Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems
It is shown that the classic Nyquist criterion can be extended in a straightforward way to feedback systems of fractional order. The proof of this extension merely requires basic notions of vector analysis and of closed-loop system transfer functions. The criterion can be used not only to ascertain...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IEEE
2021-01-01
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| Series: | IEEE Open Journal of Circuits and Systems |
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| Online Access: | https://ieeexplore.ieee.org/document/9275299/ |
| _version_ | 1826938393958809600 |
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| author | Daniele Casagrande Wieslaw Krajewski Umberto Viaro |
| author_facet | Daniele Casagrande Wieslaw Krajewski Umberto Viaro |
| author_sort | Daniele Casagrande |
| collection | DOAJ |
| description | It is shown that the classic Nyquist criterion can be extended in a straightforward way to feedback systems of fractional order. The proof of this extension merely requires basic notions of vector analysis and of closed-loop system transfer functions. The criterion can be used not only to ascertain the stability of a fractional-order system but also to detect the presence of closed-loop poles inside any given sector of the complex plane. The test is finally applied to three examples of didactic value. |
| first_indexed | 2024-04-13T09:37:55Z |
| format | Article |
| id | doaj.art-75c554151f484f8b9f60d0e161226022 |
| institution | Directory Open Access Journal |
| issn | 2644-1225 |
| language | English |
| last_indexed | 2025-02-17T18:56:11Z |
| publishDate | 2021-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Circuits and Systems |
| spelling | doaj.art-75c554151f484f8b9f60d0e1612260222024-12-11T00:07:06ZengIEEEIEEE Open Journal of Circuits and Systems2644-12252021-01-012162210.1109/OJCAS.2020.30400499275299Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback SystemsDaniele Casagrande0https://orcid.org/0000-0001-6651-1012Wieslaw Krajewski1Umberto Viaro2https://orcid.org/0000-0001-8400-7397Polytechnic Department of Engineering and Architecture, University of Udine, Udine, ItalyPolish Academy of Sciences, Systems Research Institute, Warsaw, PolandPolytechnic Department of Engineering and Architecture, University of Udine, Udine, ItalyIt is shown that the classic Nyquist criterion can be extended in a straightforward way to feedback systems of fractional order. The proof of this extension merely requires basic notions of vector analysis and of closed-loop system transfer functions. The criterion can be used not only to ascertain the stability of a fractional-order system but also to detect the presence of closed-loop poles inside any given sector of the complex plane. The test is finally applied to three examples of didactic value.https://ieeexplore.ieee.org/document/9275299/Fractional-order systemsfeedback systemsstabilityroot clusteringNyquist plot |
| spellingShingle | Daniele Casagrande Wieslaw Krajewski Umberto Viaro Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems IEEE Open Journal of Circuits and Systems Fractional-order systems feedback systems stability root clustering Nyquist plot |
| title | Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems |
| title_full | Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems |
| title_fullStr | Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems |
| title_full_unstemmed | Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems |
| title_short | Elementary Derivation of the Nyquist Criterion for Fractional-Order Feedback Systems |
| title_sort | elementary derivation of the nyquist criterion for fractional order feedback systems |
| topic | Fractional-order systems feedback systems stability root clustering Nyquist plot |
| url | https://ieeexplore.ieee.org/document/9275299/ |
| work_keys_str_mv | AT danielecasagrande elementaryderivationofthenyquistcriterionforfractionalorderfeedbacksystems AT wieslawkrajewski elementaryderivationofthenyquistcriterionforfractionalorderfeedbacksystems AT umbertoviaro elementaryderivationofthenyquistcriterionforfractionalorderfeedbacksystems |