Abstract
The robust design of fractional-order proportional-integral-differential (FOPID) controllers for controlled plants with uncertainty is a popular research topic. The well-studied “flat phase” condition is effective for the gain variation but not for variations in other parameters. This paper addresses the problem of tuning a robust FOPID controller for a plant with a known structure and an uncertain parameter (a coefficient or order in the plant transfer function). The method is based on preserving the phase margin of the open-loop system when the plant parameter varies around the nominal value. First, the partial derivatives of the gain crossover frequency with respect to the plant parameters are calculated. Then, the partial derivatives of the phase margin with respect to the plant parameters are obtained as the robust performance indexes. In addition, the equations needed to compute FOPID parameters that meet the specifications in the frequency domain are obtained and used as nonlinear constraints. Finally, the FOPID parameters can be obtained by optimizing the robust performance indexes under these constraints. Simulation experiments are carried out on examples with different types of uncertain parameters to verify the effectiveness of the tuning method. The results show that the requirements are fulfilled and that the system with the proposed FOPID controller is stable and robust to variations in the uncertain parameters. Comparisons clearly show that the controllers designed by the proposed method provide relatively robust performance.
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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 system, nonlinear control, and industrial process control.
Lifu Gao received his M.S. degree in pattern recognition and intelligent system from Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, China, in 1999 and a Ph.D. degree in pattern recognition and intelligent system from 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 Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, China. His research interests include robotics and sensor.
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Li, X., Gao, L. Robust Fractional-order PID Tuning Method for a Plant with an Uncertain Parameter. Int. J. Control Autom. Syst. 19, 1302–1310 (2021). https://doi.org/10.1007/s12555-019-0866-y
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DOI: https://doi.org/10.1007/s12555-019-0866-y