Fractional-order PID controller design via optimal selection strategy of frequency domain specifications

Abstract

In this paper, a novel fractional-order Proportional-Integral Derivative (PID) controller design depending on optimal selection of frequency domain specifications is proposed for time delay systems. The frequency domain specification sets, namely, (i) phase margin and gain crossover frequency and (ii) phase margin and gain margin are determined so that the reference model is optimal according to three time domain performance indices, i.e. Integral Square Error (ISE), Integral Time Square Error (ITSE) and Integral Absolute Error (IAE). Here, the delayed Bode's ideal transfer function is employed in the reference model. Moreover, the stability region of the reference model is given via a theorem. In simulation studies, the proposed methodology is compared with other two different methods using the same frequency domain specifications. It is observed that the proposed optimal fractional-order PID controllers outperform according to the mentioned performance indices, and they also possess considerably acceptable performance in terms of other time domain specifications such as overshoot, settling time, etc.

Keywords:

• Bode's ideal transfer function
• optimal delayed Bode's transfer function
• frequency domain specifications
• time domain criteria
• optimal fractional-order controller

Data availability statement

The data that support the findings of this study are available from the corresponding author [E. Yumuk] upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Erhan Yumuk

Erhan Yumuk received the B.Sc. degree from the Department of Electronics Engineering of Istanbul Technical University, Istanbul, Turkey, in 2012. He has got another B.Sc. degree from the Department of Control Engineering of the same university as a double major in 2013. He had M.S. and Ph.D. degrees from the Institute of Science and Technology of the same university on Control and Automation Engineering in 2015 and 2022, respectively. He is currently a lecturer in the Department of Control and Automation Engineering of Istanbul Technical University. His research interests include fractional-order system control, linear control system theory and process control.

Müjde Güzelkaya

Müjde Güzelkaya received the B.Sc. degree from the Faculty of Electrical and Electronics Engineering of Istanbul Technical University, Istanbul, Turkey, in 1982 and M.S. and Ph.D. degrees from the Institute of Science and Technology of the same university in 1984 and 1990, respectively. She is currently a professor in the Department of Control and Automation Engineering of Electrical and Electronics Engineering Faculty of Istanbul Technical University. Her research interests include intelligent control systems, linear control system theory and stochastic optimal control.

İbrahim Eksin

İbrahim Eksin received the B.Sc., M.S. and Ph.D. degrees from the Department of Electrical Engineering of Bogazici University, Istanbul, Turkey, in 1976, 1979 and 1983, respectively. He has worked in Honeywell Turkey Branch from 1983 to 1985. He then joined Control and Computers Engineering Department of Electrical and Electronics Engineering Faculty of Istanbul Technical University. He is currently working as a professor in Control and Automation Engineering Department of the same faculty and university. He is the President of Turkish National Member Organization of International Federation of Automatic Control. His research interests include intelligent control, optimal control and evolutionary computation.