<?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">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.17.547-553</article-id><article-id custom-type="elpub" pub-id-type="custom">novtexmech-340</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>МОДЕЛИРОВАНИЕ И УПРАВЛЕНИЕ В ТЕХНИЧЕСКИХ ОБЪЕКТАХ И ТЕХНОЛОГИЧЕСКИХ ПРОЦЕССАХ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>SIMULATION AND CONTROL IN TECHNICAL OBJECTS AND TECHNOLOGICAL PROCESSES</subject></subj-group></article-categories><title-group><article-title>Оптимальное управление технологическим процессом нанесения гальванического покрытия в ванне с дополнительными катодами и биполярными электродами</article-title><trans-title-group xml:lang="en"><trans-title>Optimal Control for the Electroplating Process Based on the Supplementary Cathode and Bipolar Electrode</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>Соловьев</surname><given-names>Д. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Solovjev</surname><given-names>D. S.</given-names></name></name-alternatives><email xlink:type="simple">solovjevdenis@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>Као</surname><given-names>В. З.</given-names></name><name name-style="western" xml:lang="en"><surname>Cao</surname><given-names>V. Z.</given-names></name></name-alternatives><email xlink:type="simple">hanam17389@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>Литовка</surname><given-names>Ю. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Litovka</surname><given-names>Yu. V.</given-names></name></name-alternatives><email xlink:type="simple">polychem@list.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Тамбовский государственный технический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Tambov State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2016</year></pub-date><pub-date pub-type="epub"><day>28</day><month>08</month><year>2018</year></pub-date><volume>17</volume><issue>8</issue><fpage>547</fpage><lpage>553</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Commercial Publisher «New Technologies», 2018</copyright-statement><copyright-year>2018</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/340">https://mech.novtex.ru/jour/article/view/340</self-uri><abstract><p>Поставлена задача оптимального управления гальваническим процессом в ванне с дополнительными катодами и биполярными электродами по критерию неравномерности распределения толщины покрытия. Для поставленной задачи разработана математическая модель, учитывающая изменение концентрации компонентов электролита. Описан алгоритм решения поставленной задачи, который базируется на модификации прямого метода Ритца. Рассмотрен пример гальванического процесса хромирования детали V-образной формы, для которой найдены функции изменения анодного напряжения в виде полиномов различных степеней.</p></abstract><trans-abstract xml:lang="en"><p>The article describes the main approaches (including technical parameters and equipment) to taking into account the changes and correction of the electrolyte components of the bath with the supplementary cathodes and bipolar electrodes in the electroplating processing of products. A voltage change on the anode is proposed as a manipulated variable for the galvanic process as a control object for the electroplating bath. The task of optimal control of the electroplating process by the criterion of distribution of uniformity on the surface of the coating thickness of the product is set. A mathematical model is formulated of the dynamics of the distributed coordinates for the contact criterion of the uniformity coverage with the control action in the form of changes of the anode voltage, taking into account the structural and technological assumptions. This is based on the Faraday's law, Ohm's law of the differential form and a partial differential equation of a parabolic type describing the distribution built in the amount of the electroplating bath. An algorithm was invented for solving the equations of the mathematical model of the electroplating process, which considers the task as a quasi-static one and based on the modifications of the direct Ritz method for the search function of the anode voltage in the class of the polynomials of various degrees. A comparison is proposed of the relative values of the refinement criteria of the unevenness produced during the transition to a higher polynomial degree in order to obtain the required accuracy solutions for determination of the degree of the polynomial control. An example is described of solving the problem of chrome electroplating of V-shape parts in the electroplating bath with two side cathodes and one bipolar electrode. This example describes the function of the anode voltage in the form of the polynomials of the zero, first and second degrees. A rational solution describing the anode voltage changes as the polynomials of the first degree is shown. The further increase in the degree doesn't give a significant gain in the unevenness of the coverage criterion, however, it ensures a significant increase of the duration of the search optimization. Thus, the obtained feature of the voltage change on the anode does not depends strongly on time, so, the change of the concentration of the electrolyte components is reduced slightly during a short period of coating. However, when analyzing a longer period, the process under a constant stress might lead to significant losses in the expected distribution of the coating thickness.