Journal
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
Volume 23, Issue 1, Pages 183-210Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/fca-2020-0007
Keywords
fractional calculus; stability analysis; resonance condition; non-commensurate
Funding
- National Natural Science Foundation of China [11902252]
- Fundamental Research Funds for the Central Universities of China [G2018KY0305, G2018KY0302]
- China Postdoctoral Science Foundation [2019M663811]
- Natural Science Foundation of Shaanxi Province
Ask authors/readers for more resources
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 (zeta) 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available