Construction of Open-Loop Electromechanical System Fundamental Matrix and Its Application for Calculation of State Variables Transients
The article considers the methods of calculating the transition matrix of a dynamic system, which is based on the transient matrix representation by the matrix exponent and on the use of the system signal graph. The advantages of the transition matrix calculating using a signal graph are shown. The...
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| Format: | Article |
| Language: | English |
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Lviv Polytechnic National University
2020-12-01
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| Series: | Energy Engineering and Control Systems |
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| Online Access: | https://science.lpnu.ua/jeecs/all-volumes-and-issues/volume-6-number-2-2020/construction-open-loop-electromechanical-system |
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| author | Orest Lozynskyy Yurii Biletskyi Andriy Lozynskyy Volodymyr Moroz Lidiya Kasha |
| author_facet | Orest Lozynskyy Yurii Biletskyi Andriy Lozynskyy Volodymyr Moroz Lidiya Kasha |
| author_sort | Orest Lozynskyy |
| collection | DOAJ |
| description | The article considers the methods of calculating the transition matrix of a dynamic system, which is based on the transient matrix representation by the matrix exponent and on the use of the system signal graph. The advantages of the transition matrix calculating using a signal graph are shown. The application of these methods to find the transition matrix demonstrated on the simple electromechanical system example. It is shown that the expression for the transition matrix as a matrix exponent completely corresponds to the expression found by means of the inverse matrix and based on the use of the signal graph. The transient matrix of a dynamical system thus found as a matrix exponent can be used to analyze processes in a system that is described by differential equations with integer derivatives. The formation of a transient matrix for the analysis of system processes, which is described by equations with fractional derivatives, is also considered. It is shown that the description of processes in systems with fractional derivatives based on the transient matrix and the representation of the fractional derivative in the form of Caputo-Fabrizio makes it possible to study coordinate transients without approximations in the description of the fractional derivative. |
| format | Article |
| id | doaj-art-98c9a199429a4d129c09b79a726d5ce2 |
| institution | DOAJ |
| issn | 2411-8028 2415-7287 |
| language | English |
| publishDate | 2020-12-01 |
| publisher | Lviv Polytechnic National University |
| record_format | Article |
| series | Energy Engineering and Control Systems |
| spelling | doaj-art-98c9a199429a4d129c09b79a726d5ce22025-08-20T03:23:56ZengLviv Polytechnic National UniversityEnergy Engineering and Control Systems2411-80282415-72872020-12-01211011910.23939/jeecs2020.02.110Construction of Open-Loop Electromechanical System Fundamental Matrix and Its Application for Calculation of State Variables TransientsOrest Lozynskyy0Yurii Biletskyi1Andriy Lozynskyy2Volodymyr Moroz3Lidiya Kasha4Lviv Polytechnic National UniversityLviv Polytechnic National UniversityLviv Polytechnic National University, Casimir Pulaski Radom UniversityLviv Polytechnic National UniversityLviv Polytechnic National UniversityThe article considers the methods of calculating the transition matrix of a dynamic system, which is based on the transient matrix representation by the matrix exponent and on the use of the system signal graph. The advantages of the transition matrix calculating using a signal graph are shown. The application of these methods to find the transition matrix demonstrated on the simple electromechanical system example. It is shown that the expression for the transition matrix as a matrix exponent completely corresponds to the expression found by means of the inverse matrix and based on the use of the signal graph. The transient matrix of a dynamical system thus found as a matrix exponent can be used to analyze processes in a system that is described by differential equations with integer derivatives. The formation of a transient matrix for the analysis of system processes, which is described by equations with fractional derivatives, is also considered. It is shown that the description of processes in systems with fractional derivatives based on the transient matrix and the representation of the fractional derivative in the form of Caputo-Fabrizio makes it possible to study coordinate transients without approximations in the description of the fractional derivative.https://science.lpnu.ua/jeecs/all-volumes-and-issues/volume-6-number-2-2020/construction-open-loop-electromechanical-systemcontrol theoryelectromechanical systemfractional derivativelinear systemstate representationtransient matrix |
| spellingShingle | Orest Lozynskyy Yurii Biletskyi Andriy Lozynskyy Volodymyr Moroz Lidiya Kasha Construction of Open-Loop Electromechanical System Fundamental Matrix and Its Application for Calculation of State Variables Transients Energy Engineering and Control Systems control theory electromechanical system fractional derivative linear system state representation transient matrix |
| title | Construction of Open-Loop Electromechanical System Fundamental Matrix and Its Application for Calculation of State Variables Transients |
| title_full | Construction of Open-Loop Electromechanical System Fundamental Matrix and Its Application for Calculation of State Variables Transients |
| title_fullStr | Construction of Open-Loop Electromechanical System Fundamental Matrix and Its Application for Calculation of State Variables Transients |
| title_full_unstemmed | Construction of Open-Loop Electromechanical System Fundamental Matrix and Its Application for Calculation of State Variables Transients |
| title_short | Construction of Open-Loop Electromechanical System Fundamental Matrix and Its Application for Calculation of State Variables Transients |
| title_sort | construction of open loop electromechanical system fundamental matrix and its application for calculation of state variables transients |
| topic | control theory electromechanical system fractional derivative linear system state representation transient matrix |
| url | https://science.lpnu.ua/jeecs/all-volumes-and-issues/volume-6-number-2-2020/construction-open-loop-electromechanical-system |
| work_keys_str_mv | AT orestlozynskyy constructionofopenloopelectromechanicalsystemfundamentalmatrixanditsapplicationforcalculationofstatevariablestransients AT yuriibiletskyi constructionofopenloopelectromechanicalsystemfundamentalmatrixanditsapplicationforcalculationofstatevariablestransients AT andriylozynskyy constructionofopenloopelectromechanicalsystemfundamentalmatrixanditsapplicationforcalculationofstatevariablestransients AT volodymyrmoroz constructionofopenloopelectromechanicalsystemfundamentalmatrixanditsapplicationforcalculationofstatevariablestransients AT lidiyakasha constructionofopenloopelectromechanicalsystemfundamentalmatrixanditsapplicationforcalculationofstatevariablestransients |