Root Locus Practical Sketching Rules for Fractional-Order Systems
For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the...
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/102068 |
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| author | António M. Lopes J. A. Tenreiro Machado |
| author_facet | António M. Lopes J. A. Tenreiro Machado |
| author_sort | António M. Lopes |
| collection | DOAJ |
| description | For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples. |
| format | Article |
| id | doaj-art-b9b694e4f321419a8e2674ea0b8a850e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b9b694e4f321419a8e2674ea0b8a850e2025-02-03T01:01:14ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/102068102068Root Locus Practical Sketching Rules for Fractional-Order SystemsAntónio M. Lopes0J. A. Tenreiro Machado1Institute of Mechanical Engineering, UISPA, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, PortugalInstitute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida 431, 4200-072 Porto, PortugalFor integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.http://dx.doi.org/10.1155/2013/102068 |
| spellingShingle | António M. Lopes J. A. Tenreiro Machado Root Locus Practical Sketching Rules for Fractional-Order Systems Abstract and Applied Analysis |
| title | Root Locus Practical Sketching Rules for Fractional-Order Systems |
| title_full | Root Locus Practical Sketching Rules for Fractional-Order Systems |
| title_fullStr | Root Locus Practical Sketching Rules for Fractional-Order Systems |
| title_full_unstemmed | Root Locus Practical Sketching Rules for Fractional-Order Systems |
| title_short | Root Locus Practical Sketching Rules for Fractional-Order Systems |
| title_sort | root locus practical sketching rules for fractional order systems |
| url | http://dx.doi.org/10.1155/2013/102068 |
| work_keys_str_mv | AT antoniomlopes rootlocuspracticalsketchingrulesforfractionalordersystems AT jatenreiromachado rootlocuspracticalsketchingrulesforfractionalordersystems |