Optimal PIDA Controller Design for Maglev Vehicle Suspension System by Lévy-Flight Firefly Algorithm -

Main Article Content

Deacha Puangdownreong


In modern vehicles, intelligent suspension systems have been widely applied with complex
control algorithms. The suspension design problem aims to achieve a good suspension providing a
comfortable ride and good handling within a reasonable range of road-profile deflection. In this
paper, the proportional-integral-derivative-accelerated (PIDA) controller design for the magnetically
levitated (Maglev) vehicle suspension system by the Lévy-flight firefly algorithm (LFFA), one of the
most powerful metaheuristic optimization searching techniques, is proposed. For comparison with
LFFA-based design approach, the results obtained by the PIDA controller will be compared with
those obtained by the PI, PD and PID controllers. Simulation results show that the LFFA can provide
optimal PIDA controller for a given suspension system. The PIDA controller yielded very satisfactory
response superior to PI, PD and PID, respectively.

Article Details

How to Cite
D. Puangdownreong, “Optimal PIDA Controller Design for Maglev Vehicle Suspension System by Lévy-Flight Firefly Algorithm: -”, sej, vol. 14, no. 1, pp. 12–22, May 2019.
Research Articles


[1] R. S. Sharp and D. A. Crolla, “Road vehicle supsension system design - a review,” Vehicle System Dynamics, vol. 16, no. 3, pp. 167-192, 1987.

[2] A. Shirahatt, P. S. S. Prasad, P. Panzade and M. M. Kulkarni, “Optimal design of passenger car suspension for ride and road holding,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 30, no. 1, pp. 66-76, 2008.

[3] J. S. Lin and I. Kanellakopoulos, “Nonlinear design of active suspensions,” IEEE Control Systems Magazine, vol. 17, no. 3, pp. 45-59, 1997.

[4] D. S. Armstrong, “Magnet/rail systems - a critical review of the options,” in IMechE Conference on Maglev Transport - Now and for the Future, pp. 59-66, 1984.

[5] V. Zakian, Control Systems Design: A New Framework, London Limited: pringer-Verlag, 2005.

[6] Y. Cai, S. S. Chen and D. M. Rote, Dynamics and Controls in Maglev Systems, Argonne National Laboratory, U.S. department of Energy, 1992.

[7] A. Butar and R. Sales, “Control for MagLev vehicles,” IEEE Control Systems, pp. 18-25, 1998.

[8] A. Charara, “Nonlinear control of a magnetic levitation system,” IEEE Transactions on Control System Technology, pp. 513-523, 1996.

[9] N. Katal and S. K. Singh, “Optimization of PID controller for quarter-car suspension system using genetic algorithm,” International Journal of Advanced Research in Computer Engineering & Technology, vol. 1, no. 7, pp. 30-32, 2012.

[10] A. A. Aldair and W. J. Wang, “Design of fractional order controller based on evolutionary algorithm for a full vehicle nonlinear active suspension system,” International Journal of Control and Automation, vol. 3, no. 4, pp. 33-46, 2010.

[11] A. J. Qazi, C. W. De Silva, A. Khan and M. T. Khan, “Performance analysis of a semiactive suspension system with particle swarm optimization and fuzzy logic control,” The Scientific World Journal, vol. 2014, pp. 1-12, 2014.

[12] S. Jung and R. C. Dorf, “Analytic PIDA controller design technique for a third order system,” Proc. IEEE Conference on Decision and Control, pp. 2513-2518, 1996.

[13] S. Sornmuang and S. Sujitjorn, “GA-based PIDA control design optimization with an application to AC motor speed control,” International Journal of Mathematics and Computers in Simulation, vol. 3, no. 4, pp. 67-80, 2010.

[14] D. Puangdownreong and S. Suwannarongsri, “Torsional resonance suppression via PIDA controller designed by the particle swarm optimization,” Proc. Annual International Conference Organized by Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, pp. 673-676, 2008.

[15] A. Nawikavatan, T. Jitwang, C. Thammarat and D. Puangdownreong, “Application of cuckoo search to optimal PIDA controller design for three-tank liquid-level control system,” Proc. International Conference on Engineering and Natural Science, pp. 51-59, 2018.

[16] A. Sharma, H. Sharma, A. Bhargava and N. Sharma, “Optimal design of PIDA controller for induction motor using spider monkey optimization algorithm,” International Journal of Metaheuristics, vol. 5, no. 3/4, pp. 278-290, 2016.

