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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">ntv</journal-id><journal-title-group><journal-title xml:lang="ru">Научно-технический вестник информационных технологий, механики и оптики</journal-title><trans-title-group xml:lang="en"><trans-title>Scientific and Technical Journal of Information Technologies, Mechanics and Optics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-1494</issn><issn pub-type="epub">2500-0373</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2226-1494-2023-23-1-192-201</article-id><article-id custom-type="elpub" pub-id-type="custom">ntv-349</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>МАТЕМАТИЧЕСКОЕ И КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MODELING AND SIMULATION</subject></subj-group></article-categories><title-group><article-title>Применение обратной связи переменной точности для повышения быстродействия контура тока в инверторах на базе GaN-транзисторов</article-title><trans-title-group xml:lang="en"><trans-title>Using variable-precision feedback to improve operational speed of the current loop in GaN-inverters</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-1019-756X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Анучин</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Anuchin</surname><given-names>A. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Анучин Алексей Сергеевич - доктор технических наук, профессор, заведующий кафедрой</p><p>Москва, 111250</p></bio><bio xml:lang="en"><p>Alecksey S. Anuchin - D.Sc., Professor, Head of Department</p><p>Moscow, 111250</p></bio><email xlink:type="simple">Anuchin.alecksey@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2326-1153</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гуляева</surname><given-names>М. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Gulyaeva</surname><given-names>M. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Гуляева Мария Андреевна - ассистент</p><p>Москва, 111250</p></bio><bio xml:lang="en"><p>Maria A. Gulyaeva - Assistant</p><p>Moscow, 111250</p></bio><email xlink:type="simple">tilgivelse@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9699-7145</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Лашкевич</surname><given-names>М. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Lashkevich</surname><given-names>M. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Лашкевич Максим Михайлович - кандидат технических наук, ведущий инженер-программист</p><p>Москва, 111396</p></bio><bio xml:lang="en"><p>Maxim M. Lashkevich - PhD, Leading Software Engineer</p><p>LLC, Moscow, 111396</p></bio><email xlink:type="simple">maxsoftpage@yandex.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5628-8101</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Жарков</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Zharkov</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Жарков Александр Александрович - кандидат технических наук, доцент; главныйконструктор</p><p>Москва, 111250</p><p>Москва, 111396</p></bio><bio xml:lang="en"><p>Alexandr A. Zharkov - PhD, Associate Professor, Associate Professor; Chief Designer</p><p>Moscow, 111250</p><p>Moscow, 111396</p></bio><email xlink:type="simple">zarckov@mail.ru</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-9056-3760</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Хао</surname><given-names>Чен</given-names></name><name name-style="western" xml:lang="en"><surname>Hao</surname><given-names>Chen</given-names></name></name-alternatives><bio xml:lang="ru"><p>Чен Хао - кандидат технических наук, старший инженер-исследователь</p><p>Сюйчжоу, 100083</p></bio><bio xml:lang="en"><p>Hao Chen - PhD, Senior Research Engineer</p><p>Xuzhou, 100083</p></bio><email xlink:type="simple">hchen@cumt.edu.cn</email><xref ref-type="aff" rid="aff-4"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9778-6817</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Дианов</surname><given-names>А. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Dianov</surname><given-names>A. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Дианов Антон Николаевич - кандидат технических наук, старшийинженер-исследователь</p><p>Сеул, 03140</p></bio><bio xml:lang="en"><p>Anton N. Dianov - PhD, Senior Research Engineer</p><p>Seoul, 03140</p></bio><email xlink:type="simple">anton.dianov@ieee.org</email><xref ref-type="aff" rid="aff-5"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Национальный исследовательский университет «МЭИ»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>National Research University “Moscow Power Engineering Institute” (MPEI)</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>ООО «НПФ ВЕКТОР»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>R&amp;D Company “Vector”</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Национальный