<?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">kaz29</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Казахстанско-Британского технического университета</journal-title><trans-title-group xml:lang="en"><trans-title>Herald of the Kazakh-British Technical University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1998-6688</issn><issn pub-type="epub">2959-8109</issn><publisher><publisher-name>Казахстанско-Британский Технический Университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.55452/1998-6688-2025-22-2-76-93</article-id><article-id custom-type="elpub" pub-id-type="custom">kaz29-1988</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>КОМПЬЮТЕРНЫЕ НАУКИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>COMPUTER SCIENCE</subject></subj-group></article-categories><title-group><article-title>ОПТИМИЗАЦИЯ ПАРАМЕТРОВ ПИД-РЕГУЛЯТОРА С ИСПОЛЬЗОВАНИЕМ АЛГОРИТМОВ МАШИННОГО ОБУЧЕНИЯ НА ОСНОВЕ ДАННЫХ ПРОЦЕССА СЕПАРАЦИИ НЕФТИ</article-title><trans-title-group xml:lang="en"><trans-title>OPTIMIZATION OF PID CONTROLLER PARAMETERS USING MACHINE LEARNING ALGORITHMS BASED ON OIL SEPARATION PROCESS DATA</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5862-6415</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Самигулина</surname><given-names>З.</given-names></name><name name-style="western" xml:lang="en"><surname>Samigulina</surname><given-names>Z. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p> PhD, доцент </p><p> г. Алматы </p></bio><bio xml:lang="en"><p> PhD, Associate Professor </p><p> Almaty </p></bio><email xlink:type="simple">z.samigulina@kbtu.kz</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0003-7991-9836</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Аманғалиева</surname><given-names>А.</given-names></name><name name-style="western" xml:lang="en"><surname>Amangaliyeva</surname><given-names>A. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p> бакалавр </p><p> г. Алматы </p></bio><bio xml:lang="en"><p> Bachelor </p><p> Almaty </p></bio><email xlink:type="simple">a_amangaliyeva@kbtu.kz</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Қазақстан-Британ техникалық университеті<country>Казахстан</country></aff><aff xml:lang="en">Kazakh-British Technical University<country>Kazakhstan</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>06</day><month>07</month><year>2025</year></pub-date><volume>22</volume><issue>2</issue><fpage>76</fpage><lpage>93</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Самигулина З.I., Аманғалиева А.G., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Самигулина З., Аманғалиева А.</copyright-holder><copyright-holder xml:lang="en">Samigulina Z.I., Amangaliyeva A.G.</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://vestnik.kbtu.edu.kz/jour/article/view/1988">https://vestnik.kbtu.edu.kz/jour/article/view/1988</self-uri><abstract><p>В работе исследуется процесс оптимизации параметров ПИД-регулятора с помощью использования алгоритмов машинного обучения для системы управления процессом сепарации нефти. Оптимизация параметров контроллера (Kp, Ki, Kd) важна для повышения качества управления и уменьшения количества ошибок в динамических процессах. Для решения этой проблемы было рассмотрено несколько инновационных методов, таких как алгоритм поиска кукушки (CSA), алгоритм светлячков (FA), оптимизация роя частиц (PSO) и метод опорных векторов (SVM). Все данные, включая текущие значения процессов (PV), уставки (SP) и выходные сигналы (OP), были получены от «Тенгизшевройла». Кроме того, для оценки эффективности оптимизированных регуляторов использовались такие показатели, как среднеквадратичная ошибка (MSE), время настройки, превышение и установившаяся ошибка. В целом результаты исследования свидетельствуют о значительном улучшении динамических характеристик системы за счет использования алгоритмов машинного обучения по сравнению с традиционными подходами. Полученные параметры оптимизации достигли целевого значения, оставаясь при этом более быстрыми и стабильными, что позволило повысить производительность управления технологическим процессом.