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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">Electrotechnical Systems and Complexes</journal-id>
      <journal-title-group>
        <journal-title xml:lang="en">Electrotechnical Systems and Complexes</journal-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Электротехнические системы и комплексы</trans-title>
        </trans-title-group>
      </journal-title-group>
      <issn publication-format="print">2311-8318</issn>
      <issn publication-format="electronic">2658-3151</issn>
      <publisher>
        <publisher-name xml:lang="en">Nosov Magnitogorsk State Technical University</publisher-name>
        <publisher-name xml:lang="ru-RU">Федеральное государственное бюджетное образовательное учреждение высшего образования «Магнитогорский государственный технический университет им. Г.И. Носова»</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="publisher-id">10.18503</article-id>
      <article-id pub-id-type="doi">10.18503/2311-8318-2026-1(70)-22-34</article-id>
      <article-categories>
        <subj-group subj-group-type="toc-heading" xml:lang="en">
          <subject>Theory and Practice of Automated Electric Drive</subject>
        </subj-group>
        <subj-group subj-group-type="toc-heading" xml:lang="ru">
          <subject>Теория и практика автоматизированного электропривода</subject>
        </subj-group>
        <subj-group subj-group-type="article-type">
          <subject>Research Article</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">Verification of Electromechanical System Models for Rolling Mill Stand</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Верификация моделей электромеханической системы клети прокатного стана</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2671-0241</contrib-id>
          <name-alternatives>
            <name xml:lang="en">
              <surname>Karandaev </surname>
              <given-names>Alexander S.</given-names>
            </name>
            <name xml:lang="ru">
              <surname>Карандаев </surname>
              <given-names>Александр Сергеевич</given-names>
            </name>
          </name-alternatives>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <bio xml:lang="en">
            <p></p>
          </bio>
          <bio xml:lang="ru">
            <p></p>
          </bio>
          <email>askaran@mail.ru</email>
          <xref ref-type="aff" rid="aff1" />
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid"></contrib-id>
          <name-alternatives>
            <name xml:lang="en">
              <surname>Litvinov </surname>
              <given-names>Artem V.</given-names>
            </name>
            <name xml:lang="ru">
              <surname>Литвинов </surname>
              <given-names>Артём Владиславович</given-names>
            </name>
          </name-alternatives>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <bio xml:lang="en">
            <p></p>
          </bio>
          <bio xml:lang="ru">
            <p></p>
          </bio>
          <email>litvinovartem2000@gmail.com</email>
          <xref ref-type="aff" rid="aff1" />
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3794-9028</contrib-id>
          <name-alternatives>
            <name xml:lang="en">
              <surname>Gasiyarova </surname>
              <given-names>Olga A. </given-names>
            </name>
            <name xml:lang="ru">
              <surname>Гасиярова </surname>
              <given-names>Ольга Андреевна</given-names>
            </name>
          </name-alternatives>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <bio xml:lang="en">
            <p></p>
          </bio>
          <bio xml:lang="ru">
            <p></p>
          </bio>
          <email></email>
          <xref ref-type="aff" rid="aff1" />
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3337-3148</contrib-id>
          <name-alternatives>
            <name xml:lang="en">
              <surname>Loginov </surname>
              <given-names>Boris M.</given-names>
            </name>
            <name xml:lang="ru">
              <surname>Логинов </surname>
              <given-names>Борис Михайлович </given-names>
            </name>
          </name-alternatives>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <bio xml:lang="en">
            <p></p>
          </bio>
          <bio xml:lang="ru">
            <p></p>
          </bio>
          <email>lb18@yandex.ru</email>
          <xref ref-type="aff" rid="aff2" />
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0972-2803</contrib-id>
          <name-alternatives>
            <name xml:lang="en">
              <surname>Khramshin </surname>
              <given-names>Vadim R.</given-names>
            </name>
            <name xml:lang="ru">
              <surname>Храмшин </surname>
              <given-names>Вадим Рифхатович</given-names>
            </name>
          </name-alternatives>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <bio xml:lang="en">
            <p></p>
          </bio>
          <bio xml:lang="ru">
