<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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">pribor</journal-id><journal-title-group><journal-title xml:lang="ru">Известия высших учебных заведений. Приборостроение</journal-title><trans-title-group xml:lang="en"><trans-title>Journal of Instrument Engineering</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0021-3454</issn><issn pub-type="epub">2500-0381</issn><publisher><publisher-name>Национальный исследовательский университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/0021-3454-2025-68-11-937-948</article-id><article-id custom-type="elpub" pub-id-type="custom">pribor-427</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>СИСТЕМНЫЙ АНАЛИЗ, УПРАВЛЕНИЕ И ОБРАБОТКА ИНФОРМАЦИИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>SYSTEM ANALYSIS, MANAGEMENT AND INFORMATION PROCESSING</subject></subj-group></article-categories><title-group><article-title>Настройка ПИД-регуляторов для системы квадрокоптера с использованием алгоритма 3S Optimizer</article-title><trans-title-group xml:lang="en"><trans-title>Setting up PID controllers for a quadcopter system using the 3S Optimizer algorithm</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>Май</surname><given-names>С. З.</given-names></name><name name-style="western" xml:lang="en"><surname>Mai</surname><given-names>X. D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Суан Зунг Май — аспирант; кафедра компьютерных систем в управлении и проектировании</p><p>Томск </p></bio><bio xml:lang="en"><p>Xuan Dung Mai — Post-Graduate Student; Department of Computer Control and Design Systems</p><p>Tomsk </p></bio><email xlink:type="simple">maixuandung85@gmail.com</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>Ходашинский</surname><given-names>И. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Hodashinsky</surname><given-names>I. А.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Илья Александрович Ходашинский — д-р техн. наук, профессор; кафедра компьютерных систем в управлении и проектировании</p><p>Томск </p></bio><bio xml:lang="en"><p>Ilya А. Hodashinsky — Dr. Sci., Professor; Department of Computer Control and Design Systems</p><p>Tomsk </p></bio><email xlink:type="simple">hodashn@rambler.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Томский государственный университет систем управления и радиоэлектроники</institution></aff><aff xml:lang="en"><institution>Tomsk State University of Control Systems and Radioelectronics</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>15</day><month>12</month><year>2025</year></pub-date><volume>68</volume><issue>11</issue><fpage>937</fpage><lpage>948</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Национальный исследовательский университет ИТМО, 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Национальный исследовательский университет ИТМО</copyright-holder><copyright-holder xml:lang="en">Национальный исследовательский университет ИТМО</copyright-holder><license xlink:href="https://pribor.ifmo.ru/jour/about/submissions#copyrightNotice" xlink:type="simple"><license-p>https://pribor.ifmo.ru/jour/about/submissions#copyrightNotice</license-p></license></permissions><self-uri xlink:href="https://pribor.ifmo.ru/jour/article/view/427">https://pribor.ifmo.ru/jour/article/view/427</self-uri><abstract><p>Квадрокоптеры являются одним из наиболее применяемых типов беспилотных летательных аппаратов благодаря простой конструкции, высокой маневренности, универсальности и экономичности. Однако управление движением квадрокоптера по заданной траектории является серьезной проблемой из-за нелинейностей, внешних возмущений и ограничений привода. Пропорционально-интегрально-дифференциальный (ПИД) регулятор является удобным инструментом управления при использовании современных методов оптимизации. Целью работы является повышение эффективности управления движением квадрокоптера по заданной траектории с использованием ПИД-регулятора, коэффициенты которого оптимизированы метаэвристическим алгоритмом 3S Optimizer. Управление квадрокоптером осуществляется путем формирования сигналов для четырех двигателей, которые обеспечивают соответствующие угловые скорости, позволяющие