Document Type : Original Research Paper


1 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan , Iran

2 School of Mechanical Engineering, Department of Engineering, University of Tehran, Tehran, Iran.


Proportional + Integral + Derivative (PID) controllers are widely used in engineering applications such that more than half of the industrial controllers are PID controllers. There are many methods for tuning the PID parameters in the literature. In this paper an intelligent technique based on eXtended Classifier System (XCS) is presented to tune the PID controller parameters. The PID controller with the gains obtained by the proposed method can robustly control nonlinear multiple-input–multiple-output (MIMO) plants in any form, such as robot dynamics and so on. The performance of this method is evaluated with Integral Squared Error (ISE) criteria which is one of the most popular optimizing methods for the PID controller parameters. Both methods are used to control the ball position in a magnetic levitation (MagLev) system and the performance of controllers are compared. Matlab Simulink has been used to test, analyze and compare the performance of the two optimization methods in simulations.


Main Subjects

[1] K. J. Åström, T. Hägglund, "The future of PID control", Control Eng. Practice 9, p.1163-1175, 2001.
[2] K. J. Åström, T. Hägglund, "PID Controllers", Instrument Society of America,second edition, New York, 1995.
[3] Bennett, Stuart, "A history of control engineering", IET, p. p. 48. ISBN 978-0-86341-299-8, 1993.
[4] R. Guerra, S. González and R. Reyes, "Advances in PID control", ISBN: 978-953-307-267-8, InTech 2011.
[5] M. Zhuang, D. P. Atherton, "Automatic tuning of optimum PID controllers", IEE PROCEEDINGS-D, Vol. 140, No. 3, I993.
[6] K. H. Ang, chong. G, Li. Y, "PID Control System Analysis, Design, and Technology", IEEE Transactionson Control Systems Technology, Vol. 13, No. 4, P. 559-576, 2005.
[7] P. H. Chang, J. H. Jung, "A Systematic Method for Gain Selection of Robust PID Control for Nonlinear Plants of Second-Order Controller Canonical Form", IEEE Transactions on Automatic Control, Vol. 17, No. 2, P. 473-473, 2009.
[8] L.S. Coelho, "Tuning of PID Controller for an Automatic Regulator Voltage System Using Chaotic Optimization Approach", Chaos, Solitons and Fractals, Vol. 39, P. 1504-1514, 2009.
[9] J. B. He, Q. G. Wang, T. H. Lee, "PI/PID Controller Tuning via LQR Approach", Chemical Engineering Science, Vol. 55, P. 2429-2439, 2000.
[10] A. A. Awouda, R. Mamat, "New PID Tuning Rule Using ITAE Criteria", International Journal of Engineering, Vol. 3, No. 6, P. 597-608, 2008.
[11] A. Bagis, "Determination of the PID Controller Parameters by Modified Genetic Algorithm for Improved Performance", Journal of Information Science and Engineering, Vol. 23, P. 1469-1480, 2007.
[12] Stephen. B, Martin. H and Karl. J. A, "MIMO PID tuning via iterated LMI restriction", International Journal of Robust and Nonlinear Control, Vol. 26, No. 8, P.P 1718-1731, 2016.
[13] M. Woodson. "Electromechanical Dynamics", art I. John Wiley & Sons In., New York, 1968.
[14] V. Oliveira, E. Costa, and J. Vargas, "Digital Implementation of a Magnetic Suspension Control System for Laboratory Experiments", IEEE Trans. On Education, Vol. 42, No. 4, P.315-322, 1999.
[15] G. K. M. Pedersen, Z. Yang, "Multi-Objective PID-Controller Tuning for a Magnetic Levitation System using NSDA-ll", GECCO, Seattle, Washington, USA, 2006.
[16] Larry Bull, "Applications of Learning Classifier Systems", Springer Berlin Heidelberg, 2004
[17] M. V. Butz, T. Kovacs, P. L. Lanzi, and S. W. Wilson, "Toward a Theory of Generalization and Learning in XCS", IEEE Transaction On Evolutionary Computation, Vol 8, NO 1, 2004.