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		Dejin WANG,Jianghui ZHANG.[en_title][J].Control Theory and Technology,2011,9(4):599~603.[Copy]

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DejinWANG,JianghuiZHANG
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(School of Electronic Information and Automation, Tianjin University of Science and Technology)

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Received:July 16, 2009Revised:July 13, 2010

基金项目:This work is supported by the National Natural Science Foundation of China (No. 60874028).

A graphical tuning of PI^λ controllers for fractional-delay systems

Dejin WANG,Jianghui ZHANG

(School of Electronic Information and Automation, Tianjin University of Science and Technology)

Abstract:

This article provides a graphical parameter tuning method ofPI^λ controllers for fractional-order time-delay systems. First, the complete stabilizing region of PI^λ controller in proportional-integral plane, for a fixed λ, is determined in terms of a graphical stability criterion applicable to fractional-delay systems. Then, the stabilizing region is maximized analytically with respect to parameter λ to expect the most various behaviors of the closed-loop systems. Finally, by defining appropriate functions relative to the requirements of gain and phase margins, the curves in the maximized stabilizing region satisfying the pre-specified gain and phase margins are drawn, which releases a flexible parameter tuning procedure. Numerical examples are given to illustrate the design steps.

Key words: Fractional order systems PI^λ controllers Time-delay systems Graphical stability criterion