Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function
This paper proposes new numerical algorithms for calculating the time domain responses of fractional order transfer functions (FOTFs). FOTFs are divided into two categories, explicit fractional order transfer functions (EFOTFs) and implicit fractional order transfer functions (IFOTFs). Transforming...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/2/122 |
| _version_ | 1797480057897222144 |
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| author | Lu Bai Dingyü Xue |
| author_facet | Lu Bai Dingyü Xue |
| author_sort | Lu Bai |
| collection | DOAJ |
| description | This paper proposes new numerical algorithms for calculating the time domain responses of fractional order transfer functions (FOTFs). FOTFs are divided into two categories, explicit fractional order transfer functions (EFOTFs) and implicit fractional order transfer functions (IFOTFs). Transforming an EFOTF into an equivalent fractional order differential equation, its time domain response can be obtained by solving the equation by the difference method. IFOTF cannot be transformed into an equivalent equation, so its time domain response cannot be calculated by existing difference methods. A new numerical algorithm is designed for calculating a convolution and its inverse operation, the time domain response of IFOTF can be calculated based on the algorithm. Error analysis shows that the proposed numerical algorithms are of first-order accuracy. Four calculation examples are presented, and the results are consistent with the theoretical analysis. |
| first_indexed | 2024-03-09T21:54:41Z |
| format | Article |
| id | doaj.art-45e3ecc3574d4570864f8db42792ccfc |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T21:54:41Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-45e3ecc3574d4570864f8db42792ccfc2023-11-23T19:59:32ZengMDPI AGFractal and Fractional2504-31102022-02-016212210.3390/fractalfract6020122Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer FunctionLu Bai0Dingyü Xue1School of Information Engineering, Shenyang University, Shenyang 110044, ChinaSchool of Information Science and Engineering, Northeastern University, Shenyang 110819, ChinaThis paper proposes new numerical algorithms for calculating the time domain responses of fractional order transfer functions (FOTFs). FOTFs are divided into two categories, explicit fractional order transfer functions (EFOTFs) and implicit fractional order transfer functions (IFOTFs). Transforming an EFOTF into an equivalent fractional order differential equation, its time domain response can be obtained by solving the equation by the difference method. IFOTF cannot be transformed into an equivalent equation, so its time domain response cannot be calculated by existing difference methods. A new numerical algorithm is designed for calculating a convolution and its inverse operation, the time domain response of IFOTF can be calculated based on the algorithm. Error analysis shows that the proposed numerical algorithms are of first-order accuracy. Four calculation examples are presented, and the results are consistent with the theoretical analysis.https://www.mdpi.com/2504-3110/6/2/122fractional order transfer functiontime domain responsenumerical algorithmbenchmark problem |
| spellingShingle | Lu Bai Dingyü Xue Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function Fractal and Fractional fractional order transfer function time domain response numerical algorithm benchmark problem |
| title | Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function |
| title_full | Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function |
| title_fullStr | Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function |
| title_full_unstemmed | Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function |
| title_short | Numerical Algorithm for Calculating the Time Domain Response of Fractional Order Transfer Function |
| title_sort | numerical algorithm for calculating the time domain response of fractional order transfer function |
| topic | fractional order transfer function time domain response numerical algorithm benchmark problem |
| url | https://www.mdpi.com/2504-3110/6/2/122 |
| work_keys_str_mv | AT lubai numericalalgorithmforcalculatingthetimedomainresponseoffractionalordertransferfunction AT dingyuxue numericalalgorithmforcalculatingthetimedomainresponseoffractionalordertransferfunction |