            <p></p>
          </bio>
          <email>hvrmgn@gmail.com</email>
          <xref ref-type="aff" rid="aff2" />
        </contrib>
      </contrib-group>
      <aff-alternatives id="aff1">
        <aff>
          <institution xml:lang="en">Moscow Polytech</institution>
        </aff>
        <aff>
          <institution xml:lang="ru">Московский политехнический университет</institution>
        </aff>
      </aff-alternatives>
      <aff-alternatives id="aff2">
        <aff>
          <institution xml:lang="en">Nosov Magnitogorsk State Technical University</institution>
        </aff>
        <aff>
          <institution xml:lang="ru">Магнитогорский государственный технический университет им. Г.И. Носова</institution>
        </aff>
      </aff-alternatives>
      <pub-date date-type="pub" iso-8601-date="2026-03-31" publication-format="print">
        <day>31</day>
        <month>03</month>
        <year>2026</year>
      </pub-date>
      <issue>1(70)</issue>
      <issue-title xml:lang="en" />
      <issue-title xml:lang="ru" />
      <fpage>22</fpage>
      <lpage>34</lpage>
      <history>
        <date date-type="received" iso-8601-date="2026-01-10">
          <day>10</day>
          <month>01</month>
          <year>2026</year>
        </date>
        <date date-type="accepted" iso-8601-date="2026-02-06">
          <day>06</day>
          <month>02</month>
          <year>2026</year>
        </date>
      </history>
      <permissions>
        <copyright-statement xml:lang="en">Copyright ©; Karandaev A.S., Litvinov A.V., Gasiyarova O.A., Loginov B.M., Khramshin V.R., 2026</copyright-statement>
        <copyright-statement xml:lang="ru">Copyright ©; Карандаев А.С., Литвинов А.В., Гасиярова О.А., Логинов Б.М., Храмшин В.Р., 2026</copyright-statement>
        <copyright-year>2026</copyright-year>
        <copyright-holder xml:lang="en">Karandaev A.S., Litvinov A.V., Gasiyarova O.A., Loginov B.M., Khramshin V.R.</copyright-holder>
        <copyright-holder xml:lang="ru">Карандаев А.С., Литвинов А.В., Гасиярова О.А., Логинов Б.М., Храмшин В.Р.</copyright-holder>
        <ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/" />
        <license>
          <ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by/4.0</ali:license_ref>
        </license>
      </permissions>
      <self-uri xlink:href="https://jdigitaldiagnostics.com/DD/article/view/51043">https://esik.magtu.ru/ru/arkhiv/vse-nomera/101-1-70-mart-2026-g/956-22.html</self-uri>
      <abstract xml:lang="en">
        <p>Development of Digital Twins and Digital Control Systems for Electric Drives at Industrial Units predetermines the virtual models creation that must ensure an optimal combination of result accuracy and high-speed data exchange between the control device and the object. Similar tasks arise during the digitalization of rolling mill units, which has been announced in recent years by all leading metallurgical companies. This requires the verification of models for rolling stand electrical complexes, which would ensure the fulfillment of these conflicting requirements. Such a task arose during the electric drive virtual model development of the 5000 heavy-plate rolling mill stand, which is equipped with high-power synchronous motors with variable frequency speed control. Two digital models have been developed, their difference being the degree of the closed-loop stator current control system detail. The first, the more complex model, is built based on Simscape library modules; it provides for the control of current components along the d and q axes. In the second version, the closed current control loop is represented by the first-order lag element. The characteristic feature of the individual electric drives at rolling mill stands is the nonlinearity caused by the saturation (limitation) of the speed controller output and angular backlashes in the spindle connections. These factors must be considered when creating the models and an analysis of their impact on dynamic performance in transient conditions is also necessary. In the presented paper, the verification of the above models for the 5000 mill stand electric drives is carried out. For this purpose, a comparison of the transient processes that occur during the workpiece bite by the rolls with simultaneous closure of the angular backlash was made. The simulation results are compared with the experiments result obtained at the mill and validation of the processes obtained using the studied models was also carried out. Simulations of modes occurring during the rolling cycle have been performed, namely: impact load application with simultaneous angular backlash closure and no-load reversal of the electric drive. They allow for the assessment of the backlash closure influence on the elastic torque amplitude on the spindle. The integrated implementation of simulation and experimental studies ensures the developed model verification, allows for the evaluation of the their advantages and provides recommendations for their application in the digital control systems development.

