Close loop step test used for tuning PID controller by genetic algorithms

Rubén Lagunas Jiménez, Alonzo González Aguilar, Víctor Lanz Gutiérrez De Velasco


The identification of multiple points on the process frequency response from a single step feedback test is used. These identified points are there employed to design a PID controller using the multiple-point fifting controller design method. The PID controller is design by minimizing the error between the actual and desired close-loop response in a certain frequency region. The control problem is stated as a nonlinear least squares unconstrained minimization problem. The optimization problem is solved with a simple
genetic algorithm.

Keywords: FFT, genetic algorithm, nonlinear least squares optimization, PID

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K. J. Åström, T. Hägglund, PID Controllers: Theory, Design and Tuning: Second Edition. Instrument Society of america. 1995. Research Triangle Park. NC.

B. Kristiansson, B. Lennartson, “Robust tuning of PI and PID Controllers”. IEEE Control Systems Magazine. Vol. 26. No.1. 2006. 55-69 pp.

G. Ziegler, N.B. Nichols, “Optimum Settings for Automatic Controllers”. Trans. ASME. Vol. 64. No.11. 1942. 759-768 pp.

C. C. Hang, K.J. Åström, Q. G. Wang, “Relay feedback auto-tuning of process controllers—a tutorial review”. IFAC, Journal of Process Control. Vol. 12. No. 1. 2002. 143–162 pp.

T. Liu, Q. G. Wang, H. P. Huang, “A tutorial review on process identification from step or relay feedback test”. Journal of Process Control. Vol. 23. No. 1. 2013. 1597–1623 pp.

P. K. Padhy, S. Majhi, “Relay based PI_PID design for stable and unstable FOPDT processes”. Computer & Chemical Engendering. Vol. 30. No. 5. 2006. 790-796 pp.

Q. C. Wang, Y. Zhang, “Robust identification of continuous systems with dead time from step responses”. Automatica. Vol. 37. No.1. 2001. 377-390 pp.

G. W. Shin, Y.J. Song, T.B. Lee, H.K. Choi, “Genetic Algorithm for Identification of Time Delay Systems from Step Responses”. International Journal of Control,

Automation, and Systems. Vol. 5. No. 1. 2007. 79-85 pp.

T. Liu, C. Shao, “Closed-loop step identification of low-order continuous-time process model with time delay for enhanced controller autotuning”. Int. J. Systems, Control and Communications. Vol. 4. No.4. 2012. 225-249 pp.

T. Liu, F. Gao, “A frequency domain step identification method for continuoustime”. Journal of Process Control. Vol. 20. No.1. 2010. 800-809 pp.

The Levenberg-Marquardt method for nonlinear least squares curve-fitting problems. Department of Civil and Environmental Engineering Duke University. 2013.

I. Griva, S.G Nash, S. Ariela, Linear and Nonlinear Optimization. Second Edition. 2009. Society for Industrial Mathematics. United States of America.

Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization. Cornell University. Ithaca, New York, USA. 2012.

K. J. Åström, T. Hägglund, “Automatic Tuning of simple controllers with specification on phase and amplitude margins”. Automatica. Vol. 20. No. 5. 1984. 645-651 pp.

M. Jamshidi, L. Coelho, R. A. Krohling, P. J. Fleming, Robust Control Systems with Genetic Algorithms. 2003. CRC Press LLC. Roca Baton, Florida.

Q. G. Wang, C. C. Chieh, Q. Bi, “A Frequency domain controller design method”. Chemical Eng. Research and Design. Vol. 75. 1997. 64-72 pp.

Q. G. Wang, “Process Frequency Response Estimation from Relay Feedback”. Control Eng. Practice. Vol.5. No.9. 1997.1293-1302 pp.

T. Liu, F. Gao, “A frequency domain step identification method for continuoustime”. Journal of Process Control. Vol. 20. 2010. 800-809 pp.

C. A. Coello-Coello, D. A. Van Veldhuizen, G. B. Lamont, Evolutionary Algorithms for Solving Multi-Objective Problems. 2007. Springer. New York.

Genetic Algorithms in Control Systems Engineering. Department of Automatic Control Systems Engineering. University of Sheffield. 2001.

D. E. Goldberg, Genetic Algorithms in Search, optimization, and Machine Learning. 1989. Addison Wesley.

Adaptation in Natural and Artificial Systems. University of Michigan Press. Ann Arbor, Michigan. 1975.

J. Doyle, B. A. Francis, A. R. Tannenbaum, Feedback Control Theory. 1992. Macmillan Publishing Company.

K. Zhou, J. C. Doyle, Essentials of Robust Control. 1998. Prentice Hall.

Pass Band and High frequency Robustness for PID Control. Proceeding of the 36thConference on Decision & Control. San Diego California. USA. 1997.

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