[17] X. S. Yang, Nature-Inspired Metaheuristic Algorithms, Luniver Press, 2008.

[18] X. S. Yang, “Firefly algorithms for multimodal optimization, stochastic algorithms, foundations and Applications,” SAGA 2009, Lecture Notes in Computer Sciences, vol. 5792, pp. 169-178, 2009.

[19] B. Rampriya, K. Mahadevan and S. Kannan, “Unit commitment in deregulated power system using Lagrangian firefly algorithm,” Proc. IEEE International Conference on Communication Control and Computing Technologies (ICCCCT 2010), pp. 389-393, 2010.

[20] T. Hassanzadeh, H. Vojodi and F. Mahmoudi, “Non-linear gray scale image enhancement based on firefly algorithm,” Swarm, Evolutionary, and Memetic Computing, Springer, pp.174-181, 2011.

[21] B. Basu and G. Mahanti, “Thinning of concentric two-ring circular array antenna using firefly algorithm,” Scientia Iranica, vol. 19, no. 6, pp. 1802-1809, 2012.

[22] S. Gholizadeh and H. Barati, “A comparative study of three metaheuristics for optimum design of trusses,” International Journal of Optimization in Civil Engineering, vol. 3, pp. 423-441, 2012.

[23] S. Severin and J. Rossmann, “A comparison of different metaheuristic algorithms for optimizing blended PTP movements for industrial robots,” Intelligent Robotics and Applications, pp. 321-330, 2012.

[24] C. Pop, V. Chifu, I. Salomie, R. Baico, M. Dinsoreanu and G. Copil, “A hybrid firefly-inspired approach for optimal semantic web service composition,” Scalable Computing: Practice and Experience, vol. 12, pp. 363-369, 2011.

[25] S. E. Fateen, A. Bonilla-Petriciolet and G. P. Rangaiah, “Evaluation of covariance matrix adaptation evolution strategy, shuffled complex evolution and firefly algorithms for phase stability, phase equilibrium and chemical equilibrium problems,” Chemical Engineering Research and Design, vol. 90, no. 12, pp. 2051-2071, 2012.

[26] A. F. d. Santos, H. F. d. Campos Velho, E. F. Luz, S. R. Freitas, G. Grell and M. A. Gan, “Firefly optimization to determine the precipitation field on South America,” Inverse Problems in Science and Engineering, pp. 1-16, 2013.

[27] M. Breza and J. McCann, “Lessons in implementing bio-inspired algorithms on wireless sensor networks,” Proc. IEEE NASA/ESA Conference on Adaptive Hardware and Systems (AHS'08), pp. 271-276, 2008.

[28] O. Abedinia, N. Amjady, K. Kiani and H. Shayanfar, “Fuzzy PID based on firefly algorithm: load frequency control in deregulated environment,” Proc. the 2012 International Conference on Bioinformatics and Computational Biology, pp. 1-7, 2012.

[29] D. Puangdownreong, S. Sumpunsri, M. Sukchum, C. Thammarat, S. Hlangnamthip and A. Nawikavatan, “FA-based optimal PIDA controller design for AVR system,” Proc. iEECON2018 International Conference, pp. 548-551, 2018.

[30] X.-S. Yang, “Firefly algorithm, Lévy flights and global optimization,” Research and Development in Intelligent Systems, vol. XXVI, Springer London, pp. 209-218, 2010.

[31] I. Fister, I. Fister Jr., X. S.Yang and J. Brest, “A comprehensive review of firefly algorithms,” Swarm and Evolutionary Computation, Springer, vol. 13, pp. 34-46, 2013.

[32] I. Fister, X. S. Yang, D. Fister and I. Fister Jr., “Firefly algorithm: a brief review of the expanding literature,” Cuckoo Search and Firefly Algorithm, Springer, vol. 347, pp. 347-360, 2014.

[33] G. Bohn and H. Alscher, “The magnetic train transrapid 06,” Proc. IEEE Internation Conference on Maglev and Linear Drives, pp. 233-242, 1986.

[34] G. Bohn and G. Steinmetz, “The electromagnetic suspension system of the magnetic train ‘Transrapid’,” Proc. the 1985 International Conference on Maglev Transport, pp. 107-114, 1985.