</p></abstract><trans-abstract xml:lang="en"><p>This paper presents the investigation of the process of optimizing the parameters of a PID controller using machine learning algorithms for the oil separation process control system. The optimization of the controller parameters (Kp, Ki, Kd) is important, in order to improve control quality and reduce the number of errors in dynamic processes. To solve this issue, several innovative methods were considered, such as the cuckoo search algorithm (CSA), the firefly algorithm (FA), particle swarm optimization (PSO), and the support vector machine (SVM). All the data, including the current process values (PV), setpoints (SP) and output signals (OP) were obtained from Tengizchevroil. In addition, the metrics, such as root-mean-square error (MSE), adjustment time, overshoot, and steady-state error were used to assess the effectiveness of optimized regulators. Overall, the results of the research indicate that there was a significant improvement of the dynamic characteristics of the system due to the usage of machine learning algorithms compared to the traditional approaches. The obtained parameters of optimization achieved the target value while being faster and more stable, thus increasing the productivity of control in the technological process.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>сепарация нефти</kwd><kwd>оптимизация системы автоматизации</kwd><kwd>ПИД-регулятор</kwd><kwd>оптимизация параметров</kwd><kwd>машинное обучение</kwd><kwd>алгоритм поиска кукушки</kwd><kwd>алгоритм светлячков</kwd><kwd>оптимизация роя частиц</kwd><kwd>метод опорных векторов</kwd></kwd-group><kwd-group xml:lang="en"><kwd>oil separation</kwd><kwd>automation system optimization</kwd><kwd>PID controller</kwd><kwd>parameter optimization</kwd><kwd>machine learning</kwd><kwd>Cuckoo Search Algorithm</kwd><kwd>Firefly Algorithm</kwd><kwd>Particle Swarm Optimization</kwd><kwd>Support Vector Machine</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">Sathasivam L., Elamvazuthi I., Ahamed Khan M. K. A., &amp; Parasuraman S. Tuning A Three-Phase Separator Level Controller via Particle Swarm Optimization Algorithm // Proceedings of the 2018 International Conference on Recent Trends in Electrical, Control and Communication (RTECC). – IEEE, 2018. – P. 265–268.</mixed-citation><mixed-citation xml:lang="en">Sathasivam L., Elamvazuthi I., Ahamed Khan M. K. A., &amp; Parasuraman S. Tuning A Three-Phase Separator Level Controller via Particle Swarm Optimization Algorithm // Proceedings of the 2018 International Conference on Recent Trends in Electrical, Control and Communication (RTECC). – IEEE, 2018. – P. 265–268.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Reis V.C., Santos M.F., Carmo M.J., Ferreira F.C. Control of Level in Systems Based on Arduino Platform through PC // Proceedings of the 20th International Conference on System Theory, Control and Computing (ICSTCC). – Sinaia, Romania: IEEE, 2016. – P. 251–256.</mixed-citation><mixed-citation xml:lang="en">Reis V.C., Santos M.F., Carmo M.J., Ferreira F.C. Control of Level in Systems Based on Arduino Platform through PC // Proceedings of the 20th International Conference on System Theory, Control and Computing (ICSTCC). – Sinaia, Romania: IEEE, 2016. – P. 251–256.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Charkoutsis S., Kara-Mohamed M. Particle Swarm Optimization tuned nonlinear PID controller with improved performance and robustness for First Order Plus Time Delay systems // Results in Control and Optimization. – 2023. – Vol. 12. – P. 100289.</mixed-citation><mixed-citation xml:lang="en">Charkoutsis S., Kara-Mohamed M. Particle Swarm Optimization tuned nonlinear PID controller with improved performance and robustness for First Order Plus Time Delay systems // Results in Control and Optimization. – 2023. – Vol. 12. – P. 100289.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Foss B. Process control in conventional oil and gas production: Challenges and opportunities // Control Engineering Practice. – 2012. – Vol. 20. – No. 10. – P. 1058–1064.</mixed-citation><mixed-citation xml:lang="en">Foss B. Process control in conventional oil and gas production: Challenges and opportunities // Control Engineering Practice. – 2012. – Vol. 20. – No. 10. – P. 1058–1064.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Patel V. V. Ziegler-nichols tuning method: Understanding the pid controller // Resonance. – 2020. – Vol. 25. – No. 10. – P. 1385–1397.</mixed-citation><mixed-citation xml:lang="en">Patel V. V. Ziegler-nichols tuning method: Understanding the pid controller // Resonance. – 2020. – Vol. 25. – No. 10. – P. 1385–1397.