Analysis of fractional order systems using newton iteration-based approximation technique.
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| Title: | Analysis of fractional order systems using newton iteration-based approximation technique. |
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| Authors: | Shrivastava, Nitisha1 nitishashrivastav@gmail.com, Baliyan, Arjun2 arjunbaliyaneee@gmail.com |
| Source: | International Journal of Electrical & Computer Engineering (2088-8708). Feb2023, Vol. 13 Issue 1, p116-124. 9p. |
| Subjects: | Fractional powers, Integer approximations, Approximation error |
| Abstract: | Fractional differential equations play a major role in expressing mathematically the real-world problems as they help attain good fit to the experimental data. It is also known that fractional order controllers are more flexible than integer order controllers. But when it comes to the numerical approximation of fractional order functions inaccuracies arise if the conversion technique is not chosen properly. So, when a fractional order plant model is approximated to an integer order system, it is required that the approximated model be accurate, as the overall system performance is based on the estimated integer order model. Nitisha-Pragya-Carlson (NPC) is a recent approximation technique proposed in 2018 to derive the rational approximation of fractional order differ-integrators. In this paper, three fractional order plant models having fractional powers 3.1, 1.25 and 1.3 is analyzed in frequency domain in terms of magnitude and phase response. The performance of approximated third and second order NPC based integer model is studied and compared with the integer models developed using other existing technique. The approximation error is calculated by comparing the frequency response of the developed models with the ideal response. It has been found that in all the three examples NPC based models are very much close to the ideal values. Hence proving the efficacy of NPC technique in approximation of fractional order systems. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Electrical & Computer Engineering (2088-8708) is the property of Institute of Advanced Engineering & Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: Analysis of fractional order systems using newton iteration-based approximation technique. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Shrivastava%2C+Nitisha%22">Shrivastava, Nitisha</searchLink><relatesTo>1</relatesTo><i> nitishashrivastav@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Baliyan%2C+Arjun%22">Baliyan, Arjun</searchLink><relatesTo>2</relatesTo><i> arjunbaliyaneee@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Electrical+%26+Computer+Engineering+%282088-8708%29%22">International Journal of Electrical & Computer Engineering (2088-8708)</searchLink>. Feb2023, Vol. 13 Issue 1, p116-124. 9p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Fractional+powers%22">Fractional powers</searchLink><br /><searchLink fieldCode="DE" term="%22Integer+approximations%22">Integer approximations</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Fractional differential equations play a major role in expressing mathematically the real-world problems as they help attain good fit to the experimental data. It is also known that fractional order controllers are more flexible than integer order controllers. But when it comes to the numerical approximation of fractional order functions inaccuracies arise if the conversion technique is not chosen properly. So, when a fractional order plant model is approximated to an integer order system, it is required that the approximated model be accurate, as the overall system performance is based on the estimated integer order model. Nitisha-Pragya-Carlson (NPC) is a recent approximation technique proposed in 2018 to derive the rational approximation of fractional order differ-integrators. In this paper, three fractional order plant models having fractional powers 3.1, 1.25 and 1.3 is analyzed in frequency domain in terms of magnitude and phase response. The performance of approximated third and second order NPC based integer model is studied and compared with the integer models developed using other existing technique. The approximation error is calculated by comparing the frequency response of the developed models with the ideal response. It has been found that in all the three examples NPC based models are very much close to the ideal values. Hence proving the efficacy of NPC technique in approximation of fractional order systems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Electrical & Computer Engineering (2088-8708) is the property of Institute of Advanced Engineering & Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.11591/ijece.v13i1.pp116-124 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 9 StartPage: 116 Subjects: – SubjectFull: Fractional powers Type: general – SubjectFull: Integer approximations Type: general – SubjectFull: Approximation error Type: general Titles: – TitleFull: Analysis of fractional order systems using newton iteration-based approximation technique. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Shrivastava, Nitisha – PersonEntity: Name: NameFull: Baliyan, Arjun IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 20888708 Numbering: – Type: volume Value: 13 – Type: issue Value: 1 Titles: – TitleFull: International Journal of Electrical & Computer Engineering (2088-8708) Type: main |
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