исследовательский университет «МЭИ»; ООО «НПФ ВЕКТОР»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>National Research University “Moscow Power Engineering Institute” (MPEI); R&amp;D Company “Vector”</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-4"><aff xml:lang="ru"><institution>China University of Mining &amp; Technology</institution><country>Китай</country></aff><aff xml:lang="en"><institution>China University of Mining &amp; Technology</institution><country>China</country></aff></aff-alternatives><aff-alternatives id="aff-5"><aff xml:lang="ru"><institution>Daeyoung R&amp;D Center</institution><country>Южная Корея</country></aff><aff xml:lang="en"><institution>Daeyoung R&amp;D Center</institution><country>Korea, Republic of</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2023</year></pub-date><pub-date pub-type="epub"><day>19</day><month>12</month><year>2024</year></pub-date><volume>23</volume><issue>1</issue><fpage>192</fpage><lpage>201</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Анучин А.С., Гуляева М.А., Лашкевич М.М., Жарков А.А., Хао Ч., Дианов А.Н., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Анучин А.С., Гуляева М.А., Лашкевич М.М., Жарков А.А., Хао Ч., Дианов А.Н.</copyright-holder><copyright-holder xml:lang="en">Anuchin A.S., Gulyaeva M.A., Lashkevich M.M., Zharkov A.A., Hao C., Dianov A.N.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://ntv.elpub.ru/jour/article/view/349">https://ntv.elpub.ru/jour/article/view/349</self-uri><abstract><p>Предмет исследования. С появлением силовых электронных устройств на полупроводниках с широкой запрещенной зоной, таких как SiC (карбид кремния) и GaN (нитрид галлия), частота широтно-импульсной модуляции увеличилась. В современных сервоприводах, использующих транзисторы на базе GaN, частота коммутации может достигать 100 кГц и более. В этом случае быстродействие электропривода ограничивается не частотой широтно-импульсной модуляции, а задержкой в измерении обратной связи по току. Однако при использовании в электроприводе датчиков тока с дельта-сигма модуляцией, задержку в обратной связи можно регулировать соответствующим изменением точности измерения.Метод. Рассмотрено применение менее точной, но более быстрой обратной связи в случае, когда ошибка между заданным и реальным значениями тока двигателя велика. В случае небольшой ошибки значения тока предложено использование более медленной, но точной обратной связи. Изменение скорости отработки задания требует одновременного изменения параметров регулятора тока.Основные результаты. Выполнено исследование представленного алгоритма на виртуальной модели сервопривода. Проведено сравнение адаптивного регулятора тока со стандартным регулятором при разных настройках. Показано, что за счет применения предложенного алгоритма быстродействие контура тока увеличивается вдвое без потери точности поддержания сигнала по сравнению со стандартным вариантом. Применение алгоритма позволило вдвое повысить частоту среза контура тока. Результаты получены для сигнала с линейной частотной модуляцией в качестве регулируемой величины.Практическая значимость. Предложенный способ измерения обратной связи в контуре тока позволяет увеличить быстродействие сервопривода в целом за счет увеличения быстродействия его внутреннего контура без потери точности регулирования.</p></abstract><trans-abstract xml:lang="en"><p>With the advent of wide band-gap semiconductors like SiC and GaN, the frequency of pulse-width modulation has increased. In modern electric drives, the switching frequency can reach 100 kHz or more. In this case the performance of the drive is limited by the delay in the current feedback measurement. This delay can be changed by using deltasigma modulators. This type of current sensors allows setting the measurement time. However, as the measurement time decreases, the accuracy of the feedback reduces. This paper proposes the algorithm in which the current controller uses variable-precision feedback. When the error between the reference and feedback is large, it uses faster but less accurate current feedback. When the error is small, it uses slower but accurate feedback. Changing the feedback measurement time requires changing the current controller gains. The algorithm was investigated on a virtual servo drive model. To evaluate the performance of the proposed regulator, the results were compared with standard regulators with different settings. It was proved that this approach allows increasing the speed of the current loop without loss in the transient performance. Besides, the algorithm increases the cut-off frequency in comparison with the standard slow and accurate controller.