достичь заданного положения и ориентации в пространстве. Схема управления квадрокоптером разработана по иерархической модели, включающей три вложенных контура управления. Проектирование ПИД-регуляторов с использованием 3S Optimizer формулируется как задача оптимизации с ограничениями на перерегулирование, время нарастания и время переходного процесса. Проведены два типа экспериментов: 1) проверка реакции системы управления на входные сигналы в виде единичных скачков; 2) проверка способности системы управления следовать заданной траектории. В обоих экспериментах системы управления с настройками алгоритмом 3S Optimizer практически по всем критериям показали лучшие результаты.</p></abstract><trans-abstract xml:lang="en"><p>Quadcopters are one of the most widely used types of unmanned aerial vehicles due to their simple design, high maneuverability, versatility and cost-effectiveness. However, controlling the movement of the quadcopter along a given trajectory is a serious problem due to non-linearities, external disturbances and drive limitations. The proportionalintegral-differential (PID) controller is a convenient control tool when using modern optimization methods. The aim of the work is to increase the efficiency of controlling the movement of a quadcopter along a given trajectory using a PID controller, the coefficients of which are optimized by the 3S Optimizer metaheuristic algorithm. The quadcopter is controlled by generating signals for four engines, which provide the appropriate angular velocities to achieve a given position and orientation in space. The quadcopter’s control scheme is designed according to a hierarchical model that includes three nested control circuits. The design of PID controllers using 3S Optimizer is formulated as an optimization problem with limitations on overshoot, rise time, and transition time. Two types of experiments are conducted: 1) checking the response of the control system to input signals in the form of single jumps; 2) checking the ability of the control system to follow a given trajectory. In both experiments, control systems with settings using the 3S Optimizer algorithm shows the best results by almost all criteria.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>квадрокоптер</kwd><kwd>ПИД-регулятор</kwd><kwd>алгоритм 3S Optimizer</kwd><kwd>параметрическая оптимизация</kwd><kwd>метаэвристические алгоритмы</kwd></kwd-group><kwd-group xml:lang="en"><kwd>quadcopter</kwd><kwd>PID controller</kwd><kwd>3S Optimizer algorithm</kwd><kwd>parametric optimization</kwd><kwd>metaheuristic algorithms</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">Trinh L. M., Tran N. T., Vo V. A. Cascade PID Control for Altitude and Angular Position Stabilization of 6–DOF UAV Quadcopter // International Journal of Robotics and Control Systems. 2024. Vol. 4, N 2. P. 814–831. DOI: 10.31763/ijrcs.v4i2.1410.</mixed-citation><mixed-citation xml:lang="en">Trinh L.M., Tran N.T., Vo V.A. International Journal of Robotics and Control Systems, 2024, no. 2(4), pp. 814–831, DOI: 10.31763/ijrcs.v4i2.1410.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Elkhatem A. S., Engin S. N. Robust LQR and LQR–PI control strategies based on adaptive weightingmatrix selection for a UAV position and attitude tracking control // Alexandria Engineering Journal. 2022. Vol. 61, N 8. P. 6275–6292. DOI: 110.1016/j.aej.2021.11.057.</mixed-citation><mixed-citation xml:lang="en">Elkhatem A.S., Engin S.N. Alexandria Engineering Journal, 2022, no. 8(61), pp. 6275–6292, DOI: 110.1016/j.aej.2021.11.057.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Cai Z., Zhang S., Jing X. Model Predictive Controller for Quadcopter Trajectory Tracking Based on Feedback Linearization // IEEE Access. 2021. Vol. 9. P. 162909–162918. DOI: 10.1109/ACCESS.2021.3134009.</mixed-citation><mixed-citation xml:lang="en">Cai Z., Zhang S., Jing X. IEEE Access, 2021, vol. 9, рр. 162909–162918, DOI: 10.1109/ACCESS.2021.3134009.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Rodríguez–Abreo O., Rodríguez–Reséndiz J., García–Cerezo A., García–Martínez J. R. Fuzzy logic controller for UAV with gains optimized via genetic algorithm // Heliyon. 