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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">novtexmech</journal-id><journal-title-group><journal-title xml:lang="ru">Мехатроника, автоматизация, управление</journal-title><trans-title-group xml:lang="en"><trans-title>Mekhatronika, Avtomatizatsiya, Upravlenie</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1684-6427</issn><issn pub-type="epub">2619-1253</issn><publisher><publisher-name>Commercial Publisher «New Technologies»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17587/mau.27.373-382</article-id><article-id custom-type="elpub" pub-id-type="custom">novtexmech-2056</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>ДИНАМИКА, БАЛЛИСТИКА, УПРАВЛЕНИЕ ДВИЖЕНИЕМ ЛЕТАТЕЛЬНЫХ АППАРАТОВ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>DYNAMICS, BALLISTICS AND CONTROL OF AIRCRAFT</subject></subj-group></article-categories><title-group><article-title>Синтез системы стабилизации углового движения квадрокоптера методом роевой оптимизации</article-title><trans-title-group xml:lang="en"><trans-title>Synthesis of Quadrotor Angular Motion Stabilization System Using Particle Swarm Optimization</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Шон</surname><given-names>К. Б.</given-names></name><name name-style="western" xml:lang="en"><surname>Son</surname><given-names>K. B.</given-names></name></name-alternatives><bio xml:lang="ru"><p>К. Б. Шон, аспирант</p><p>г. Ханой</p></bio><bio xml:lang="en"><p>K. B. Son, Postgraduate Student</p><p>236 Hoang Quoc Viet Street, Hanoi</p></bio><email xlink:type="simple">kbichson@lqdtu.edu.vn</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Тиен</surname><given-names>В. Х.</given-names></name><name name-style="western" xml:lang="en"><surname>Tien</surname><given-names>V. H.</given-names></name></name-alternatives><bio xml:lang="ru"><p>В. Х. Тиен, канд. техн. наук, доц.</p><p>г. Ханой</p></bio><bio xml:lang="en"><p>V. H. Tien, PhD, Associate Professor</p><p>236 Hoang Quoc Viet Street, Hanoi</p></bio><email xlink:type="simple">hoatien57@lqdtu.edu.vn</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Тинь</surname><given-names>К. Х.</given-names></name><name name-style="western" xml:lang="en"><surname>Tinh</surname><given-names>C. H.</given-names></name></name-alternatives><bio xml:lang="ru"><p>К. Х. Тинь, канд. техн. наук, преподаватель</p><p>г. Ханой</p></bio><bio xml:lang="en"><p>C. H. Tinh, PhD, Lecturer</p><p>236 Hoang Quoc Viet Street, Hanoi</p></bio><email xlink:type="simple">caohuutinh@lqdtu.edu.vn</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Технический университет Ле Куи Дон</institution><country>Вьетнам</country></aff><aff xml:lang="en"><institution>Le Quy Don Technical University</institution><country>Viet Nam</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>20</day><month>07</month><year>2026</year></pub-date><volume>27</volume><issue>7</issue><fpage>373</fpage><lpage>382</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Commercial Publisher «New Technologies», 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Commercial Publisher «New Technologies»</copyright-holder><copyright-holder xml:lang="en">Commercial Publisher «New Technologies»</copyright-holder><license xlink:href="https://mech.novtex.ru/jour/about/submissions#copyrightNotice" xlink:type="simple"><license-p>https://mech.novtex.ru/jour/about/submissions#copyrightNotice</license-p></license></permissions><self-uri xlink:href="https://mech.novtex.ru/jour/article/view/2056">https://mech.novtex.ru/jour/article/view/2056</self-uri><abstract><p>Предлагается процедура синтеза робастного регулятора с формированием частотных характеристик (loop shaping) в структуре с двумя степенями свободы, основанная на применении алгоритма роя частиц (Particle Swarm Optimization, PSO). Целью является обеспечение заранее заданных требований к качеству управления как во времен-</p><p>ной, так и в частотной областях. Основная идея заключается в использовании обобщенной весовой функции вместо простой функции первого порядка, что обеспечивает большую гибкость при проектировании регулятора. Коэффициенты этой обобщенной весовой функции рассматриваются как параметры задачи оптимизации с ограничениями. Благодаря сочетанию преимуществ робастного управления с loop shaping и высокой вычислительной эффективности алгоритма PSO в процессе проектирования синтезированный регулятор обладает высокой устойчивостью к значительным изменениям параметров системы, снижает перерегулирование, сокращает время переходного процесса и повышает способность подавления возмущений. Результаты моделирования на примере задачи управления ориентацией квадрокоптера показывают, что предложенный регулятор обеспечивает требуемое качество при сложных условиях полета. Кроме того, характеристики качества и робастности полученного решения сравниваются с регулятором, синтезированным с использованием метода NOMAD (Nonlinear Optimization with Mesh Adaptive Direct search).</p></abstract><trans-abstract xml:lang="en"><p>This paper proposes a synthesis procedure for a two-degree-of-freedom (2DOF) robust loop-shaping controller using the Particle Swarm Optimization (PSO) algorithm. The controller is designed to satisfy predefined performance constraints in both time and frequency domains. А key idea is the use of a generalized weighting function instead of a simple first-order one. This provides a more flexible framework for controller design. Coefficients of this generalized function are treated as decision variables in a constrained optimization problem. By integrating strengths of 2DOF robust loop shaping with computational capabilities of PSO in a closed-loop design, the synthesized controller demonstrates high robustness to significant system parameter variations. In addition, it helps reduce overshoot, shorten settling time, and improve disturbance rejection. Simulation results from a quadrotor attitude control system indicate that the proposed controller can provide robust performance under complex flight conditions. Moreover, its performance and robustness are validated through comparison with a controller designed using the NOMAD (Nonlinear Optimization with Mesh Adaptive Direct search)</p></trans-abstract><kwd-group xml:lang="ru"><kwd>робастное управление</kwd><kwd>формирование петли Н ∞</kwd><kwd>управление с двухстепенной структурой</kwd><kwd>управление ориентацией квадрокоптера</kwd><kwd>оптимизация роя частиц (PSO)</kwd><kwd>нелинейная оптимизация с использованием метода адаптивного поиска по сетке (NOMAD)</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Robust control</kwd><kwd>Н ∞ loop-shaping design</kwd><kwd>two-degree-of-freedom control</kwd><kwd>quadrotor attitude control</kwd><kwd>Particle Swarm Optimization (PSO)</kwd><kwd>Nonlinear Optimization with Mesh Adaptive Direct search (NOMAD)</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">Cai G., Dias J., Seneviratne L. 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