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>контур тока</kwd><kwd>шунтовой датчик тока</kwd><kwd>GaN</kwd><kwd>сервопривод</kwd><kwd>дельта-сигма модуляция</kwd><kwd>адаптивный регулятор</kwd></kwd-group><kwd-group xml:lang="en"><kwd>current loop</kwd><kwd>shunt current sensor</kwd><kwd>GaN</kwd><kwd>servo drive</kwd><kwd>delta-sigma modulation</kwd><kwd>adaptive controller</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено за счет гранта Российского научного фонда (проект № 21-19-00696).</funding-statement><funding-statement xml:lang="en">The research was carried out at the expense of a grant from the Russian Science Foundation (project No. 21-19-00696).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Homann M., Schumacher W. High bandwidth phase voltage and phase current control loop of a permanent magnet synchronous motor based on delta sigma bitstreams // Proc. of the 2016 18th European Conference on Power Electronics and Applications (EPE’16 ECCE Europe). 2016. P. 1–10. https://doi.org/10.1109/EPE.2016.7695308</mixed-citation><mixed-citation xml:lang="en">Homann M., Schumacher W. High bandwidth phase voltage and phase current control loop of a permanent magnet synchronous motor based on delta sigma bitstreams. Proc. of the 2016 18th European Conference on Power Electronics and Applications (EPE’16 ECCE Europe), 2016, pp. 1–10. https://doi.org/10.1109/EPE.2016.7695308</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Hirota A., Saha S., Mun S.-P., Nakaoka M. An advanced simple configuration delta-sigma modulation three-phase inverter implementing space voltage vector approach // Proc. of the 2007 IEEE Power Electronics Specialists Conference. 2007. P. 453–457. https://doi.org/10.1109/PESC.2007.4342030</mixed-citation><mixed-citation xml:lang="en">Hirota A., Saha S., Mun S.-P., Nakaoka M. An advanced simple configuration delta-sigma modulation three-phase inverter implementing space voltage vector approach. Proc. of the 2007 IEEE Power Electronics Specialists Conference, 2007, pp. 453–457. https:// doi.org/10.1109/PESC.2007.4342030</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Jarzebowicz L. Impact of low switching-to-fundamental frequency ratio on predictive current control of PMSM: A simulation study // Proc. of the 2018 25th International Workshop on Electric Drives: Optimization in Control of Electric Drives (IWED). 2018. P. 1–5. https://doi.org/10.1109/IWED.2018.8321400</mixed-citation><mixed-citation xml:lang="en">Jarzebowicz L. Impact of low switching-to-fundamental frequency ratio on predictive current control of PMSM: A simulation study. Proc. of the 2018 25th International Workshop on Electric Drives: Optimization in Control of Electric Drives (IWED), 2018, pp. 1–5. https://doi.org/10.1109/IWED.2018.8321400</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Li C., Vankayalapati B., Akin B. Latency compensation of SD-ADC for high performance motor control and diagnosis // Proc. of the IEEE 13th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED). 2021. P. 289–294. https://doi.org/10.1109/SDEMPED51010.2021.9605522</mixed-citation><mixed-citation xml:lang="en">Li C., Vankayalapati B., Akin B. Latency compensation of SD-ADC for high performance motor control and diagnosis. Proc. of the IEEE 13th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), 2021, pp. 289–294. https://doi.org/10.1109/SDEMPED51010.2021.9605522</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Anuchin D., Surnin D., Lashkevich M. Accuracy analysis of shunt current sensing by means of delta-sigma modulation in electric drives // Proc. of the 2018 17th International Ural Conference on AC Electric Drives (ACED). 2018. P. 1–5. https://doi.org/10.1109/ACED.2018.8341706</mixed-citation><mixed-citation xml:lang="en">Anuchin D., Surnin D., Lashkevich M. Accuracy analysis of shunt current sensing by means of delta-sigma modulation in electric drives. Proc. of the 2018 17th International Ural Conference on AC Electric Drives (ACED), 2018, pp. 1–5. https://doi.org/10.1109/ACED.2018.8341706</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Zhuo Y.-C., Hsu C.-J., Qiu Z.-H., Lai Y.-S. Bandwidth boost method of current control for servo motor drives with current observer // Proc. of the 2021 IEEE International Future Energy Electronics Conference (IFEEC). 2021. P. 1–6. https://doi.org/10.1109/IFEEC53238.2021.9661769</mixed-citation><mixed-citation xml:lang="en">Zhuo Y.-C., Hsu C.-J., Qiu Z.-H., Lai Y.-S. Bandwidth boost method of current control for servo motor drives with current observer. Proc. of the 2021 IEEE International Future Energy Electronics Conference (IFEEC), 2021, pp. 1–6. https://doi.org/10.1109/IFEEC53238.2021.9661769</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Anuchin A., Lashkevich M., Shpak D., Aliamkin D., Zharkov A., Briz F. Current control of ac drives using shunt current sensors and delta-sigma modulation // Proc. of the IECON 2018 — 44th Annual Conference of the IEEE Industrial Electronics Society. 