2024. Vol. 10. Р. e26363. DOI: 10.1016/j.heliyon.2024.e26363.</mixed-citation><mixed-citation xml:lang="en">Rodríguez–Abreo O., Rodríguez–Reséndiz J., García–Cerezo A., García–Martínez J.R. Heliyon, 2024, vol. 10, рр. e26363, DOI: 10.1016/j.heliyon.2024.e26363.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Labbadi M., Boukal Y., Cherkaoui M., Djemai M. Fractional–order global sliding mode controller for an uncertain quadrotor UAVs subjected to external disturbances // Journal of the Franklin Institute. 2021. Vol. 358, N 9. P. 4822– 4847. DOI: 10.1016/j.jfranklin.2021.04.032.</mixed-citation><mixed-citation xml:lang="en">Labbadi M., Boukal Y., Cherkaoui M., Djemai M. Journal of the Franklin Institute, 2021, no. 9(358), pp. 4822–4847, DOI: 10.1016/j.jfranklin.2021.04.032.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Eltayeb A., Rahmat M. F., Basri M. A. M., Mohammed Eltoum M. A., Mahmoud M. S. Integral Adaptive Sliding Mode Control for Quadcopter UAV Under Variable Payload and Disturbance // IEEE Access. 2022. Vol. 10. P. 94754–94764. DOI: 10.1109/ACCESS.2022.3203058.</mixed-citation><mixed-citation xml:lang="en">Eltayeb A., Rahmat M.F., Basri M.A.M., Mohammed Eltoum M.A., Mahmoud M.S. IEEE Access, 2022, vol. 10, рр. 94754–94764, DOI: 10.1109/ACCESS.2022.3203058.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Nguyen N. P., Nguyen X. M., Ha L. N. N. T., Huynh T. T., Lam N. T., Hong S. K. Adaptive Sliding Mode Control for Attitude and Altitude System of a Quadcopter UAV via Neural Network // IEEE Access. 2021. Vol. 9. P. 40076–40085. DOI: 10.1109/ACCESS.2021.3064883.</mixed-citation><mixed-citation xml:lang="en">Nguyen N.P., Nguyen X.M., Ha L.N.N.T., Huynh T.T., Lam N.T., Hong S.K. IEEE Access, 2021, vol. 9, рр. 40076– 40085, DOI: 10.1109/ACCESS.2021.3064883.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Тран В. Т., Кориков А. М. Синтез адаптивного скользящего режима управления полетом квадрокоптера в условиях переменной нагрузки и помех // Доклады ТУСУР. 2022. Т. 25, № 2. С. 37–44. DOI: 10.21293/1818-0442-2022-25-2-37-44.</mixed-citation><mixed-citation xml:lang="en">Tran V.T., Korikov A.M. Proceedings of TUSUR University, 2022, no. 2(25), pp. 37–44, DOI: 10.21293/1818-0442-2022-25-2-37-44. (in Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Ким С. А., Пыркин А. А., Борисов О. И. Алгоритм согласованного траекторного управления движением квадрокоптера // Изв. вузов. Приборостроение. 2024. Т. 67, № 5. С. 385–394. DOI: 10.17586/0021-3454-2024-67–5-385-394.</mixed-citation><mixed-citation xml:lang="en">Kim S.A., Pyrkin A.A., Borisov O.I. Journal of Instrument Engineering, 2024, no. 5(67), pp. 385–394, DOI: 10.17586/0021-3454-2024-67-5-385-394.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Ким С. А., Пыркин А. А., Борисов О. И. Алгоритмы управления движением квадрокоптера в режиме динамического позиционирования // Изв. вузов. Приборостроение. 2023. Т. 66, № 10. С. 834–844. DOI: 10.17586/0021-3454-2023-66-10-834-844.</mixed-citation><mixed-citation xml:lang="en">Kim S.A., Pyrkin A.A., Borisov O.I. Journal of Instrument Engineering, 2023, no. 10(66), pp. 834–844, DOI: 10.17586/0021-3454-2023-66-10-834-844. (in Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Polat O., Sezgin A. Position control of a quadcopter with pid and fuzzy-pid controller // Journal of Engineering Sciences and Design. 2024. Vol. 12, N 1. P. 34–48. DOI: 10.21923/jesd.1223998.</mixed-citation><mixed-citation xml:lang="en">Polat O., Sezgin A. Journal of Engineering Sciences and Design, 2024, no. 1(12), pp. 34–48, DOI: 10.21923/jesd.1223998.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Baharuddin A., Basri M. A. M. Self–Tuning PID Controller for Quadcopter using Fuzzy Logic // International Journal of Robotics and Control Systems. 2023. Vol. 3, N 4. P. 728–748. DOI: 10.31763/ijrcs.v3i4.1127.</mixed-citation><mixed-citation xml:lang="en">Baharuddin A., Basri M.A.M. International Journal of Robotics and Control Systems, 2023, no. 4(3), pp. 728–748, DOI: 10.31763/ijrcs.v3i4.1127.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Sahrir N. H., Basri M. A. M. Intelligent PID Controller Based on Neural Network for AIDriven Control Quadcopter UAV // International Journal of Robotics and Control Systems. 