Automated Linearization of a System of Nonlinear Ordinary Differential Equations
This paper investigates the possibility of automatically linearizing nonlinear models. Constructing a linearised model for a nonlinear system is quite labor-intensive and practically unrealistic when the dimension is greater than 3. Therefore, it is important to automate the process of linearisation...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2023-11-01
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| Series: | International Journal of Electronics and Telecommunications |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/129105/PDF/3-4207-Ziyatbekova-sk.pdf |
| _version_ | 1797628126633656320 |
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| author | Aigerim Mazakova Sholpan Jomartova Waldemar Wójcik Talgat Mazakov Gulzat Ziyatbekova |
| author_facet | Aigerim Mazakova Sholpan Jomartova Waldemar Wójcik Talgat Mazakov Gulzat Ziyatbekova |
| author_sort | Aigerim Mazakova |
| collection | DOAJ |
| description | This paper investigates the possibility of automatically linearizing nonlinear models. Constructing a linearised model for a nonlinear system is quite labor-intensive and practically unrealistic when the dimension is greater than 3. Therefore, it is important to automate the process of linearisation of the original nonlinear model. Based on the application of computer algebra, a constructive algorithm for the linearisation of a system of non-linear ordinary differential equations was developed. A software was developed on MatLab. The effectiveness of the proposed algorithm has been demonstrated on applied problems: an unmanned aerial vehicle dynamics model and a twolink robot model. The obtained linearized models were then used to test the stability of the original models. In order to account for possible inaccuracies in the measurements of the technical parameters of the model, an interval linearized model is adopted. For such a model, the procedure for constructing the corresponding interval characteristic polynomial and the corresponding Hurwitz matrix is automated. On the basis of the analysis of the properties of the main minors of the Hurwitz matrix, the stability of the studied system was analyzed. |
| first_indexed | 2024-03-11T10:34:02Z |
| format | Article |
| id | doaj.art-e053dc170b8c4daba0cffa09c01e45db |
| institution | Directory Open Access Journal |
| issn | 2081-8491 2300-1933 |
| language | English |
| last_indexed | 2024-03-11T10:34:02Z |
| publishDate | 2023-11-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | International Journal of Electronics and Telecommunications |
| spelling | doaj.art-e053dc170b8c4daba0cffa09c01e45db2023-11-14T12:28:04ZengPolish Academy of SciencesInternational Journal of Electronics and Telecommunications2081-84912300-19332023-11-01vol. 69No 4655600https://doi.org/10.24425/ijet.2023.147684Automated Linearization of a System of Nonlinear Ordinary Differential EquationsAigerim Mazakova0Sholpan Jomartova1Waldemar Wójcik2Talgat Mazakov3Gulzat Ziyatbekova4Al-Farabi Kazakh NationalUniversity, KazakhstanAl-Farabi Kazakh NationalUniversity, KazakhstanLublin Technical University, PolandInstitute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, KazakhstanInstitute of Information and Computational Technologies CS MES RK, Al-Farabi Kazakh National University, KazakhstanThis paper investigates the possibility of automatically linearizing nonlinear models. Constructing a linearised model for a nonlinear system is quite labor-intensive and practically unrealistic when the dimension is greater than 3. Therefore, it is important to automate the process of linearisation of the original nonlinear model. Based on the application of computer algebra, a constructive algorithm for the linearisation of a system of non-linear ordinary differential equations was developed. A software was developed on MatLab. The effectiveness of the proposed algorithm has been demonstrated on applied problems: an unmanned aerial vehicle dynamics model and a twolink robot model. The obtained linearized models were then used to test the stability of the original models. In order to account for possible inaccuracies in the measurements of the technical parameters of the model, an interval linearized model is adopted. For such a model, the procedure for constructing the corresponding interval characteristic polynomial and the corresponding Hurwitz matrix is automated. On the basis of the analysis of the properties of the main minors of the Hurwitz matrix, the stability of the studied system was analyzed.https://journals.pan.pl/Content/129105/PDF/3-4207-Ziyatbekova-sk.pdfordinary differential equationcomputer algebrastabilitycontrollabilitymatlab |
| spellingShingle | Aigerim Mazakova Sholpan Jomartova Waldemar Wójcik Talgat Mazakov Gulzat Ziyatbekova Automated Linearization of a System of Nonlinear Ordinary Differential Equations International Journal of Electronics and Telecommunications ordinary differential equation computer algebra stability controllability matlab |
| title | Automated Linearization of a System of Nonlinear Ordinary Differential Equations |
| title_full | Automated Linearization of a System of Nonlinear Ordinary Differential Equations |
| title_fullStr | Automated Linearization of a System of Nonlinear Ordinary Differential Equations |
| title_full_unstemmed | Automated Linearization of a System of Nonlinear Ordinary Differential Equations |
| title_short | Automated Linearization of a System of Nonlinear Ordinary Differential Equations |
| title_sort | automated linearization of a system of nonlinear ordinary differential equations |
| topic | ordinary differential equation computer algebra stability controllability matlab |
| url | https://journals.pan.pl/Content/129105/PDF/3-4207-Ziyatbekova-sk.pdf |
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