A non integer order, state space model for one dimensional heat transfer process
In the paper a new, state space, non integer order model for one dimensional heat transfer process is presented. The model is based on known semigroup model. The derivative with respect to time is described by the non integer order Caputo operator, the spatial derivative is described by integer orde...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2016-06-01
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| Series: | Archives of Control Sciences |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/acsc.2016.26.issue-2/acsc-2016-0015/acsc-2016-0015.xml?format=INT |
| _version_ | 1818148252295364608 |
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| author | Oprzedkiewicz Krzysztof Gawin Edyta |
| author_facet | Oprzedkiewicz Krzysztof Gawin Edyta |
| author_sort | Oprzedkiewicz Krzysztof |
| collection | DOAJ |
| description | In the paper a new, state space, non integer order model for one dimensional heat transfer process is presented. The model is based on known semigroup model. The derivative with respect to time is described by the non integer order Caputo operator, the spatial derivative is described by integer order operator. The elementary properties of the state operator are proven. The solution of state equation is calculated with the use of Laplace transform. Results of experiments show, that the proposed model is more accurate than analogical integer order model in the sense of square cost function. |
| first_indexed | 2024-12-11T12:48:11Z |
| format | Article |
| id | doaj.art-bd132dab82574102b5b7754d097a03f3 |
| institution | Directory Open Access Journal |
| issn | 2300-2611 |
| language | English |
| last_indexed | 2024-12-11T12:48:11Z |
| publishDate | 2016-06-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Control Sciences |
| spelling | doaj.art-bd132dab82574102b5b7754d097a03f32022-12-22T01:06:45ZengPolish Academy of SciencesArchives of Control Sciences2300-26112016-06-0126226127510.1515/acsc-2016-0015acsc-2016-0015A non integer order, state space model for one dimensional heat transfer processOprzedkiewicz Krzysztof0Gawin Edyta1AGH University of Science and Technology in Krakow, Poland (Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, Dept. of Automatics and Biomedical EngineeringHigh Vocational School in Tarnów, Polytechnic Institute, PolandIn the paper a new, state space, non integer order model for one dimensional heat transfer process is presented. The model is based on known semigroup model. The derivative with respect to time is described by the non integer order Caputo operator, the spatial derivative is described by integer order operator. The elementary properties of the state operator are proven. The solution of state equation is calculated with the use of Laplace transform. Results of experiments show, that the proposed model is more accurate than analogical integer order model in the sense of square cost function.http://www.degruyter.com/view/j/acsc.2016.26.issue-2/acsc-2016-0015/acsc-2016-0015.xml?format=INTnon-integer order systemsheat transfer processdiffusion equationinfinite dimensional systemsFeller semigroups |
| spellingShingle | Oprzedkiewicz Krzysztof Gawin Edyta A non integer order, state space model for one dimensional heat transfer process Archives of Control Sciences non-integer order systems heat transfer process diffusion equation infinite dimensional systems Feller semigroups |
| title | A non integer order, state space model for one dimensional heat transfer process |
| title_full | A non integer order, state space model for one dimensional heat transfer process |
| title_fullStr | A non integer order, state space model for one dimensional heat transfer process |
| title_full_unstemmed | A non integer order, state space model for one dimensional heat transfer process |
| title_short | A non integer order, state space model for one dimensional heat transfer process |
| title_sort | non integer order state space model for one dimensional heat transfer process |
| topic | non-integer order systems heat transfer process diffusion equation infinite dimensional systems Feller semigroups |
| url | http://www.degruyter.com/view/j/acsc.2016.26.issue-2/acsc-2016-0015/acsc-2016-0015.xml?format=INT |
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