Full Text:   <2116>

Summary:  <1316>

CLC number: TP391

On-line Access: 2018-05-07

Received: 2016-08-23

Revision Accepted: 2017-02-14

Crosschecked: 2018-03-10

Cited: 0

Clicked: 5654

Citations:  Bibtex RefMan EndNote GB/T7714


Pritesh Shah


-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2018 Vol.19 No.3 P.437-445


Design of a fractional PIλDμ controller using the cohort intelligence method

Author(s):  Pritesh Shah, Sudhir Agashe, Anand J. Kulkarni

Affiliation(s):  Symbiosis Institute of Technology, Symbiosis International University, Pune 412115, India; more

Corresponding email(s):   pritesh.ic@gmail.com

Key Words:  Cohort intelligence, Fractional calculus, Fractional PID controller, Tuning

Pritesh Shah, Sudhir Agashe, Anand J. Kulkarni. Design of a fractional PIλDμ controller using the cohort intelligence method[J]. Frontiers of Information Technology & Electronic Engineering, 2018, 19(3): 437-445.

@article{title="Design of a fractional PIλDμ controller using the cohort intelligence method",
author="Pritesh Shah, Sudhir Agashe, Anand J. Kulkarni",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Design of a fractional PIλDμ controller using the cohort intelligence method
%A Pritesh Shah
%A Sudhir Agashe
%A Anand J. Kulkarni
%J Frontiers of Information Technology & Electronic Engineering
%V 19
%N 3
%P 437-445
%@ 2095-9184
%D 2018
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1601495

T1 - Design of a fractional PIλDμ controller using the cohort intelligence method
A1 - Pritesh Shah
A1 - Sudhir Agashe
A1 - Anand J. Kulkarni
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 19
IS - 3
SP - 437
EP - 445
%@ 2095-9184
Y1 - 2018
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1601495

The cohort intelligence (CI) method has recently evolved as an optimization method based on artificial intelligence. We use the CI method for the first time to optimize the parameters of the fractional proportional-integral-derivative (PID) controller. The performance of the CI method in designing the fractional PID controller was validated and compared with those of some other popular algorithms such as particle swarm optimization, the genetic algorithm, and the improved electromagnetic algorithm. The CI method yielded improved solutions in terms of the cost function, computing time, and function evaluations in comparison with the other three algorithms. In addition, the standard deviations of the CI method demonstrated the robustness of the proposed algorithm in solving control problems.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Abramowitz M, 1972. Handbook of Mathematical Functions:with Formulas, Graphs, and Mathematical Tables. Dover Publications Incorporated.

[2]Aghababa MP, 2016. Optimal design of fractional-order PID controller for five bar linkage robot using a new particle swarm optimization algorithm. Soft Comput, 20(10):4055-4067.

[3]Anwar MN, Pan S, 2014. A frequency domain design of PID controller for an AVR system. J Zhejiang Univ-Sci C (Comput & Electron), 15(4):293-299.

[4]Astrom KJ, Hagglund T, 1995. PID Controllers:Theory, Design, and Tuning (2rd Ed.). The Instrument, Systems and Automation Society, Research Triangle Park, NC.

[5]Barbosa RS, Machado JAT, Galhano AM, 2007. Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena. J Vibr Contr, 13(9-10):1407-1418.

[6]Biswas A, Das S, Abraham A, et al., 2009. Design of fractional-order PIλDμ controllers with an improved differential evolution. Eng Appl Artif Intell, 22(2):343-350.

[7]Cafagna D, 2007. Fractional calculus:a mathematical tool from the past for present engineers. IEEE Ind Electron Mag, 1(2):35-40.

[8]Cao JY, Cao BG, 2006. Design of fractional order controllers based on particle swarm optimization. Int J Contr Autom Syst, 4(6):775-781.

[9]Cao JY, Liang J, Cao BG, 2005. Optimization of fractional order PID controllers based on genetic algorithms. Int Conf on Machine Learning and Cybernetics, p.5686-5689.

[10]Chang LY, Chen HC, 2009. Tuning of fractional PID controllers using adaptive genetic algorithm for active magnetic bearing system. WSEA Trans Syst, 8(1):158-167.

[11]Chen YQ, Petras I, Xue DY, 2009. Fractional order control—a tutorial. American Control Conf, p.1397-1411.

[12]Das S, 2011. Functional Fractional Calculus. Springer Berlin Heidelberg, p.51-100.

[13]Das S, Pan I, Das S, et al., 2012. A novel fractional order fuzzy pid controller and its optimal time domain tuning based on integral performance indices. Eng Appl Artif Intell, 25(2):430-442.

[14]De A, Sen S, 2011. Root locus method for any fractional order commensurate system. IEEE Students' Technology Symp, p.323-328.

[15]Dhavle SV, Kulkarni AJ, Shastri A, et al., 2017. Design and economic optimization of shell-and-tube heat exchanger using cohort intelligence algorithm. Neur Comput Appl, in press.

[16]Karimi-Ghartemani M, Zamani M, Sadati N, et al., 2007. An optimal fractional order controller for an AVR system using particle swarm optimization algorithm. Large Engineering Systems Conf on Power Engineering, p.244-249.

[17]Keyser DR, Muresan CI, Ionescu CM, 2016. A novel auto-tuning method for fractional order PI/PD controllers. ISA Trans, 62:268-275.

[18]Kulkarni AJ, Shabir H, 2016. Solving 0-1 knapsack problem using cohort intelligence algorithm. Int J Mach Learn Cybern, 7(3):427-441.

