Stability and resonance analysis of a general non-commensurate elementary fractional-order system-Reference-Cited by-同舟云学术

Stability and resonance analysis of a general non-commensurate elementary fractional-order system

Published:2020-02-01 Issue:1 Volume:23 Page:183-210
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Zhang Shuo¹,Liu Lu²,Xue Dingyu³,Chen YangQuan⁴

Affiliation:

1. Department of Applied Mathematics , Northwestern Polytechnical University , No. 127, Youyi West Road , Xi’an , 710072 , China

2. School of Marine Science and Technology , Northwestern Polytechnical University , No. 127, Youyi West Road , Xi’an , 710072 , China

3. Department of Information Science and Engineering , Northeastern University , No. 3-11, Wenhua Road, Heping District , Shenyang , 110819 , China

4. Mechatronics, Embedded Systems and Automation (MESA) Lab, School of Engineering , University of California , Merced 5200 North Lake Road , Merced , CA 95343 , USA

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0007/pdf

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