On the construction of stable periodic solutions for the dynamical motion of AC machines
This article discusses the stability of periodic responses for the dynamical motion of AC machines from the perspective of Lyapunov function approach. The dynamical motion of AC machines is prototypically modeled as an equivalent linear RLC series circuit with time-variant inductance represented by...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023446?viewType=HTML |
| _version_ | 1811162012852420608 |
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| author | Mohamed El-Borhamy Essam Eddin M. Rashad Arafa A. Nasef Ismail Sobhy Samah M. Elkholy |
| author_facet | Mohamed El-Borhamy Essam Eddin M. Rashad Arafa A. Nasef Ismail Sobhy Samah M. Elkholy |
| author_sort | Mohamed El-Borhamy |
| collection | DOAJ |
| description | This article discusses the stability of periodic responses for the dynamical motion of AC machines from the perspective of Lyapunov function approach. The dynamical motion of AC machines is prototypically modeled as an equivalent linear RLC series circuit with time-variant inductance represented by a linear differential equation with periodic coefficients. Based on the deduced stability conditions, some special identities among the equivalent circuit parameters to ensure the stability of responses and their periodic structures are concluded. Through these conditions, the periodic structure of responses is obtained by using the method of strained parameters. Through a comparison with the experimental results from the specialized practical literatures, a strong agreement with the obtained analytical results is achieved. In addition, from a practical point of views, some future points within the discussion are raised to improve the mathematical modeling of AC machines to obtain a better model and simulation. |
| first_indexed | 2024-04-10T06:22:55Z |
| format | Article |
| id | doaj.art-885d398654de47f096bd9cb8ffd336d0 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T06:22:55Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-885d398654de47f096bd9cb8ffd336d02023-03-02T01:15:12ZengAIMS PressAIMS Mathematics2473-69882023-02-01848902892710.3934/math.2023446On the construction of stable periodic solutions for the dynamical motion of AC machinesMohamed El-Borhamy0Essam Eddin M. Rashad 1Arafa A. Nasef2Ismail Sobhy3Samah M. Elkholy41. Department of Engineering Mathematics and Physics, Faculty of Engineering, University of Tanta, Tanta 31527, Egypt 2. Department of Basic Sciences, Faculty of Engineering, Horus University, New Damietta, Egypt3. Department of Electrical Power and Machines Engineering, Faculty of Engineering, University of Tanta, Tanta 31527, Egypt4. Department of Engineering Mathematics and Physics, Faculty of Engineering, University of Kafrelsheikh, Kafer Elsheikh 33516, Egypt4. Department of Engineering Mathematics and Physics, Faculty of Engineering, University of Kafrelsheikh, Kafer Elsheikh 33516, Egypt4. Department of Engineering Mathematics and Physics, Faculty of Engineering, University of Kafrelsheikh, Kafer Elsheikh 33516, EgyptThis article discusses the stability of periodic responses for the dynamical motion of AC machines from the perspective of Lyapunov function approach. The dynamical motion of AC machines is prototypically modeled as an equivalent linear RLC series circuit with time-variant inductance represented by a linear differential equation with periodic coefficients. Based on the deduced stability conditions, some special identities among the equivalent circuit parameters to ensure the stability of responses and their periodic structures are concluded. Through these conditions, the periodic structure of responses is obtained by using the method of strained parameters. Through a comparison with the experimental results from the specialized practical literatures, a strong agreement with the obtained analytical results is achieved. In addition, from a practical point of views, some future points within the discussion are raised to improve the mathematical modeling of AC machines to obtain a better model and simulation.https://www.aimspress.com/article/doi/10.3934/math.2023446?viewType=HTMLlinear differential equationsstability theoryperiodic solutionsperturbation techniques |
| spellingShingle | Mohamed El-Borhamy Essam Eddin M. Rashad Arafa A. Nasef Ismail Sobhy Samah M. Elkholy On the construction of stable periodic solutions for the dynamical motion of AC machines AIMS Mathematics linear differential equations stability theory periodic solutions perturbation techniques |
| title | On the construction of stable periodic solutions for the dynamical motion of AC machines |
| title_full | On the construction of stable periodic solutions for the dynamical motion of AC machines |
| title_fullStr | On the construction of stable periodic solutions for the dynamical motion of AC machines |
| title_full_unstemmed | On the construction of stable periodic solutions for the dynamical motion of AC machines |
| title_short | On the construction of stable periodic solutions for the dynamical motion of AC machines |
| title_sort | on the construction of stable periodic solutions for the dynamical motion of ac machines |
| topic | linear differential equations stability theory periodic solutions perturbation techniques |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023446?viewType=HTML |
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