</p>
      </abstract>
      <trans-abstract xml:lang="ru">
        <p>Разработка цифровых двойников (ЦД) и цифровых систем управления электроприводов промышленных установок предопределяет создание виртуальных моделей, которые должны обеспечить оптимальное сочетание точности воспроизведения результатов и высокой скорости обмена данными между устройством управления и объектом. Подобные задачи возникают при цифровизации агрегатов прокатного производства, о которой в последние годы заявляют все ведущие металлургические компании. Это требует верификации моделей электротехнических комплексов прокатных клетей, которые (модели) обеспечивали бы выполнение указанных противоречивых требований. Такая задача возникла при разработке виртуальной модели электропривода клети толстолистового прокатного стана 5000, которая оснащена мощными синхронными двигателями с частотным регулированием скорости. Разработаны две цифровые модели, их отличием является степень детализации замкнутой системы (контура) регулирования тока статора. Первая, более сложная модель, построена на основе модулей библиотеки Simscape, в ней предусмотрено регулирование составляющих тока по осям d, q. Во втором варианте замкнутый контур регулирования тока представлен инерционным звеном первого порядка. Характерной особенностью индивидуальных электроприводов клетей прокатных станов является нелинейность, обусловленная ограничением выхода регулятора скорости и угловыми зазорами в шпиндельных соединениях. Эти факторы должны быть учтены при создании моделей, также необходим анализ их влияния на динамические показатели в переходных режимах. В представленной публикации выполняется верификация названных моделей электроприводов клети стана 5000. С этой целью проводится сопоставление переходных процессов, возникающих при захвате раската валками при одновременном замыкании углового зазора. Сравниваются результаты моделирования с результатами экспериментов, выполненных на стане, также выполняется валидация процессов, полученных при применении исследуемых моделей. Выполнено моделирование режимов, возникающих за цикл прокатки, это ударное приложение нагрузки при одновременном замыкании угловых зазоров и реверс электропривода без нагрузки. Они позволяют оценить влияние замыкания зазора на амплитуду упругого момента на шпинделе. Комплексное проведение моделирования и экспериментальных исследований обеспечивает верификацию разработанных моделей, позволяет оценить преимущества каждой из них и дать рекомендации по их применению при разработке цифровых систем управления.

</p>
      </trans-abstract>
      <kwd-group xml:lang="en">
        <kwd>digital twin</kwd>
        <kwd>virtual model</kwd>
        <kwd>verification</kwd>
        <kwd>mill 5000</kwd>
        <kwd>rolling stand</kwd>
        <kwd>electromechanical system</kwd>
        <kwd>dynamic modes</kwd>
        <kwd>simulation</kwd>
        <kwd>experiment</kwd>
        <kwd>angular backlash</kwd>
        <kwd>influence</kwd>
        <kwd>recommendations</kwd>
      </kwd-group>
      <kwd-group xml:lang="ru">
        <kwd>цифровой двойник</kwd>
        <kwd>виртуальная модель</kwd>
        <kwd>верификация</kwd>
        <kwd>стан 5000</kwd>
        <kwd>прокатная клеть</kwd>
        <kwd>электромеханическая система</kwd>
        <kwd>динамические режимы</kwd>
        <kwd>моделирование</kwd>
        <kwd>эксперимент</kwd>
        <kwd> угловой зазор</kwd>
        <kwd>влияние</kwd>
        <kwd>рекомендации</kwd>
      </kwd-group>
      <funding-group />
    </article-meta>
  </front>
  <body />
  <back>
    <ref-list>
      <ref id="B1">
        <label>1.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Radionov A.A., Karandaev A.S., Loginov B.M., Gasiyarova O.A. Conceptual directions for creating digital twins of electrical systems at rolling mill units. Izvestiya vysshikhuchebnykhzavedeniy. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 2021, vol. 64, no. 1, pp. 54-68. (In Russian). doi: 10.17213/0136-3360-2021-1-54-68</mixed-citation>