2024. Vol. 4, N 2. P. 691–708. DOI: 10.31763/ijrcs.v4i2.1374.</mixed-citation><mixed-citation xml:lang="en">Sahrir N.H., Basri M.A.M. International Journal of Robotics and Control Systems, 2024, no. 2(4), pp. 691–708, DOI: 10.31763/ijrcs.v4i2.1374.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang L., Bai L., Liang J., Qin Z., Zhao Y. Intelligent PID Control Method for Quadrotor UAV with Serial Humanoid Intelligence // Computer Systems Science and Engineering. 2024. Vol. 48, N 6. P. 1557–1579. DOI: 10.32604/csse.2024.054237.</mixed-citation><mixed-citation xml:lang="en">Zhang L., Bai L., Liang J., Qin Z., Zhao Y. Computer Systems Science and Engineering, 2024, no. 6(48), pp. 1557– 1579, DOI: 10.32604/csse.2024.054237.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Ходашинский И. А. Методы повышения эффективности роевых алгоритмов оптимизации // Автоматика и телемеханика. 2021. № 6. С. 3–45. DOI: 10.31857/S0005231021060015.</mixed-citation><mixed-citation xml:lang="en">Hodashinsky I.A. Automation and Remote Control, 2021, no. 6(82), pp. 935–967, DOI: https://doi.org/10.1134/S0005117921060011.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Soyinka O. K., Ikpaya M. N., Luka L. Study on PID gain parameter optimization for a quadcopter under static wind turbulence using bio-inspired algorithms // Discover Electronics. 2025. Vol. 2. Art. nо. 8. DOI: 10.1007/s44291-025-00049-y.</mixed-citation><mixed-citation xml:lang="en">Soyinka O.K., Ikpaya M.N., Luka L. Discover Electronics, 2025, vol. 2, art. nо. 8, DOI: 10.1007/s44291–025–00049–y.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Sheta A., Braik M., Maddi D. R., Mahdy A., Aljahdali S., Turabieh H. Optimization of PID Controller to Stabilize Quadcopter Movements Using Meta–Heuristic Search Algorithms // Applied Sciences. 2021. Vol. 11, N 14. P. 6492. DOI: 0.3390/app11146492.</mixed-citation><mixed-citation xml:lang="en">Sheta A., Braik M., Maddi D.R., Mahdy A., Aljahdali S., Turabieh H. Applied Sciences, 2021, no. 14(11), pp. 6492, DOI: 0.3390/app11146492.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Sahrir N. H., Basri M. A. M. PSO–PID Controller for Quadcopter UAV: Index Performance Comparison // Arabian Journal for Science and Engineering. 2023. Vol. 48, N 2. P. 6492. DOI: 10.1007/s13369-023-08088-x.</mixed-citation><mixed-citation xml:lang="en">Sahrir N.H., Basri M.A.M. Arabian Journal for Science and Engineering, 2023, no. 2(48), pp. 6492, DOI: 10.1007/s13369-023-08088-x.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Wolpert D., Macready W. No free lunch theorems for optimization // IEEE Transactions on Evolutionary Computation. 1997. Vol. 1. P. 67–82. DOI: 10.1109/4235.585893.</mixed-citation><mixed-citation xml:lang="en">Wolpert D., Macready W. IEEE Transactions on Evolutionary Computation, 1997, vol. 1, рр. 67–82, DOI: 10.1109/4235.585893.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Li Y. 3S optimizer: a new meta heuristic global optimization algorithm // Evolutionary Intelligence. 2024. Vol. 17. P. 3535–3552. DOI: 10.1007/s12065-024-00943-6.</mixed-citation><mixed-citation xml:lang="en">Li Y. Evolutionary Intelligence, 2024, vol. 17, рр. 3535–3552, DOI: 10.1007/s12065-024-00943-6.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Mohanraj D., Aruldavid R., Verma R., Sathyasekar K., Barnawi A. B., Chokkalingam B., Mihet–Popa L. L. A Review of BLDC Motor: State of Art, Advanced Control Techniques, and Applications // IEEE Access. 2022. Vol. 10. P. 54833–54869. DOI: 10.1109/ACCESS.2022.3175011.</mixed-citation><mixed-citation xml:lang="en">Mohanraj D., Aruldavid R., Verma R., Sathyasekar K., Barnawi A.B., Chokkalingam B., Mihet-Popa L.L. IEEE Access, 2022, vol. 10, рр. 54833–54869, DOI: 10.1109/ACCESS.2022.3175011.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">EMAX Multicopter motor MT1806 [Электронный ресурс]: &lt;https://emaxmodel.com/products/emax–multicopter–motor–mt1806&gt;. (дата обращения: 15.05.2025)</mixed-citation><mixed-citation xml:lang="en">EMAX Multicopter motor MT1806, https://emaxmodel.com/products/emax–multicopter–motor–mt1806.</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>
