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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">izvestswsu</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Юго-Западного государственного университета</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the Southwest State University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2223-1560</issn><issn pub-type="epub">2686-6757</issn><publisher><publisher-name>ЮЗГУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21869/2223-1560-2025-29-2-55-70</article-id><article-id custom-type="elpub" pub-id-type="custom">izvestswsu-1456</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>Информатика, вычислительная техника и управление</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Computer science, computer engineering and IT managment</subject></subj-group></article-categories><title-group><article-title>Математическое моделирование системы автоматического регулирования численным интегрированием</article-title><trans-title-group xml:lang="en"><trans-title>Mathematical modeling of automatic control system by numerical integration</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5212-0616</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Хандожко</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Khandozhko</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Хандожко Виктор Александрович, кандидат технических наук, доцент, заведующий кафедрой «Автоматизированные технологические системы»,</p><p>б-р 50 лет Октября, д.7, г. Брянск 241035.</p></bio><bio xml:lang="en"><p>Viktor A. Khandozhko, Cand. of Sci. (Engineering), Associate Professor, Head of the Automated Technological Systems Department, </p><p>50 Let Oktyabrya Ave., 7, Bryansk 241035.</p></bio><email xlink:type="simple">vichandozhko@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/0000-0002-3511-699X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Федонин</surname><given-names>О. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Fedonin</surname><given-names>O. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Федонин Олег Николаевич, доктор технических наук, профессор, профессор кафедры «Автоматизированные технологические системы», </p><p>б-р 50 лет Октября, д.7, г. Брянск 241035.</p></bio><bio xml:lang="en"><p>Oleg N. Fedonin, Dr. of Sci. (Engineering), Professor, Professor of the Automated Technological Systems Department,</p><p>50 Let Oktyabrya Ave., 7, Bryansk 241035.</p></bio><email xlink:type="simple">fedonin@tu-bryansk.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/0009-0006-8779-9565</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Матлахов</surname><given-names>В. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Matlakhov</surname><given-names>V. P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Матлахов Виталий Павлович, кандидат  технических наук, доцент, доцент кафедры «Автоматизированные технологические системы», </p><p>б-р 50 лет Октября, д.7, г. Брянск 241035.</p></bio><bio xml:lang="en"><p>Vitaly P. Matlakhov, Cand. of Sci. (Engineering), Associate Professor, Associate Professor of the of Automated Technological Systems Department,</p><p>50 Let Oktyabrya Ave., 7, Bryansk 241035.</p></bio><email xlink:type="simple">jed80@mail.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/0000-0002-0604-8537</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Хандожко</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Khandozhko</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Хандожко Александр Владимирович, доктор технических наук, доцент, профессор кафедры «Металлорежущие станки и инструменты»,</p><p>б-р 50 лет Октября, д.7, г. Брянск 241035.</p></bio><bio xml:lang="en"><p>Alexander V. Khandozhko, Dr. of Sci. (Engineering), Professor, Professor of the Metal-Cutting Machines and Tools Department,</p><p>50 Let Oktyabrya Ave., 7, Bryansk 241035.</p></bio><email xlink:type="simple">chandosh@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Брянский государственный технический университет</institution></aff><aff xml:lang="en"><institution>Bryansk State Technical University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>01</day><month>10</month><year>2025</year></pub-date><volume>29</volume><issue>2</issue><fpage>55</fpage><lpage>70</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Хандожко В.А., Федонин О.Н., Матлахов В.П., Хандожко А.В., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Хандожко В.А., Федонин О.Н., Матлахов В.П., Хандожко А.В.</copyright-holder><copyright-holder xml:lang="en">Khandozhko V.A., Fedonin O.N., Matlakhov V.P., Khandozhko A.V.</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://izvestswsu.elpub.ru/jour/article/view/1456">https://izvestswsu.elpub.ru/jour/article/view/1456</self-uri><abstract><sec><title>Цель исследования</title><p>Цель исследования. Целью работы является исследование математической модели системы автоматического регулирования (САР), состоящей из регулятора и объекта управления для исполнения на микропроцессорной системе с поддержкой операционной системы реального времени. В качестве изменяемых параметров приняты структура САР, коэффициенты передачи передаточных функций звеньев, постоянные времени и транспортные задержки. Выходные данные представлены в виде переходных процессов. Задачей является сравнение аналитического и численных методов для программной реализации математической модели САР с применением программируемого логического контроллера (ПЛК) в составе испытательного стенда с микропроцессорным электроприводом. Задачей является сравнение аналитического и численных методов для программной реализации математической модели САР с применением программируемого логического контроллера (ПЛК) в составе испытательного стенда с микропроцессорным электроприводом.</p></sec><sec><title>Методы</title><p>Методы. Использованы метод системного анализа, теория автоматического управления, численные методы дифференцирования и интегрирования, дифференциальные и разностные уравнения.</p></sec><sec><title>Результаты</title><p>Результаты. Практические рекомендации для выбора ПЛК при решении задач моделирования объектов и систем управления исходя из инерционности входящих в контур регулирования звеньев. В качестве критерия оценки используется относительная погрешность (интегральная, для САР в целом) и выпол-нение требования устойчивости цифровой модели.</p></sec><sec><title>Заключение</title><p>Заключение. Исследования показали, что для канонических САР с объектами 1-го и 2-го порядка и транспортной задержкой с определенными критериями, такими как устойчивость цифровой модели и относительная погрешность (интегральная), существует связь между инерционностью моделируемых звеньев САР и производительностью ПЛК. Для практического подтверждения полученных результатов требуются дополнительные исследования.  </p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Purpose of research</title><p>Purpose of research. The aim of the work is to study the mathematical model of the automatic control system (ACS), consisting of a regulator and a control object for execution on a microprocessor system with support for a realtime operating system. The structure of the ACS, the coefficients of transfer of the transfer functions of the links, time constants and transport delays are adopted as variable parameters. The output data are presented in the form of transient processes. The task is to compare the analytical and numerical methods for software implementation of the mathematical model of the ACS using a programmable logical controller (PLC) as part of a test bench with a microprocessor electric drive. The objective is to compare analytical and numerical methods for software implementation of a mathematical model of automatic control system using a programmable logic controller (PLC) as part of a test bench with a microprocessor electric drive.</p></sec><sec><title>Methods</title><p>Methods. The methods of system analysis, automatic control theory, numerical methods of differentiation and integration, differential and difference equations were used.</p></sec><sec><title>Results</title><p>Results. Practical recommendations for choosing a PLC when solving problems of modeling objects and control systems based on the inertia of the links included in the control loop. The relative error (integral, for the ACS as a whole) and the fulfillment of the requirement for the stability of the digital model are used as an evaluation criterion.</p></sec><sec><title>Conclusion</title><p>Conclusion. The studies have shown that for canonical ACS with 1st and 2nd order objects and transport delay with certain criteria, such as digital model stability and relative error (integral), there is a connection between the speed of the simulated ACS links and the PLC performance. Additional studies are required for practical confirmation of the obtained results.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>математическая модель</kwd><kwd>система автоматического регулирования</kwd><kwd>ПИД-регулятор</kwd><kwd>ПЛК</kwd><kwd>САР</kwd></kwd-group><kwd-group xml:lang="en"><kwd>mathematical model</kwd><kwd>automatic control system</kwd><kwd>PID controller</kwd><kwd>PLC</kwd><kwd>ACS</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Денисенко В.В. ПИД-регуляторы: принципы построения и модификации // Современные технологии автоматизации. 2006. № 4. С. 66-74; 2007. № 1. 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