID controller. The simulation results reveal the effectiveness of the proposed method in comparison with the results produced by the fractional-order PID controllers.

Cite this article as:

A. Hajiloo and W. Xie, “Multi-Objective Optimal Fuzzy Fractional-Order PID Controller Design,” J. Adv. Comput. Intell. Intell. Inform., Vol.18, No.3, pp. 262-270, 2014.

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References

[1] Y.-Q. Chen, I. Petras, and D. Xue, “Fractional order control – A tutorial,” In American Control Conf. 2009 (ACC ’09), pp. 1397-1411, June 2009.
[2] A. Hajiloo, N. Nariman-zadeh, and A. Moeini, “Pareto optimal robust design of fractional-order PID controllers for systems with probabilistic uncertainties,” Mechatronics, Vol.22, No.6, pp. 788-801, 2012.
[3] C. A. Monje, B. M. Vinagre, V. Feliu, and Y. Chen, “Tuning and auto-tuning of fractional order controllers for industry applications,” Control Engineering Practice, Vol.16, No.7, pp. 798-812, 2008.
[4] A. Biswas, S. Das, A. Abraham, and S. Dasgupta, “Design of Fractional-order PI^λ D^μ Controllers with an Improved Differential Evolution,” Eng. Appl. Artif. Intell., Vol.22, No.2, pp. 343-350, March 2009.
[5] R. S. Barbosa, J. T. Machado, and A. M. Galhano, “Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena,” J. of Vibration and Control, Vol.13, No.9-10, pp. 1407-1418, 2007.
[6] M. K. Bouafoura and N. B. Braiek, “PI^λ D^μ controller design for integer and fractional plants using piecewise orthogonal functions,” Communications in Nonlinear Science and Numerical Simulation, Vol.15, No.5, pp. 1267-1278, 2010.
[7] I. Podlubny, “Fractional-order systems and PI^λ D^μ -controllers,” IEEE Trans. on Automatic Control, Vol.44, No.1, pp. 208-214, 1999.
[8] M. Zamani, M. Karimi-Ghartemani, N. Sadati, and M. Parniani, “Design of a fractional order PID controller for an AVR using particle swarm optimization,” Control Engineering Practice, Vol.17, No.12, pp. 1380-1387, 2009.
[9] P. Chan, W. Xie, and A. Rad, “Tuning of fuzzy controller for an open-loop unstable system: a genetic approach,” Fuzzy sets and Systems, Vol.111, No.2, pp. 137-152, 2000.
[10] Y. J. Park, H. S. Cho, and D. H. Cha, “Genetic algorithm-based optimization of fuzzy logic controller using characteristic parameters,” In IEEE Int. Conf. on Evolutionary Computation 1995, Vol.2, pp. 831-836, 1995.
[11] C. A. Monje and C. A. Monje, “Fractional-order systems and controls: fundamentals and applications,” Springer London, 2010.
[12] X. Blasco, J. Herrero, J. Sanchis, and M. Martínez, “A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization,” Information Sciences, Vol.178, No.20, pp. 3908-3924, 2008.
[13] R. Toscano, “A simple robust PI/PID controller design via numerical optimization approach,” J. of Process Control, Vol.15, No.1, pp. 81-88, 2005.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] Y.-Q. Chen, I. Petras, and D. Xue, “Fractional order control – A tutorial,” In American Control Conf. 2009 (ACC ’09), pp. 1397-1411, June 2009.

[2] [2] A. Hajiloo, N. Nariman-zadeh, and A. Moeini, “Pareto optimal robust design of fractional-order PID controllers for systems with probabilistic uncertainties,” Mechatronics, Vol.22, No.6, pp. 788-801, 2012.

[3] [3] C. A. Monje, B. M. Vinagre, V. Feliu, and Y. Chen, “Tuning and auto-tuning of fractional order controllers for industry applications,” Control Engineering Practice, Vol.16, No.7, pp. 798-812, 2008.

[4] [4] A. Biswas, S. Das, A. Abraham, and S. Dasgupta, “Design of Fractional-order PI^λ D^μ Controllers with an Improved Differential Evolution,” Eng. Appl. Artif. Intell., Vol.22, No.2, pp. 343-350, March 2009.

[5] [5] R. S. Barbosa, J. T. Machado, and A. M. Galhano, “Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena,” J. of Vibration and Control, Vol.13, No.9-10, pp. 1407-1418, 2007.

[6] [6] M. K. Bouafoura and N. B. Braiek, “PI^λ D^μ controller design for integer and fractional plants using piecewise orthogonal functions,” Communications in Nonlinear Science and Numerical Simulation, Vol.15, No.5, pp. 1267-1278, 2010.

[7] [7] I. Podlubny, “Fractional-order systems and PI^λ D^μ -controllers,” IEEE Trans. on Automatic Control, Vol.44, No.1, pp. 208-214, 1999.

[8] [8] M. Zamani, M. Karimi-Ghartemani, N. Sadati, and M. Parniani, “Design of a fractional order PID controller for an AVR using particle swarm optimization,” Control Engineering Practice, Vol.17, No.12, pp. 1380-1387, 2009.

[9] [9] P. Chan, W. Xie, and A. Rad, “Tuning of fuzzy controller for an open-loop unstable system: a genetic approach,” Fuzzy sets and Systems, Vol.111, No.2, pp. 137-152, 2000.

[10] [10] Y. J. Park, H. S. Cho, and D. H. Cha, “Genetic algorithm-based optimization of fuzzy logic controller using characteristic parameters,” In IEEE Int. Conf. on Evolutionary Computation 1995, Vol.2, pp. 831-836, 1995.

[11] [11] C. A. Monje and C. A. Monje, “Fractional-order systems and controls: fundamentals and applications,” Springer London, 2010.

[12] [12] X. Blasco, J. Herrero, J. Sanchis, and M. Martínez, “A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization,” Information Sciences, Vol.178, No.20, pp. 3908-3924, 2008.

[13] [13] R. Toscano, “A simple robust PI/PID controller design via numerical optimization approach,” J. of Process Control, Vol.15, No.1, pp. 81-88, 2005.