2018. P. 445–449. https://doi.org/10.1109/IECON.2018.8591705</mixed-citation><mixed-citation xml:lang="en">Anuchin A. Lashkevich M., Shpak D., Aliamkin D., Zharkov A., Briz F. Current control of ac drives using shunt current sensors and deltasigma modulation. Proc. of the IECON 2018 — 44th Annual Conference of the IEEE Industrial Electronics Society, 2018, pp. 445–449. https://doi.org/10.1109/IECON.2018.8591705</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Anuchin A., Kozachenko V. Current loop dead-beat control with the digital PI-controller // Proc. of the 2014 16th European Conference on Power Electronics and Applications. 2014. P. 1–8. https://doi.org/10.1109/EPE.2014.6910795</mixed-citation><mixed-citation xml:lang="en">Anuchin A., Kozachenko V. Current loop dead-beat control with the digital PI-controller. Proc. of the 2014 16th European Conference on Power Electronics and Applications, 2014, pp. 1–8. https://doi.org/10.1109/EPE.2014.6910795</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Ohta K., Kanazawal Y., Akatuka H., Hori S., Doki S., Tadano H., Shiozaki K. Variable switching frequency control for efficiency improvement of motor drive system by using GaN three phase inverter // Proc. of the 2020 IEEE International Conference on Industrial Technology (ICIT). 2020. P. 119–123. https://doi.org/10.1109/ICIT45562.2020.9067266</mixed-citation><mixed-citation xml:lang="en">Ohta K., Kanazawal Y., Akatuka H., Hori S., Doki S., Tadano H., Shiozaki K. Variable switching frequency control for efficiency improvement of motor drive system by using GaN three phase inverter. Proc. of the 2020 IEEE International Conference on Industrial Technology (ICIT), 2020, pp. 119–123. https://doi.org/10.1109/ICIT45562.2020.9067266</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Lu J., Hou R., Di Maso P., Styles J. A GaN/Si hybrid T-Type Threelevel configuration for electric vehicle traction inverter // Proc. of the 2018 IEEE 6th Workshop on Wide Bandgap Power Devices and Applications (WiPDA). 2018. P. 77–81. https://doi.org/10.1109/WiPDA.2018.8569194</mixed-citation><mixed-citation xml:lang="en">Lu J., Hou R., Di Maso P., Styles J. A GaN/Si hybrid T-Type Threelevel configuration for electric vehicle traction inverter. Proc. of the 2018 IEEE 6th Workshop on Wide Bandgap Power Devices and Applications (WiPDA), 2018, pp. 77–81. https://doi.org/10.1109/WiPDA.2018.8569194</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Shang S., Yang M., Xu D. Design and research of servo drive system based on GaN power device // Proc. of the 2018 21st International Conference on Electrical Machines and Systems (ICEMS). 2018. P. 1313–1317. https://doi.org/10.23919/ICEMS.2018.8549260</mixed-citation><mixed-citation xml:lang="en">Shang S., Yang M., Xu D. Design and research of servo drive system based on GaN power device. Proc. of the 2018 21st International Conference on Electrical Machines and Systems (ICEMS), 2018, pp. 1313–1317. https://doi.org/10.23919/ICEMS.2018.8549260</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Kurniawan A.W., Firmansyah E., Wijaya F.D. Experiment result of high frequency switching SiC mosfet gate driver // Proc. of the 2022 14th International Conference on Information Technology and Electrical Engineering (ICITEE). 2022. P. 54–57. https://doi.org/10.1109/ICITEE56407.2022.9954115</mixed-citation><mixed-citation xml:lang="en">Kurniawan A.W., Firmansyah E., Wijaya F.D. Experiment result of high frequency switching SiC mosfet gate driver. Proc. of the 2022 14th International Conference on Information Technology and Electrical Engineering (ICITEE), 2022, pp. 54–57. https://doi.org/10.1109/ICITEE56407.2022.9954115</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Spang M., Hofstoetter N. Evaluation of current measurement accuracy for a power module with integrated shunt resistors // Proc. of the PCIM Europe 2017; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management. 2017. P. 1–8.</mixed-citation><mixed-citation xml:lang="en">Spang M., Hofstoetter N. Evaluation of current measurement accuracy for a power module with integrated shunt resistors. Proc. of the PCIM Europe 2017; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, 2017, pp. 1–8.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">AMC1305x Small High-Precision Reinforced Isolated Delta-Sigma Modulators Datasheet Texas Instruments. 2017.</mixed-citation><mixed-citation xml:lang="en">AMC1305x Small High-Precision Reinforced Isolated Delta-Sigma Modulators Datasheet Texas Instruments, 2017.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Schreier R. Second and Higher-Order Delta-Sigma Modulators. MEAD, March 2008.</mixed-citation><mixed-citation xml:lang="en">Schreier R. Second and Higher-Order Delta-Sigma Modulators. MEAD, March 2008.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