          <mixed-citation xml:lang="ru">Концептуальные направления создания цифровых двойников электротехнических систем агрегатов прокатного производства / А.А. Радионов, А.С. Карандаев, Б.М. Логинов, О.А. Гасиярова // Известия вузов. Электромеханика. 2021. Т. 64. № 1. С. 54-68. doi: 10.17213/0136-3360-2021-1-54-68</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B2">
        <label>2.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Oztemel E., Gursev S. Literature review of Industry 4.0 and related technologies. Journal of Intelligent Manufacturing. 2020, no. 31, pp. 127-182. doi: 10.1007/s10845-018-1433-8</mixed-citation>
          <mixed-citation xml:lang="ru">Oztemel E., Gursev S. Literature review of Industry 4.0 and related technologies. Journal of Intelligent Manufacturing. 2020. No. 31. Pp. 127-182. doi: 10.1007/s10845-018-1433-8</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B3">
        <label>3.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Tsifrovye dvoiniki v promyshlennosti: istoki, kontseptsii, sovremennyy uroven razvitiya i primeryvnedreniya [Digital twins in industry: origins, concepts, current state of development and implementation examples]. Available at: https://digitaltwin.ru/articles/digital-twins-in-industry/ (accessed 26 February 2026)</mixed-citation>
          <mixed-citation xml:lang="ru">Цифровые двойники в промышленности: истоки, концепции, современный уровень развития и примеры внедрения. URL:https://digitaltwin.ru/articles/digital-twins-in-industry/ (дата обращения 26.02.2026)</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B4">
        <label>4.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Kunath M., Winkler H. Integrating the Digital Twin of the manufacturing system into a decision support system for improving the order management process. Procedia CIRP. 2018, vol. 72, pp. 225-231. doi: 10.1016/j.procir.2018.03.192</mixed-citation>
          <mixed-citation xml:lang="ru"> Kunath M., Winkler H. Integrating the Digital Twin of the manufacturing system into a decision support system for improving the order management process // Procedia CIRP. 2018. Vol. 72. Pp. 225-231. doi: 10.1016/j.procir.2018.03.192</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B5">
        <label>5.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Kritzinger W., Karner M., Traar G., Henjes J., Sihn W. Digital Twin in manufacturing: A categorical literature review and classification. IFAC-PapersOnLine. 2018, no. 51(11), pp. 1016-1022. doi: 10.1016/j.ifacol.2018.08.474</mixed-citation>
          <mixed-citation xml:lang="ru">Digital Twin in manufacturing: A categorical literature review and classification / W. Kritzinger, M. Karner, G. Traar, J. Henjes, W. Sihn // IFAC-PapersOnLine. 2018. No. 51(11). Pp. 1016-1022. doi: 10.1016/j.ifacol.2018.08.474</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B6">
        <label>6.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Zeballos R. J.-P. Digital Twin and Simulation: Replicating Industrial Systems to Enable Improvement. Available at: https://automation.com/article/digital-twin-simulation-industrial-systems-improve (accessed 26 February 2026)</mixed-citation>
          <mixed-citation xml:lang="ru">Zeballos R. J.-P. Digital Twin and Simulation: Replicating Industrial Systems to Enable Improvement. URL: https://automation.com/article/digital-twin-simulation-industrial-systems-improve (дата обращения 26.02.2026)</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B7">
        <label>7.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Menghal P.M., Laxmi A.J. Real time control of electrical machine drives: A review. International Conference on Power, Control and Embedded Systems. IEEE, 2010. Pp. 1-6. doi: 10.1109/ICPCES.2010.5698697</mixed-citation>
          <mixed-citation xml:lang="ru">Menghal P.M., Laxmi A.J. Real time control of electrical machine drives: A review // International Conference on Power, Control and Embedded Systems. IEEE, 2010. Pp. 1-6, doi: 10.1109/ICPCES.2010.5698697</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B8">
