International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.10, No.5, May. 2018

A Genetic Algorithm based Fractional Fuzzy PID Controller for Integer and Fractional order Systems

Full Text (PDF, 500KB), PP.23-32

Views:57   Downloads:4


Ambreesh Kumar, Rajneesh Sharma

Index Terms

Fractional systems;Oustaloup Approximation;Fuzzy PID Control;Genetic Algorithm assisted Fractional Order PID Controller


This work aims at designing a fractional Proportional-Integral-Derivative controller wherein we hybridize a genetic algorithm based fractional Proportional-Integral-Derivative controller with a fuzzy logic Proportional-Integral-Derivative controller. We attempt at optimizing the fractional order Proportional-Integral-Derivative controller parameters by incorporating a Genetic Algorithm based mechanism. Thereafter, the optimized genetic algorithm based fractional Proportional-Integral-Derivative control is further fine tuned and hybridized to a fuzzy Proportional-Integral-Derivative control. Here, fuzzy logic based inference mechanism is used to tackle system uncertainties and use of rule firing strengths produces an adaptive control. Genetic Algorithm has been used to generate the most optimal controller by a natural selection of the fittest. Amalgamating Genetic Algorithm and fuzzy control approaches on fractional order systems produces a highly efficient and noise tolerant control regime. We give simulation results and compare our hybrid approach against conventional and fractional Proportional-Integral-Derivative approaches on various integer and fractional order systems (with dead time) to elucidate its superiority and effectiveness.

Cite This Paper

Ambreesh Kumar, Rajneesh Sharma, "A Genetic Algorithm based Fractional Fuzzy PID Controller for Integer and Fractional order Systems", International Journal of Intelligent Systems and Applications(IJISA), Vol.10, No.5, pp.23-32, 2018. DOI: 10.5815/ijisa.2018.05.03


[1]K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equation, New York: John Wiley Son’s, 1993.

[2]K.B. Oldham and J. Spanier, The Fractional Calculus, New York: Academic press, 1974.

[3]R.L. Bagley and R.A. Calico, “Fractional-order state equation for the control of viscoelastically damped structures,” J. Gui. Cont. Dyn., vol. 14,  no. 2, pp. 304-311, 1991. 

[4]S. Wheatcraft and M. Meerschaert, “Fractional conservation of mass,” J. Advance Water Resources, vol. 31, pp. 1377-1381, 2008.

[5]A. Oustaloup, B. Mathieu and P. Lanussa, “The CRONE control of resonant plants: application of flexible transmission,” Eur. J. Control, vol. 1, no. 2, pp.  113-121, 1995.

[6]Y.Q. Chen, D. Xue and H. Dou, “Fractional calculus and biomimetic control,” IEEE Int. Conf. Rob. Bio., China, pp. 901-906, 2004.

[7]Y. Luo, H Sheng, and 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,”48th IEEE CDC., China, pp. 5460-5465, Dec 2009.

[8]I. Podlubny, L. Dorcak, and I. Kostial, “On fractional derivative, fractional-order dynamics system and PIDµ -controllers,” 36th IEEE CDC, USA, pp. 4985-4990, Dec. 1997.

[9]S.N. Sivanandam, S. Sumathi and S.N. Deepa, Introduction to Fuzzy Logic Using MATLAB, Springer-Verlag, Heidelberg, 2007.

[10]S. Yasunobu, S. Miyamoto and H. Ihara, “Fuzzy control for automatic train operation system,” 4th Int. Cong. Cont. Transp. Sys., Baden, 1983.

[11]H. Oshima, S. Yasunobu and S. Sekino, “Automatic train operation system based on predictive fuzzy control,” Int. Work. Art. Intel. Industrial Applications, Japan, pp. 485-489, May 1988.

[12]S. Yasunobu, S. Sekino and T. Hasequwa, “Automatic train operation and automatic crane operation system based on predictive fuzzy control,” 2nd IFSA Congress, Japan, pp. 835-838, 1987.

[13]F. Fujitec, Flex-8800 series elevator group control system, Fujitec Co. Ltd., Japan, 1988.

[14]M. Kinoshita, T. Fuzuzaki, T. Satoh and M. Miyake, “An automatic operation method for control rods in BWR plants,” Specialists Meeting on In-core Instrumentation Reactor Core Assignment, France, 1988.

[15]K.M. Passino and S. Yurkovich, Fuzzy-Control, California: Addision Wesley Longman, 1988.

[16]M. Sakawa, Genetic Algorithms and Fuzzy Multiobjective Optimization, Massachusetts: Kluwer Academic Publishers, 2002.

[17]J. Nordvik and J. Renders, “Genetic algorithms and their potential for use in process control: a case study,” Int. Conf. GA, pp. 480-486, 1991.

[18]A. Chipperfield and P.J. Fleming, “Genetic algorithms in control systems engineering,” J. Computers Control, Vol. 24, no.1, 1996.

[19]J.P. Cohoon, S.U. Hedge, W.N. Martin and D.S. Richards, “Distributed GA for the floorplan design  Problem,” IEEE Trans. CAD, Vol. 10, no. 4, pp. 483-492, 1991.

[20]G.A. Rauwolf and V.L. C-Carroll, “Near-optimal low-thrust orbit transfers generated by a genetic algorithm,” J. Spacecraft Rockets, Vol. 33, no. 6, pp. 859-862, 1996.