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Ribeiro J.M.S., Santos M.F., Carmo M.J., Silva M.F. Comparison of PID Controller Tuning Methods: Analytical/Classical Techniques versus Optimization Algorithms // Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics (ICSMC). – 2017. – P. 533–538.</mixed-citation><mixed-citation xml:lang="en">Ribeiro J.M.S., Santos M.F., Carmo M.J., Silva M.F. Comparison of PID Controller Tuning Methods: Analytical/Classical Techniques versus Optimization Algorithms // Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics (ICSMC). – 2017. – P. 533–538.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Garpinger O., Hägglund T., Åström K. J. Performance and robustness trade-offs in PID control // Journal of Process Control. – 2014. – Vol. 24. – No. 5. – P. 748–760.</mixed-citation><mixed-citation xml:lang="en">Garpinger O., Hägglund T., Åström K. J. Performance and robustness trade-offs in PID control // Journal of Process Control. – 2014. – Vol. 24. – No. 5. – P. 748–760.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Shahrokhi M., Zamorrodi A. Comparison of PID controller adjustment methods // Journal of Process Control. – 2024. – No. 2. – P. 1–15.</mixed-citation><mixed-citation xml:lang="en">Shahrokhi M., Zamorrodi A. Comparison of PID controller adjustment methods // Journal of Process Control. – 2024. – No. 2. – P. 1–15.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Eltayeb A., Ahmed G., Imran I.H., Alyazidi N.M., Abubaker A. Comparative Analysis: Fractional PID vs. PID Controllers for Robotic Arm Using Genetic Algorithm Optimization // Automation. – 2024. – Vol. 5. – P. 230–245.</mixed-citation><mixed-citation xml:lang="en">Eltayeb A., Ahmed G., Imran I.H., Alyazidi N.M., Abubaker A. Comparative Analysis: Fractional PID vs. PID Controllers for Robotic Arm Using Genetic Algorithm Optimization // Automation. – 2024. – Vol. 5. – P. 230–245.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Hekimoğlu B. Optimal tuning of fractional order PID controller for DC motor speed control via chaotic atom search optimization algorithm // IEEE Access. – 2019. – Vol. 7. – P. 38100–38114.</mixed-citation><mixed-citation xml:lang="en">Hekimoğlu B. Optimal tuning of fractional order PID controller for DC motor speed control via chaotic atom search optimization algorithm // IEEE Access. – 2019. – Vol. 7. – P. 38100–38114.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Mehta S.A., Katrodiya J., Mankad B. Simulation, Design and Practical Implementation of IMC Tuned Digital PID Controller for Liquid Level Control System // Proceedings of the International Conference on Current Trends in Technology (NUiCONE-2011). Ahmedabad, India: IEEE, 2011. – P. 1–5.</mixed-citation><mixed-citation xml:lang="en">Mehta S.A., Katrodiya J., Mankad B. Simulation, Design and Practical Implementation of IMC Tuned Digital PID Controller for Liquid Level Control System // Proceedings of the International Conference on Current Trends in Technology (NUiCONE-2011). Ahmedabad, India: IEEE, 2011. – P. 1–5.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Alsmadi M.K., Mohammad R.M.A., Alzaqebah M., Jawarneh S., AlShaikh M., Al Smadi A., Alghamdi F.A., Alqurni J. S., &amp; Alfagham H. Intrusion Detection Using an Improved Cuckoo Search Optimization Algorithm // Journal of Wireless Mobile Networks, Ubiquitous Computing, and Dependable Applications. – 2024. – Vol. 15. – No. 2. – P. 73–93. https://doi.org/10.58346/JOWUA.2024.I2.006.</mixed-citation><mixed-citation xml:lang="en">Alsmadi M.K., Mohammad R.M.A., Alzaqebah M., Jawarneh S., AlShaikh M., Al Smadi A., Alghamdi F.A., Alqurni J. S., &amp; Alfagham H. Intrusion Detection Using an Improved Cuckoo Search Optimization Algorithm // Journal of Wireless Mobile Networks, Ubiquitous Computing, and Dependable Applications. – 2024. – Vol. 15. – No. 2. – P. 73–93. https://doi.org/10.58346/JOWUA.2024.I2.006.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Ali E.S., Abd Elazim S.M., Abdelaziz A.Y. Ant Lion Optimization Algorithm for optimal location and sizing of renewable distributed generations // Renewable Energy. – 2017. – Vol. 101. – P. 1311–1324.</mixed-citation><mixed-citation xml:lang="en">Ali E.S., Abd Elazim S.M., Abdelaziz A.Y. Ant Lion Optimization Algorithm for optimal location and sizing of renewable distributed generations // Renewable Energy. – 2017. – Vol. 101. – P. 1311–1324.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Debbarma S., Saikia L.C., Sinha N. Solution to automatic generation control problem using firefly algorithm optimized IλDμ controller // ISA Transactions. – 2014. – Vol. 53. – Issue 2. – P. 358–366.