        <label>8.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Mihalic F., Truntic M., Hren A. Hardware-in-the-Loop Simulations: A Historical Overview of Engineering Challenges. Electronics. 2022, no. 11(15), 2462. doi: 10.3390/ electronics11152462</mixed-citation>
          <mixed-citation xml:lang="ru">Mihalic F., Truntic M., Hren A. Hardware-in-the-Loop Simula-tions: A Historical Overview of Engineering Challenges// Electronics. 2022. No. 11(15). 2462. doi: 10.3390/electronics11152462</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B9">
        <label>9.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Math Works Simulink Real-Time Simulation and Testing. Available at: https: //www.windows-soft.ru/catalog/product/kupit-mathworks-simulink-real-time-simulation-and-testing-po-dostupnoy-tsene#det-description (accessed 26 February 2026)</mixed-citation>
          <mixed-citation xml:lang="ru">MathWorks Simulink Real-Time Simulation and Testing. URL: https://www.windows-soft.ru/catalog/product/kupit-mathworks-simulink-real-time-simulation-and-testing-po-dostupnoy-tsene#det-description (дата обращения 26.02.2026)</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B10">
        <label>10.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Karandaev A.S., Radionov A.A., Loginov B.M., Gasiyarova O.A., Gartlib E.A., Khramshin V.R. Experimental determination of parameters of a two-mass electromechanical system at a rolling mill. Izvestiya vysshikhuchebnykhzavedeniy. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 2021, vol. 64, no. 3, pp. 24-35. (In Russian). doi: 10.17213/0136-3360-2021-3-24-35</mixed-citation>
          <mixed-citation xml:lang="ru">Экспериментальное определение параметров двухмассовой электромеханической системы прокатного стана / А.С. Карандаев, А.А. Радионов, Б.М. Логинов, О.А. Гасиярова, Е.А. Гартлиб, В.Р. Храмшин // Известия вузов. Электромеханика. 2021. Т. 64. № 3. С. 24-35. doi:10.17213/0136-3360-2021-3-24-35</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B11">
        <label>11.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Gasiyarov V.R., Radionov A.A., Loginov B.M., Zinchenko M.A., Gasiyarova O.A., Karandaev A.S., Khramshin V.R. Method for Defining Parameters of Electromechanical System Model as Part of Digital Twin of Rolling Mill. Journal of Manufacturing and Materials Processing. 2023, no. 7(5), 183. doi:10.3390/jmmp7050183</mixed-citation>
          <mixed-citation xml:lang="ru">Method for Defining Parameters of Electromechanical System Model as Part of Digital Twin of Rolling Mill / V.R. Gasiyarov, A.A. Radionov, B.M. Loginov, M.A. Zinchenko, O.A. Gasiyarova, A.S. Karandaev, V.R. Khramshin // Journal of Manufacturing and Materials Processing. 2023. No. 7(5). 183. doi:10.3390/jmmp7050183</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B12">
        <label>12.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Soltani A., Assadian F. A Hardware-in-the-Loop Facility for Integrated Vehicle Dynamics Control System Design and Validation. IFAC-PapersOnLine. 2016, no. 49(21), pp. 32-38. doi: 10.1016/j.ifacol.2016.10.507</mixed-citation>
          <mixed-citation xml:lang="ru">Soltani A., Assadian F. A Hardware-in-the-Loop Facility for Integrated Vehicle Dynamics Control System Design and Validation // IFAC-PapersOnLine. 2016. No. 49(21). Pp. 32-38. doi: 10.1016/j.ifacol.2016.10.507</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B13">
        <label>13.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Gasiyarova O.A. Povyshenie resursa elektroprivodov kleti tolstolistovogo prokatnogo stana za schet ogranicheniya dinamicheskikh nagruzok. Kand. Diss. [Increasing the service life of electric drives of a heavy-plate rolling mill stand by limiting dynamic loads. Kand. Diss.]. Moscow, 2025. 170 p. (In Russian)</mixed-citation>
          <mixed-citation xml:lang="ru">Гасиярова О.А. Повышение ресурса электроприводов клети толстолистового прокатного стана за счет ограничения динамических нагрузок: дис. … канд. техн. наук: 2.4.2 / Гасиярова Ольга Андреевна. Москва: ФГАОУ ВО «МПУ», 2025. 170 с.</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B14">