[21]A.M.S. Zalzala and P.J. Fleming, “Genetic Algorithm in Engineering Systems,” J. IET, London, 1997.

[22]Y.W. Chen, Z. Nakao, K. Arakai and S. Tamura, “Blind deconvolution based on genetic algorithms,” IEICE Trans. Fund. Elect., Comm. Comp. Sc., Vol. E80A 12, pp. 2603-2607, 1997.

[23]T. Kawaguchi, T. Baba and R. Nagata, “3D object recognition using a genetic algorithm based search scheme,” IEICE Trans. Inf. Sys., Vol. E80D 11, pp. 1064-1073, 1997.

[24]Y. Tsujimura and M. Gen, “Genetic algorithms for solving multiprocessor scheduling problems,” Springer Berlin Heidelberg, J. Simulated Evol. Learning, Vol. 1285, pp. 106-115, 1997.

[25]M.S. Bright and T. Arslan, “Synthesis of low-power DSP systems using a GA,” IEEE Trans. Evo. Comp., Vol. 5, no. 1, pp. 27-40, 2001.

[26]Y. Cao, J. Liang and B. Cao, “Optimization of fractional order PID controllers based on genetic algorithm,” Int. Conf. Machine Learning Cybernetics, China, pp. 5686-5689, Aug. 2005.

[27]L. Meng and D. Xue, “Design of an optimal fractional-order PID controller using Multi-Objective GA optimization,” Int. CCDC, Guilin, pp. 3849-3853, June 2009.

[28]D. Maiti, A. Acharya, M. Chakraborty, A. Konar and R. Janarthanon, “Tuning PID and PIλDµ controllers using the integral time absolute error criteria,” ICIAFS, Colombo, pp. 457-462, Dec. 2008.

[29]M. Zamani, M. K.Ghartemani and N. Sadate, “Design of an H∞-optimal FOPID controller using PSO,” CCC, Hunan, pp. 435-440, 2007.

[30]V. K. Kadiyala, R. K. Jatoth and S. Pothalaiah, “Design and implementation of fractional-order PID controller for aerofin control system,” NABIC, India, pp.696-701, Dec. 2009.

[31]G. Feng and Z. X.-Ping, “Research on fractional-order two-degree-of-freedom flight control technology of unmanned air vehicle,” CSIP, Shaanxi, pp. 807-812, Aug. 2012.

[32]A. Rajasekhar, A. Abraham, P. Kunathi and M. Pant, “Fractional order speed control of dc motor using levy mutated artificial bee colony algorithm,” WICT, Mumbai, pp. 7-13,  Dec. 2011.

[33]V. Mehra, S. Srivastava and P. Varshney, “Fractional-order PID controller design for speed control of DC motor,” Int. Conf. Emerg.  Trends Eng. Tech., Goa, pp. 422-425, Nov. 2010.

[34]H. Arpaci and O.F. Ogzuven, “ANFIS and PIλDµ controller design and comparison of overhead cranes,” Ind. J. Eng. Mat. Sc., vol. 18, pp. 191-203, 2011.

[35]S. Das, I. Pan, K. Halder, S. Das and A. Das, “Optimum weight selection based LQR formulation for the design of fractional-order PIλDµ controllers to handle a class of fractional-order system,” ICCCI Coimbatore, pp.1-6, Jan 2013.

[36]H. Yuchun and W. Jianping, “Fuzzy fractional order controller optimal design for PMSM of electric vehicle in sports competition,” Int. ICDMA, Guilin, pp. 439-441, 2012. 

[37]L. Jiangyan, L. Fucai and H.  Huishan, “Application of Fuzzy Fractional Order Controller in Wind Power Convertor,” Int. CCC, Hefei, pp. 6741-6746, July 2012.

[38]S. Das, I. Pan, S. Das and A. Gupta, “A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices,” J. EAAI, vol. 25, no. 2, pp. 430-442, 2012.

[39]Ammar SOUKKOU, M.C. BELHOUR, Salah LEULMI,"Review, Design, Optimization and Stability Analysis of Fractional-Order PID Controller", International Journal of Intelligent Systems and Applications(IJISA), Vol.8, No.7, pp.73-96, 2016. DOI: 10.5815/ijisa.2016.07.08

[40]Ammar Soukkou, Salah Leulmi,"Controlling and Synchronizing of Fractional-Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller", International Journal of Intelligent Systems and Applications(IJISA), Vol.8, No.6, pp.56-69, 2016. DOI: 10.5815/ijisa.2016.06.07

[41]P.M. Pawar and R. Ganguli, Structural Health Monitoring using Genetic Fuzzy Systems, London: Springer, 2011.

[42]A. Oustaloup, J. Sabatier and P. Lanusse, “From fractional robustness to crone control,” Fract. Cal. App. Anal., vol. 2, no. 1, pp.  1-30, 1999.

[43]D.Y. Xue and Y.Q. Chen, “Sub-optimum H2 rational approximations to fractional-order linear systems,” IDETC Conf., USA, pp. 01-10, 2005. 

[44]C.A. Monje, Y.Q. Chen, B.M. Vinagre, D. Xue and V. Feliu, Fractional-Order Systems and Controls, London: Springer, 2010.

[45]T. Michalowski, Applications of MATLAB in Science and Engineering. INTECH, Croatia, 2011.