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

  • Shuo Zhang EMAIL logo , Lu Liu , Dingyu Xue and YangQuan Chen
Published/Copyright: February 27, 2020

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.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No.11902252), the Fundamental Research Funds for the Central Universities of China (No. G2018KY0305 and No. G2018KY0302), China Postdoctoral Science Foundation (No.2019M663811), the Natural Science Foundation of Shaanxi Province (No.2019JQ-164).

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Received: 2018-08-22
Revised: 2019-12-12
Published Online: 2020-02-27
Published in Print: 2020-02-25

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