</mixed-citation><mixed-citation xml:lang="en">Debbarma S., Saikia L.C., Sinha N. Solution to automatic generation control problem using firefly algorithm optimized IλDμ controller // ISA Transactions. – 2014. – Vol. 53. – Issue 2. – P. 358–366.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Guha D., Roy P.K., Banerjee S. Optimal tuning of 3 degree-of-freedom proportional-integralderivative controller for hybrid distributed power system using dragonfly algorithm // Computers and Electrical Engineering. – 2018. – Vol. 72. –P. 137–153.</mixed-citation><mixed-citation xml:lang="en">Guha D., Roy P.K., Banerjee S. Optimal tuning of 3 degree-of-freedom proportional-integralderivative controller for hybrid distributed power system using dragonfly algorithm // Computers and Electrical Engineering. – 2018. – Vol. 72. –P. 137–153.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Mohamed M.J., Oleiwi B.K., Azar A.T., Hameed I.A. Coot optimization algorithm-tuned neural network-enhanced PID controllers for robust trajectory tracking of three-link rigid robot manipulator // Heliyon. – 2024. – Vol. 10. Article e32661.</mixed-citation><mixed-citation xml:lang="en">Mohamed M.J., Oleiwi B.K., Azar A.T., Hameed I.A. Coot optimization algorithm-tuned neural network-enhanced PID controllers for robust trajectory tracking of three-link rigid robot manipulator // Heliyon. – 2024. – Vol. 10. Article e32661.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Saravanan G., Suresh K.P., Pazhanimuthu C., Kumar R.S. Artificial rabbits optimization algorithm based tuning of PID controller parameters for improving voltage profile in AVR system using IoT // e-Prime – Advances in Electrical Engineering, Electronics and Energy. – 2024. – Vol. 8. Article 100523.</mixed-citation><mixed-citation xml:lang="en">Saravanan G., Suresh K.P., Pazhanimuthu C., Kumar R.S. Artificial rabbits optimization algorithm based tuning of PID controller parameters for improving voltage profile in AVR system using IoT // e-Prime – Advances in Electrical Engineering, Electronics and Energy. – 2024. – Vol. 8. Article 100523.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Mosaad A. M., Attia M. A., Abdelaziz A. Y. Whale optimization algorithm to tune PID and PIDA controllers on AVR system // Ain Shams Engineering Journal. – 2019. – Vol. 10. – P. 755–767.</mixed-citation><mixed-citation xml:lang="en">Mosaad A. M., Attia M. A., Abdelaziz A. Y. Whale optimization algorithm to tune PID and PIDA controllers on AVR system // Ain Shams Engineering Journal. – 2019. – Vol. 10. – P. 755–767.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Mohamed M.J., Oleiwi B.K., Azar A.T., Hameed I.A. Coot optimization algorithm-tuned neural network-enhanced PID controllers for robust trajectory tracking of three-link rigid robot manipulator // Heliyon. – 2024. – Vol. 10. Article e32661.</mixed-citation><mixed-citation xml:lang="en">Mohamed M.J., Oleiwi B.K., Azar A.T., Hameed I.A. Coot optimization algorithm-tuned neural network-enhanced PID controllers for robust trajectory tracking of three-link rigid robot manipulator // Heliyon. – 2024. – Vol. 10. Article e32661.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Güven A.F., Mengi O.Ö., Elseify M.A., &amp; Kamel, S. Comprehensive Optimization of PID Controller Parameters for DC Motor Speed Management Using a Modified Jellyfish Search Algorithm // Optimal Control Applications and Methods. – 2024. – Vol. 0. – P. 1–23.</mixed-citation><mixed-citation xml:lang="en">Güven A.F., Mengi O.Ö., Elseify M.A., &amp; Kamel, S. Comprehensive Optimization of PID Controller Parameters for DC Motor Speed Management Using a Modified Jellyfish Search Algorithm // Optimal Control Applications and Methods. – 2024. – Vol. 0. – P. 1–23.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Güven A.F., &amp; Mengi O.Ö. Nature-inspired algorithms for optimizing fractional order PID controllers in time-delayed systems // Optimal Control Applications and Methods. – 2024. – Vol. 45. – No. 3. – P. 1251–1279.</mixed-citation><mixed-citation xml:lang="en">Güven A.F., &amp; Mengi O.Ö. Nature-inspired algorithms for optimizing fractional order PID controllers in time-delayed systems // Optimal Control Applications and Methods. – 2024. – Vol. 45. – No. 3. – P. 1251–1279.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Vanchinathan K., Selvaganesan N. Adaptive fractional order PID controller tuning for brushless DC motor using Artificial Bee Colony algorithm // Results in Control and Optimization. – 2021. – Vol. 4. – P. 100032.</mixed-citation><mixed-citation xml:lang="en">Vanchinathan K., Selvaganesan N. Adaptive fractional order PID controller tuning for brushless DC motor using Artificial Bee Colony algorithm // Results in Control and Optimization. – 2021. – Vol. 4. – P. 100032.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Sharif Naser Makhadmeh, Mohammed Azmi Al-Betar, Iyad Abu Doush, Mohammed A. Awadallah, Sofian Kassaymeh, Seyedali Mirjalili, Raed Abu Zitar. Recent advances in Grey Wolf Optimizer, its versions and applications: Review // IEEE Access. – 2023.</mixed-citation><mixed-citation xml:lang="en">Sharif Naser Makhadmeh, Mohammed Azmi Al-Betar, Iyad Abu Doush, Mohammed A. Awadallah, Sofian Kassaymeh, Seyedali Mirjalili, Raed Abu Zitar. Recent advances in Grey Wolf Optimizer, its versions and applications: Review // IEEE Access. – 2023.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Hui T., Zeng W., Yu T. Core power control of the ADS based on genetic algorithm tuning PID controller // Nuclear Engineering and Design. – 2020. – Vol. 370. – P. 110835.</mixed-citation><mixed-citation xml:lang="en">Hui T., Zeng W., Yu T. Core power control of the ADS based on genetic algorithm tuning PID controller // Nuclear Engineering and Design. – 2020. – Vol. 370. – P. 110835.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Izci D., Ekinci S., Hedley J., Demirören A. HHO Algorithm Based PID Controller Design for Aircraft Pitch Angle Control System // Proceedings of the 2020 International Conference on Advances in Computing, Communication, and Automation (ICACCA). Piscataway, NJ: IEEE. – 2020. – P. 9152897.</mixed-citation><mixed-citation xml:lang="en">Izci D., Ekinci S., Hedley J., Demirören A. HHO Algorithm Based PID Controller Design for Aircraft Pitch Angle Control System // Proceedings of the 2020 International Conference on Advances in Computing, Communication, and Automation (ICACCA). Piscataway, NJ: IEEE. – 2020. – P. 9152897.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Serdar Ekinci, Davut Izci, Baran Hekimoğlu. Henry Gas Solubility Optimization Algorithm Based FOPID Controller Design for Automatic Voltage Regulator // Proceedings of the 2nd International Conference on Electrical, Communication and Computer Engineering (ICECCE). Istanbul, Turkey: IEEE, 2020. – P. 1–6.</mixed-citation><mixed-citation xml:lang="en">Serdar Ekinci, Davut Izci, Baran Hekimoğlu. Henry Gas Solubility Optimization Algorithm Based FOPID Controller Design for Automatic Voltage Regulator // Proceedings of the 2nd International Conference on Electrical, Communication and Computer Engineering (ICECCE). Istanbul, Turkey: IEEE, 2020. – P. 1–6.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Patil S.R., Agashe S. RelaxC controller and PID for time delay systems: Experimental test results on Boiler pilot plant // Results in Control and Optimization. – 2024. – Vol. 9. Article 100297.</mixed-citation><mixed-citation xml:lang="en">Patil S.R., Agashe S. RelaxC controller and PID for time delay systems: Experimental test results on Boiler pilot plant // Results in Control and Optimization. – 2024. – Vol. 9. Article 100297.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Murugesan D., Jagatheesan K., Shah P., Sekhar R. Fractional order PIλDμ controller for microgrid power system using cohort intelligence optimization // Results in Control and Optimization. – 2023. – Vol. 11. Article 100218.</mixed-citation><mixed-citation xml:lang="en">Murugesan D., Jagatheesan K., Shah P., Sekhar R. Fractional order PIλDμ controller for microgrid power system using cohort intelligence optimization // Results in Control and Optimization. – 2023. – Vol. 11. Article 100218.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Ataşlar-Ayyıldız B. Robust Trajectory Tracking Control for Serial Robotic Manipulators Using Fractional Order-Based PTID Controller // Fractal Fract. – 2023. – Vol. 7. – Issue 3. – P. 250.</mixed-citation><mixed-citation xml:lang="en">Ataşlar-Ayyıldız B. Robust Trajectory Tracking Control for Serial Robotic Manipulators Using Fractional Order-Based PTID Controller // Fractal Fract. – 2023. – Vol. 7. – Issue 3. – P. 250.</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>
