Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter
Fractional-order (FO) differential equations are more and more frequently applied to describe real-world applications or models of phenomena. Despite such models exhibiting high flexibility and good fits to experimental data, they introduce their inherent inaccuracy related to the order of approxima...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/11/1898 |
| _version_ | 1797547469595213824 |
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| author | Józef Wiora Alicja Wiora |
| author_facet | Józef Wiora Alicja Wiora |
| author_sort | Józef Wiora |
| collection | DOAJ |
| description | Fractional-order (FO) differential equations are more and more frequently applied to describe real-world applications or models of phenomena. Despite such models exhibiting high flexibility and good fits to experimental data, they introduce their inherent inaccuracy related to the order of approximation. This article shows that the chosen model influences the dynamic properties of signals. First, we calculated symbolically the steady-state values of an FO inertia using three variants of the Oustaloup filter approximation. Then, we showed how the models influence the Nyquist plots in the frequency domain. The unit step responses calculated using different models also have different plots. An example of FO control system evidenced different trajectories dependent on applied models. We concluded that publicized parameters of FO models should also consist of the name of the model used in calculations in order to correctly reproduce described phenomena. For this reason, the inappropriate use of FO models may lead to drawing incorrect conclusions about the described system. |
| first_indexed | 2024-03-10T14:44:35Z |
| format | Article |
| id | doaj.art-256151135fc54dde9abff576e998d3c4 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T14:44:35Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-256151135fc54dde9abff576e998d3c42023-11-20T21:30:33ZengMDPI AGSymmetry2073-89942020-11-011211189810.3390/sym12111898Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup FilterJózef Wiora0Alicja Wiora1Department of Measurements and Control Systems, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, PolandDepartment of Measurements and Control Systems, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, PolandFractional-order (FO) differential equations are more and more frequently applied to describe real-world applications or models of phenomena. Despite such models exhibiting high flexibility and good fits to experimental data, they introduce their inherent inaccuracy related to the order of approximation. This article shows that the chosen model influences the dynamic properties of signals. First, we calculated symbolically the steady-state values of an FO inertia using three variants of the Oustaloup filter approximation. Then, we showed how the models influence the Nyquist plots in the frequency domain. The unit step responses calculated using different models also have different plots. An example of FO control system evidenced different trajectories dependent on applied models. We concluded that publicized parameters of FO models should also consist of the name of the model used in calculations in order to correctly reproduce described phenomena. For this reason, the inappropriate use of FO models may lead to drawing incorrect conclusions about the described system.https://www.mdpi.com/2073-8994/12/11/1898model errorfractional-order differential equationOustaloup filter approximationcontrol systemNyquist plotstep response |
| spellingShingle | Józef Wiora Alicja Wiora Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter Symmetry model error fractional-order differential equation Oustaloup filter approximation control system Nyquist plot step response |
| title | Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter |
| title_full | Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter |
| title_fullStr | Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter |
| title_full_unstemmed | Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter |
| title_short | Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter |
| title_sort | influence of methods approximating fractional order differentiation on the output signal illustrated by three variants of oustaloup filter |
| topic | model error fractional-order differential equation Oustaloup filter approximation control system Nyquist plot step response |
| url | https://www.mdpi.com/2073-8994/12/11/1898 |
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