PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES
A cubic Bezier curve formulation is used for generating phase portrait of an inverted pendulum system. Assuming that the cart and pendulum masses, pendulum length, and friction coefficient values in the inverted pendulum model are unknown, its finite number of experimentally obtained...
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| Format: | Article |
| Language: | English |
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Eskişehir Osmangazi University
2020-08-01
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| Series: | Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/1260345 |
| _version_ | 1797921764244717568 |
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| author | Gökhan DINDIŞ Abdurrahman KARAMANCIOĞLU |
| author_facet | Gökhan DINDIŞ Abdurrahman KARAMANCIOĞLU |
| author_sort | Gökhan DINDIŞ |
| collection | DOAJ |
| description | A cubic Bezier curve formulation is used for generating phase portrait of an inverted pendulum system. Assuming that the cart and pendulum masses, pendulum length, and friction coefficient values in the inverted pendulum model are unknown, its finite number of experimentally obtained trajectories are utilized as a basis for generating the experimentally unavailable trajectories. It is shown that both the experimentally obtained and the remaining computationally generated trajectories can be formulated as an overlapping sequence of cubic Bezier curves in a computationally efficient manner. In the case of having no model of system dynamics, cubic Bezier curve formulation accurately relates experimentally obtained trajectories to the computationally generated trajectories corresponding to different initial conditions. A case study presented in this manuscript verifies that the computational approach using a cubic Bezier curves formulation has far better approximation performance compared to the ones obtained by the linear interpolation. |
| first_indexed | 2024-04-10T14:21:55Z |
| format | Article |
| id | doaj.art-7c4f26625f0f450c99c6743073645602 |
| institution | Directory Open Access Journal |
| issn | 2630-5712 2630-5712 |
| language | English |
| last_indexed | 2024-04-10T14:21:55Z |
| publishDate | 2020-08-01 |
| publisher | Eskişehir Osmangazi University |
| record_format | Article |
| series | Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi |
| spelling | doaj.art-7c4f26625f0f450c99c67430736456022023-02-15T16:09:17ZengEskişehir Osmangazi UniversityEskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi2630-57122630-57122020-08-01282210218https://doi.org/10.31796/ogummf.736651PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVESGökhan DINDIŞ0https://orcid.org/0000-0001-5642-7212Abdurrahman KARAMANCIOĞLU1https://orcid.org/0000-0003-2898-186XEskişehir Osmangazi Üniversitesi, MMF, Elektrik Elektronik Müh. Böl. ,Eskişehir Osmangazi Üniversitesi, MMF, Elektrik Elektronik Müh. Böl. ,A cubic Bezier curve formulation is used for generating phase portrait of an inverted pendulum system. Assuming that the cart and pendulum masses, pendulum length, and friction coefficient values in the inverted pendulum model are unknown, its finite number of experimentally obtained trajectories are utilized as a basis for generating the experimentally unavailable trajectories. It is shown that both the experimentally obtained and the remaining computationally generated trajectories can be formulated as an overlapping sequence of cubic Bezier curves in a computationally efficient manner. In the case of having no model of system dynamics, cubic Bezier curve formulation accurately relates experimentally obtained trajectories to the computationally generated trajectories corresponding to different initial conditions. A case study presented in this manuscript verifies that the computational approach using a cubic Bezier curves formulation has far better approximation performance compared to the ones obtained by the linear interpolation.https://dergipark.org.tr/tr/download/article-file/1260345cubic bezier curveinverted pendulumphase portrait |
| spellingShingle | Gökhan DINDIŞ Abdurrahman KARAMANCIOĞLU PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi cubic bezier curve inverted pendulum phase portrait |
| title | PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES |
| title_full | PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES |
| title_fullStr | PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES |
| title_full_unstemmed | PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES |
| title_short | PRECISE PHASE PORTRAIT CONSTRUCTION FOR AN INVERTED PENDULUM USING CUBIC BEZIER CURVES |
| title_sort | precise phase portrait construction for an inverted pendulum using cubic bezier curves |
| topic | cubic bezier curve inverted pendulum phase portrait |
| url | https://dergipark.org.tr/tr/download/article-file/1260345 |
| work_keys_str_mv | AT gokhandindis precisephaseportraitconstructionforaninvertedpendulumusingcubicbeziercurves AT abdurrahmankaramancioglu precisephaseportraitconstructionforaninvertedpendulumusingcubicbeziercurves |