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

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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.

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Author information

Authors and Affiliations

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

    Shuo Zhang

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

    Lu Liu

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

    Dingyu Xue

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

    YangQuan Chen

Authors
  1. Shuo Zhang
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  2. Lu Liu
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  3. Dingyu Xue
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  4. YangQuan Chen
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Correspondence to Shuo Zhang.

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Zhang, S., Liu, L., Xue, D. et al. Stability and Resonance Analysis of a General Non-Commensurate Elementary Fractional-Order System. Fract Calc Appl Anal 23, 183–210 (2020). https://doi.org/10.1515/fca-2020-0007

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  • DOI: https://doi.org/10.1515/fca-2020-0007

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