Abstract
The fractional-order proportional-integral-derivative (FOPID) controller is an improvement over the traditional PID controller. However, most existing methods of FOPID controller design are complex and not suitable for practical application. This paper presents a simple and efficient design method of FOPID controllers for fractional-order controlled plants with time delays. The method is based on four frequency-domain specifications—namely, gain crossover frequency, phase margin, phase crossover frequency and gain margin. The implicit nonlinear equations related to the controller parameters are formulated using these specifications. To simplify the mathematical calculation, the explicit equations of the controller parameters are analytically derived. Then, the FOPID controller parameters can be adjusted in a graphical manner. Two fractional-order plus time-delay plants are considered as simulation examples. The results show that the design requirements are successfully met and superior control performance is obtained via the proposed tuning method.
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Xu Li received his M.S. degree from the Hefei University of Technology, Hefei, China, in 2014. He is currently pursuing a Ph.D. degree in the Department of Automation, University of Science and Technology of China, Hefei, China. His research interests include fractional order systems, nonlinear systems, nonlinear control, and industrial process control.
Lifu Gao received his M.S. degree in pattern recognition and intelligent systems from the Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, China, in 1999 and a Ph.D. degree in pattern recognition and intelligent systems from the University of Science and Technology of China, Hefei, China, in 2002. From 2005 to 2011, he was a postdoctoral fellow and a senior engineer with European Molecular Biology Laboratory, Hamburg, Germany. Since 2011, he has been a research fellow with the Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, China. His research interests include robotics and sensors.
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Li, X., Gao, L. A Simple Frequency-domain Tuning Method of Fractional-order PID Controllers for Fractional-order Delay Systems. Int. J. Control Autom. Syst. 20, 2159–2168 (2022). https://doi.org/10.1007/s12555-021-0206-x
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DOI: https://doi.org/10.1007/s12555-021-0206-x