[19]Kulkarni AJ, Durugkar IP, Kumar M, 2013. Cohort intelligence:a self supervised learning behavior. IEEE Int Conf on Systems, Man and Cybernetics, p.1396-1400.

[20]Kulkarni AJ, Baki MF, Chaouch BA, 2016. Application of the cohort-intelligence optimization method to three selected combinatorial optimization problems. Eur J Oper Res, 250(2):427-447.

[21]Kulkarni AJ, Krishnasamy G, Abraham A, 2017. Cohort Intelligence:a Socio-inspired Optimization Method. Springer, Cham.

[22]Kulkarni O, Kulkarni N, Kulkarni AJ, et al., 2016. Constrained cohort intelligence using static and dynamic penalty function approach for mechanical components design. Int J Parall Emerg Distr Syst, p.1-19.

[23]Lee CH, Chang FK, 2010. Fractional-order PID controller optimization via improved electromagnetism-like algorithm. Expert Syst Appl, 37(12):8871-8878.

[24]Li CS, Chang L, Huang ZJ, et al., 2016. Parameter identification of a nonlinear model of hydraulic turbine governing system with an elastic water hammer based on a modified gravitational search algorithm. Eng Appl Artif Intell, 50:177-191.

[25]Luo Y, Chen YQ, Wang CY, et al., 2010. Tuning fractional order proportional integral controllers for fractional order systems. J Process Contr, 20(7):823-831.

[26]Luo Y, Chao HC, Di LP, et al., 2011. Lateral directional fractional order PI control of a small fixed-wing unmanned aerial vehicles:controller designs and flight tests. IET Contr Theory Appl, 5(18):2156-2167.

[27]Malek H, Luo Y, Chen YQ, 2013. Identification and tuning fractional order proportional integral controllers for time delayed systems with a fractional pole. Mechatronics, 23(7):746-754.

[28]Meng L, Xue DY, 2009. Design of an optimal fractional-order PID controller using multi-objective GA optimization. Chinese Control and Decision Conf, p.3849-3853.

[29]Mishra P, Kumar V, Rana KPS, 2015. A fractional order fuzzy PID controller for binary distillation column control. Expert Syst Appl, 42(22):8533-8549.

[30]Monje CA, Vinagre BM, Feliu V, et al., 2008. Tuning and auto-tuning of fractional order controllers for industry applications. Contr Eng Pract, 16(7):798-812.

[31]Monje CA, Chen YQ, Vinagre BM, et al., 2010. Fractional-Order Systems and Controls:Fundamentals and Applications. Springer, London.

[32]Pan I, Das S, 2012. Chaotic multi-objective optimization based design of fractional order PIλDμ controller in AVR system. Int J Electr Power Energy Syst, 43(1):393-407.

[33]Pan I, Das S, 2015. Fractional-order load-frequency control of interconnected power systems using chaotic multi-objective optimization. Appl Soft Comput, 29:328-344.

[34]Petráš I, 2008. Stability of fractional-order systems with rational orders. Fract Calc Appl Anal, 10(3):269-298.

[35]Podlubny I, 1994. Fractional-order systems and fractional-order controllers. Proc Conf on Int Francophone d‘Automatique, p.43-54.

[36]Podlubny I, 1999. Fractional Differential Equations:an Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press, San Diego.

[37]Podlubny I, Dorcak L, Kostial I, 1997. On fractional derivatives, fractional-order dynamic systems and PIλDμ-controllers. IEEE Conf on Decision Control, p.4985-4990.

[38]Rajasekhar A, Jatoth RK, Abraham A, 2014. Design of intelligent PIλDμ speed controller for chopper fed DC motor drive using opposition based artificial bee colony algorithm. Eng Appl Artif Intell, 29:13-32.

[39]Sabatier J, Aoun M, Oustaloup A, et al., 2006. Fractional system identification for lead acid battery state of charge estimation. Signal Process, 86(10):2645-2657.

[40]Shah P, Agashe S, 2016. Review of fractional PID controller. Mechatronics, 38:29-41.

[41]Shah P, Agashe SD, Singh AP, 2013. Design of fractional order controller for undamped control system. Nirma University Int Conf on Engineering, p.1-5.

[42]Tang YG, Cui MY, Hua CC, et al., 2012. Optimum design of fractional order PIλDμ controller for AVR system using chaotic ant swarm. Expert Syst Appl, 39(8):6887-6896.

[43]Tepljakov A, Petlenkov E, Belikov J, 2011. FOMCON:fractional-order modeling and control toolbox for Matlab. Int Conf on Mixed Design of Integrated Circuits and Systems, p.684-689.

[44]Tepljakov A, Petlenkov E, Belikov J, et al., 2013. Fractional-order controller design and digital implementation using FOMCON toolbox for MATLAB. IEEE Conf on Computer Aided Control System Design, p.340-345.

[45]Valerio D, Costa JSD, 2006. Tuning of fractional PID controllers with Ziegler-Nichols-type rules. Signal Process, 86(10):2771-2784.

[46]Valério D, Costa JSD, 2010. A review of tuning methods for fractional PIDs. Proc 4th IFAC Workshop on Fractional Differentiation and its Applications.

[47]Zhao CN, Xue DY, Chen YQ, 2005. A fractional order PID tuning algorithm for a class of fractional order plants. IEEE Int Conf on Mechatronics Automation, p.216-221.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE