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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.21.67-73</article-id><article-id custom-type="elpub" pub-id-type="custom">novtexmech-752</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, CONTROL AND INFORMATION PROCESSING</subject></subj-group></article-categories><title-group><article-title>Синтез робастных ПИД регуляторов методом двойной оптимизации</article-title><trans-title-group xml:lang="en"><trans-title>Synthesis of Robust PID Controllers by Double Optimization Method</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>Жмудь</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Zhmud</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д-р техн. наук, зав. каф.</p></bio><email xlink:type="simple">oao_nips@bk.ru</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>Востриков</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Vostrikov</surname><given-names>A. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д-р техн. наук, проф.</p></bio><email xlink:type="simple">a.s.vostrikov@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>Ивойлов</surname><given-names>А. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Ivoilov</surname><given-names>A. Yu.</given-names></name></name-alternatives><bio xml:lang="ru"><p>аспирант</p></bio><bio xml:lang="en"><p>Ivoilov Andrei Yu., PhD-student of Department of Automation</p></bio><email xlink:type="simple">iau13hv@mail.ru</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>Саблина</surname><given-names>Г. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Sablina</surname><given-names>G. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>канд. техн. наук, доц.</p></bio><email xlink:type="simple">sablina@corp.nstu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Новосибирский государственный технический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Novosibirsk State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2020</year></pub-date><pub-date pub-type="epub"><day>10</day><month>02</month><year>2020</year></pub-date><volume>21</volume><issue>2</issue><fpage>67</fpage><lpage>74</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Commercial Publisher «New Technologies», 2020</copyright-statement><copyright-year>2020</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/752">https://mech.novtex.ru/jour/article/view/752</self-uri><abstract><p>Проектирование адаптивных регуляторов позволяет решать задачу управления объектом с нестационарными параметрами. Однако если параметры объекта изменяются не слишком сильно или если известен лишь некоторый интервал их изменения, может оказаться, что адаптивный регулятор не требуется, поскольку задача может быть решена с помощью робастного регулятора. Робастный регулятор позволяет обеспечить приемлемое качество управления даже в том случае, если параметры математической модели объекта изменяются в некотором наперед заданном интервале. Известен способ проектирования таких регуляторов методом численной оптимизации ансамбля регуляторов, используемых в ансамбле систем, в которых модели объектов различны, а модели регуляторов идентичны. При этом в ансамбле используются модели объектов с крайними значениями параметров. Недостаток этого метода состоит в слишком большом числе систем, которые требуется одновременно моделировать и оптимизировать, если изменяемых параметров несколько. Кроме того, наихудшее сочетание параметров модели может быть не граничным, а серединным, в этом случае данный метод не применим. В данной статье авторы предлагают и анализируют на численном примере альтернативный метод проектирования робастного регулятора. Суть данного метода заключается в численной оптимизации регулятора для модели с наихудшим сочетанием значений всех изменяемых параметров. Поиск наихудшего сочетания параметров осуществляется также с помощью метода численной оптимизации. При этом отыскивается такое сочетание параметров модели, при котором наилучшее соотношение коэффициентов регулятора дает наихудший результат работы системы. Задача решается в несколько циклов оптимизации с чередованием целевых функций. Целевая функция представляет собой некоторую интегральную оценку ошибки управления в системе, ее вид определяется решаемой задачей. Полезность предложенного метода проиллюстрирована численно на примере динамического объекта третьего порядка с последовательно включенным звеном запаздывания.</p></abstract><trans-abstract xml:lang="en"><p>The design of adaptive controllers allows to solve the problem of control of the object with non-stationary parameters. However, if the parameters of the object do not change too much or if only a certain interval of their change is known, it may turn out that an adaptive controller is not required, since the problem can be solved with the help of a robust controller. The robust controller allows to provide an acceptable quality of control even if the parameters of the mathematical model of the object change in some predetermined interval. A method of designing such controllers is known as the method of numerical optimization of the controllers used in the ensemble of systems in which the models of objects are different and the models of controllers are identical. The ensemble uses object models with extreme parameter values. The disadvantages of this method are too many systems that need to be modeled and optimized at the same time if there are several parameters to be changed. In addition, the worst combination of model parameters may not be boundary, but middle, in this case this method is not applicable. This article offers and analyzes an alternative method of designing a robust controller on a numerical example. The essence of this method is the numerical optimization of the regulator for the model with the worst combination of the values of all modifiable parameters. The search for the worst combination of parameters is also carried out using the method of numerical optimization. In this case, a combination of model parameters is found in which the best relation of regulator coefficients gives the worst result of the system. The problem is solved in several optimization cycles with alternating cost functions. The utility of the method is illustrated numerically by an example of a third order dynamic object with a series linked delay element.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>численная оптимизация</kwd><kwd>регулирование</kwd><kwd>робастная система</kwd><kwd>симуляция</kwd><kwd>моделирование</kwd><kwd>математическая модель</kwd><kwd>объект</kwd><kwd>ПИД регулятор</kwd></kwd-group><kwd-group xml:lang="en"><kwd>numerical optimization</kwd><kwd>regulation</kwd><kwd>robust system</kwd><kwd>simulation</kwd><kwd>mathematical model</kwd><kwd>object</kwd><kwd>PID controller</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">Veselý V. A new method to robust controller design // Proc. of 2016 17th International Carpathian Control Conference (ICCC). Tatranska Lomnica. 2016. P. 779—781.</mixed-citation><mixed-citation xml:lang="en">Veselý V. 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