Extending the Root-Locus Method to Fractional-Order Systems
The well-known root-locus method is developed for special subset of linear time-invariant systems known as fractional-order systems. Transfer functions of these systems are rational functions with polynomials of rational powers of the Laplace variable s. Such systems are defined on a Riemann surface...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2008/528934 |
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| author | Farshad Merrikh-Bayat Mahdi Afshar |
| author_facet | Farshad Merrikh-Bayat Mahdi Afshar |
| author_sort | Farshad Merrikh-Bayat |
| collection | DOAJ |
| description | The well-known root-locus method is developed for special subset of linear time-invariant systems known as fractional-order systems. Transfer functions of these systems are rational functions with polynomials of rational powers of the Laplace variable s. Such systems are defined on a Riemann surface because of their multivalued nature. A set of rules for plotting the root loci on the first Riemann sheet is presented. The important features of the classical root-locus method such as asymptotes, roots condition on the real axis, and breakaway points are extended to fractional case. It is also shown that the proposed method can assess the closed-loop stability of fractional-order systems in the presence of a varying gain in the loop. Three illustrative examples are presented to confirm the effectiveness of the proposed algorithm. |
| format | Article |
| id | doaj-art-d92c20f470e14fcbb73ed4d47c3e4837 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d92c20f470e14fcbb73ed4d47c3e48372025-02-03T01:25:35ZengWileyJournal of Applied Mathematics1110-757X1687-00422008-01-01200810.1155/2008/528934528934Extending the Root-Locus Method to Fractional-Order SystemsFarshad Merrikh-Bayat0Mahdi Afshar1Department of Electrical Engineering, Zanjan University, Zanjan, IranDepartment of Mathematics, Zanjan Azad University, Zanjan, IranThe well-known root-locus method is developed for special subset of linear time-invariant systems known as fractional-order systems. Transfer functions of these systems are rational functions with polynomials of rational powers of the Laplace variable s. Such systems are defined on a Riemann surface because of their multivalued nature. A set of rules for plotting the root loci on the first Riemann sheet is presented. The important features of the classical root-locus method such as asymptotes, roots condition on the real axis, and breakaway points are extended to fractional case. It is also shown that the proposed method can assess the closed-loop stability of fractional-order systems in the presence of a varying gain in the loop. Three illustrative examples are presented to confirm the effectiveness of the proposed algorithm.http://dx.doi.org/10.1155/2008/528934 |
| spellingShingle | Farshad Merrikh-Bayat Mahdi Afshar Extending the Root-Locus Method to Fractional-Order Systems Journal of Applied Mathematics |
| title | Extending the Root-Locus Method to Fractional-Order Systems |
| title_full | Extending the Root-Locus Method to Fractional-Order Systems |
| title_fullStr | Extending the Root-Locus Method to Fractional-Order Systems |
| title_full_unstemmed | Extending the Root-Locus Method to Fractional-Order Systems |
| title_short | Extending the Root-Locus Method to Fractional-Order Systems |
| title_sort | extending the root locus method to fractional order systems |
| url | http://dx.doi.org/10.1155/2008/528934 |
| work_keys_str_mv | AT farshadmerrikhbayat extendingtherootlocusmethodtofractionalordersystems AT mahdiafshar extendingtherootlocusmethodtofractionalordersystems |