A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments

• Published in: IEEE transactions on control systems technology Vol. 18; no. 2; pp. 516 - 520
• Main Authors: Li, HongSheng, Luo, Ying, Chen, YangQuan
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Automation; Computer science; control theory; systems; Control system synthesis; Control theory; Control theory. Systems; Crossovers; Derivatives; Design engineering; Design methodology; Dynamical systems; Dynamics; Exact sciences and technology; Fractional calculus; fractional order controller (FOC); Frequency; Gain; gain variations; iso-damping; Motion control; PD control; PI^{\lambda}D^{\mu} controller; Proportional control; Robustness; second-order plant; Studies; System theory; Transfer functions; Tuning; controller; D; Control synthesis; PD control; Fractional calculus; Fractional derivative; iso-damping; Closed feedback; gain variations; fractional order controller (FOC); PI; Robustness; Phase margin; ISO standard; second-order plant; Motion control
• DOI: 10.1109/TCST.2009.2019120
• ISSN: 1063-6536

In recent years, it is remarkable to see the increasing number of studies related to the theory and application of fractional order controller (FOC), specially PI ¿ D ¿ controller, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods for fractional order controllers as an extension of classical control theory. In this paper, a new tuning method for fractional order proportional and derivative ( PD ¿ ) or FO-PD controller is proposed for a class of typical second-order plants. The tuned FO-PD controller can ensure that the given gain crossover frequency and phase margin are fulfilled, and furthermore, the phase derivative w. r. t. the frequency is zero, i.e., the phase Bode plot is flat at the given gain crossover frequency. Consequently, the closed-loop system is robust to gain variations. The FOC design method proposed in the paper is practical and simple to apply. Simulation and experimental results show that the closed-loop system can achieve favorable dynamic performance and robustness.