Stability and Resonance Analysis of a General Non-Commensurate Elementary Fractional-Order System

被引：0
|
作者：
Shuo Zhang
Lu Liu
Dingyu Xue
YangQuan Chen
机构：
[1] Northwestern Polytechnical University,Department of Applied Mathematics
[2] Northwestern Polytechnical University,School of Marine Science and Technology
[3] Northeastern University,Department of Information Science and Engineering
[4] University of California,Mechatronics, Embedded Systems and Automation (MESA) Lab, School of Engineering
来源：
Fractional Calculus and Applied Analysis | 2020年 / 23卷
关键词：
Primary 26A33; Secondary 34A08, 93C05, 93D20, 70J40; fractional calculus; stability analysis; resonance condition; non-commensurate;
D O I：
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学科分类号：
摘要：
The elementary fractional-order models are the extension of first and second order models which have been widely used in various engineering fields. Some important properties of commensurate or a few particular kinds of non-commensurate elementary fractional-order transfer functions have already been discussed in the existing studies. However, most of them are only available for one particular kind elementary fractional-order system. In this paper, the stability and resonance analysis of a general kind non-commensurate elementary fractional-order system is presented. The commensurate-order restriction is fully released. Firstly, based on Nyquist’s Theorem, the stability conditions are explored in details under different conditions, namely different combinations of pseudo-damping (ζ) factor values and order parameters. Then, resonance conditions are established in terms of frequency behaviors. At last, an example is given to show the stable and resonant regions of the studied systems.
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页码：183 / 210
页数：27
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