        <label>14.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Karandaev A.S., Loginov B.M., Zinchenko M.A., Khramshin V.R. Electric drive speed control of a heavy-plate rolling mill stand in the "skid" formation mode. Izvestiya vysshikhuchebnykhzavedeniy. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 2022, vol. 65, no. 3, pp. 26-41. (In Russian). doi: 10.17213/0136-3360-2022-3-26-41</mixed-citation>
          <mixed-citation xml:lang="ru">Регулирование скоростей электроприводов клети толстолистового прокатного стана в режиме формирования «лыжи» / А.С. Карандаев, Б.М. Логинов, М.А. Зинченко, В.Р. Храмшин // Известия вузов. Электромеханика. 2022. Т. 65. № 3. С. 26-41. doi: 10.17213/0136-3360-2022-3-26-41</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B15">
        <label>15.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Gasiyarova O.A., Karandaev A.S., Erdakov I.N., Loginov B.M., Khramshin V.R. Developing Digital Observer of Angular Gaps in Rolling Stand Mechatronic System. Machines. 2022, no. 10, 141. doi: 10.3390/machines10020141</mixed-citation>
          <mixed-citation xml:lang="ru">Developing Digital Observer of Angular Gaps in Rolling Stand Mechatronic System / O.A. Gasiyarova, A.S. Karandaev, I.N. Erdakov, B.M. Loginov, V.R. Khramshin // Machines. 2022. No. 10. 141. doi: 10.3390/machines10020141</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B16">
        <label>16.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Zherebtsov A.L., Chuikov V.Yu., Shulpin A.A. Field current control method as a means of ensuring the synchronous motor operation stability. Vestnik Ivanovskogo gosudarstvennogo energeticheskogo universiteta [Vestnik IGEU], 2018, no. 2, pp. 21-31. (In Russian). doi: 10.17588/2072-2672.2018.2.021-031</mixed-citation>
          <mixed-citation xml:lang="ru">Жеребцов А.Л., Чуйков В.Ю., Шульпин А.А. Способ управления током возбуждения как средство обеспечения устойчивости работы синхронного двигателя // Вестник Ивановского государственного энергетического университета. 2018. №2. С. 21-31. doi: 10.17588/2072-2672.2018.2.021-031</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B17">
        <label>17.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Maximum Torque Per Ampere (MTPA). Available at: https://microchiptech.github.io/mcaf-doc/7.0.2/algorithms/ flux_control/mtpa.html (accessed 26 February 2026)</mixed-citation>
          <mixed-citation xml:lang="ru">Maximum Torque Per Ampere (MTPA). URL: https://microchiptech.github.io/mcaf-doc/7.0.2/algorithms/flux_control/mtpa.html (дата обращения 26.02.2026)</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B18">
        <label>18.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">HESM Torque Control. Available at: https://www.mathworks.com/help/physmod/sps/ug/hesm-torque-control.html (accessed 26 February 2026)</mixed-citation>
          <mixed-citation xml:lang="ru">HESM Torque Control. URL: https://www.mathworks.com/help/physmod/sps/ug/hesm-torque-control.html (дата обращения 26.02.2026)</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B19">
        <label>19.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">SM Current Controller. Available at: https:// www.mathworks.com/help/physmod/sps/ref/smcurrentcontroller.html (accessed 26 February 2026)</mixed-citation>
          <mixed-citation xml:lang="ru">SM Current Controller. https://www.mathworks.com/help/physmod/sps/ref/smcurrentcontroller.html (дата обращения 26.02.2026)</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B20">
        <label>20.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">White D.C., Woodson H.H. Elektromekhanicheskoe preobrazovanie energii [Electromechanical Energy Conversion]. Moscow-Leningrad, Energiya Publ., 1964. 528 p. (In Russian)</mixed-citation>
          <mixed-citation xml:lang="ru"> Уайт Д.С., Вудсон Г.Х. Электромеханическое преобразование энергии: пер. с англ. М.; Л.: Энергия, 1964, 528 с.</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B21">
        <label>21.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Sadovoi O., Nazarova O., Bondarenko V., Pirozhok A., Hutsol T., Nurek T., Glowacki Sz. Modeling and research of electromechanical systems of cold rolling mills: monograph. Krakow, 2020. 138 p.</mixed-citation>
          <mixed-citation xml:lang="ru">Modeling and research of electromechanical systems of cold rolling mills: monograph // Sadovoi O., Nazarova O., Bondarenko V., Pirozhok A., Hutsol Т., Nurek T., Glowacki Sz. Krakow, 2020. 138 p.</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B22">
        <label>22.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Klyuchev V.I. Ogranichenie dinamicheskikh nagruzok elektroprivoda [Limitation of electric drive dynamic loads]. Moscow, Energiya Publ., 1971. 320 p. (In Russian)</mixed-citation>
          <mixed-citation xml:lang="ru">Ключев В.И. Ограничение динамических нагрузок электропривода. М.: Энергия, 1971. 320 с.</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B23">
        <label>23.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Karandaev A.S., Khramshin V.R., Galkin V.V., Lukin A.A. Mathematical modeling of a thyristor electric drive with a switching structure. Izvestiya vysshikh uchebnykh zavedeniy. Elektromekhanika [Bulletin of Higher Educational Institutions. Electromechanics], 2010, no. 3, pp. 47-53. (In Russian)</mixed-citation>
          <mixed-citation xml:lang="ru">Математическое моделирование тиристорного электропривода с переключающейся структурой / А.С. Карандаев, В.Р. Храмшин, В.В. Галкин, А.А. Лукин // Известия вузов. Электромеханика. 2010. № 3. С. 47-53.</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B24">
        <label>24.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Gasiyarov V.R., Baskov S.N., Gasiyarova O.A., Loginov B.M., Usatyy D.Yu. Dynamic torque Reduction in the main line of a heavy-plate mill rolling stand. Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Mashinostroenie [Bulletin of the South Ural State University. Series "Mechanical engineering industry"], 2019, no. 3, pp. 22-32. (In Russian). doi: 10.14529/engin190303</mixed-citation>
          <mixed-citation xml:lang="ru">Снижение динамического момента в главной линии прокатной клети толстолистового стана / В.Р. Гасияров, С.Н. Басков, О.А. Гасиярова, Б.М. Логинов, Д.Ю. Усатый // Вестник Южно-Уральского государственного университета. Серия: Машиностроение. 2019. № 3. С. 22-32. doi: 10.14529/engin190303</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B25">
        <label>25.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Gasiyarov V.R., Radionov A.A., Loginov B.M., Karandaev A.S., Gasiyarova O.A., Khramshin V.R. Development and Practical Implementation of Digital Observer for Elastic Torque of Rolling Mill Electromechanical System. J. Manuf. Mater. Process. 2023, no. 7(1), 41. doi: 10.3390/ jmmp7010041</mixed-citation>
          <mixed-citation xml:lang="ru">Development and Practical Implementation of Digital Observer for Elastic Torque of Rolling Mill Electromechanical System / V.R. Gasiyarov, A.A. Radionov, B.M. Loginov, A.S. Karandaev, O.A. Gasiyarova, V.R. Khramshin // J. Manuf. Mater. Process. 2023. No. 7(1). 41. doi: 10.3390/jmmp7010041</mixed-citation>
        </citation-alternatives>
      </ref>
      <ref id="B26">
        <label>26.</label>
        <citation-alternatives>
          <mixed-citation xml:lang="en">Karandaev A.S., Loginov B.M., Bodrov E.G., Khramshin V.R., Samodurova M.N. Elastic torque observer of a two-mass electromechanical system. Vestnik Yuzhno-Uralskogo gosudarstvennog ouniversiteta. Seriya "Energetika" [Bulletin of South Ural State University. Series "Power Engineering"], 2022, vol. 22, no. 4, pp. 23-33. (In Russian). doi: 10.14529/power220403.</mixed-citation>
          <mixed-citation xml:lang="ru">Наблюдатель упругого момента двухмассовой электромеханической системы / А.С. Карандаев, Б.М. Логинов, Е.Г. Бодров, В.Р. Храмшин, М.Н. Самодурова // Вестник ЮУрГУ. Серия «Энергетика». 2022. Т. 22. № 4. С. 23-33. doi: 10.14529/power220403</mixed-citation>
        </citation-alternatives>
      </ref>
    </ref-list>
  </back>
</article>