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>оптимальное управление</kwd><kwd>объект управления</kwd><kwd>математическая модель</kwd><kwd>дополнительные катоды</kwd><kwd>биполярные электроды</kwd><kwd>модифицированный метод Ритца</kwd><kwd>гальванический процесс</kwd><kwd>неравномерность толщины покрытия</kwd><kwd>концентрация компонентов электролита</kwd><kwd>optimal control</kwd><kwd>control object</kwd><kwd>mathematical model</kwd><kwd>supplementary cathodes</kwd><kwd>bipolar electrodes</kwd><kwd>modified Ritz method</kwd><kwd>electroplating process</kwd><kwd>anode voltage</kwd><kwd>unevenness of the coating thickness</kwd><kwd>concentration of the electrolyte components</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">Герасименко А. А. Защита от коррозии, старения и биоповреждений машин, оборудования и сооружений. Справочник: В 2-х т. Т. 1 / Под ред. А. А. Герасименко. М.: Машиностроение, 1987. 688 с.</mixed-citation><mixed-citation xml:lang="en">Герасименко А. А. Защита от коррозии, старения и биоповреждений машин, оборудования и сооружений. Справочник: В 2-х т. Т. 1 / Под ред. А. А. Герасименко. М.: Машиностроение, 1987. 688 с.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Антропов Л. И. Теоретическая электрохимия. М.: Высшая школа, 1975. 560 с.</mixed-citation><mixed-citation xml:lang="en">Антропов Л. И. Теоретическая электрохимия. М.: Высшая школа, 1975. 560 с.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">А. с. № 717158 СССР, МКИ2 С 25 D 21/12. Способ автоматического регулирования состава электролита и устройство для осуществления этого способа / Н. В. Засько, В. И. Захаров. 1980. Бюл. № 7.</mixed-citation><mixed-citation xml:lang="en">А. с. № 717158 СССР, МКИ2 С 25 D 21/12. Способ автоматического регулирования состава электролита и устройство для осуществления этого способа / Н. В. Засько, В. И. Захаров. 1980. Бюл. № 7.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Tuaweri T. J., Adigio E. M., Jombo P. P. A Study of process parameters for zinc electrodeposition from a sulphate bath // International Journal of Engineering Science Invention. 2013. Vol. 2 (8). P. 17-24.</mixed-citation><mixed-citation xml:lang="en">Tuaweri T. J., Adigio E. M., Jombo P. P. A Study of process parameters for zinc electrodeposition from a sulphate bath // International Journal of Engineering Science Invention. 2013. Vol. 2 (8). P. 17-24.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Khorasani S., Motieifar A., Rashidian B. Optimal pulse shapes for periodic reverse electroplating // Iranian Journal of Science &amp; Transaction B. 2003. Vol. 27, No. B4. P. 701-711.</mixed-citation><mixed-citation xml:lang="en">Khorasani S., Motieifar A., Rashidian B. Optimal pulse shapes for periodic reverse electroplating // Iranian Journal of Science &amp; Transaction B. 2003. Vol. 27, No. B4. P. 701-711.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Литовка Ю. В., Као В. З. Моделирование и оптимизация гальванической ванны с дополнительными катодами // Вестник Тамбовского государственного технического университета. 2016. Т. 22. № 1. С. 68-74.</mixed-citation><mixed-citation xml:lang="en">Литовка Ю. В., Као В. З. Моделирование и оптимизация гальванической ванны с дополнительными катодами // Вестник Тамбовского государственного технического университета. 2016. Т. 22. № 1. С. 68-74.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Maksimović M. D., Mišković-Stanković V. B., Krstajić N. V. The effect of applied voltage on the cathodic electrodeposition process // Surface and Coatings Technology. 1986. Vol. 27, Iss. 1. P. 89-94.</mixed-citation><mixed-citation xml:lang="en">Maksimović M. D., Mišković-Stanković V. B., Krstajić N. V. The effect of applied voltage on the cathodic electrodeposition process // Surface and Coatings Technology. 1986. Vol. 27, Iss. 1. P. 89-94.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Бояринов А. И., Кафаров В. В. Методы оптимизации в химической технологии. М.: Химия, 1975. 576 с.</mixed-citation><mixed-citation xml:lang="en">Бояринов А. И., Кафаров В. В. Методы оптимизации в химической технологии. М.: Химия, 1975. 576 с.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Гнусин Н. П., Поддубный Н. П., Маслий А. И. Основы теории расчета и моделирования электрических полей в электролитах. Новосибирск: Наука, 1972. 276 с.</mixed-citation><mixed-citation xml:lang="en">Гнусин Н. П., Поддубный Н. П., Маслий А. И. Основы теории расчета и моделирования электрических полей в электролитах. Новосибирск: Наука, 1972. 276 с.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Braun T. M., Schwartz D. T. Localized electrodeposition and patterning using bipolar electrochemistry // J. Electrochem. Soc. 2015. Vol. 162, Iss. 4. P. 180-185.</mixed-citation><mixed-citation xml:lang="en">Braun T. M., Schwartz D. T. Localized electrodeposition and patterning using bipolar electrochemistry // J. Electrochem. Soc. 2015. Vol. 162, Iss. 4. P. 180-185.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Литовка Ю. В. Математическое описание изменения концентрации электролита в гальванической ванне // Журнал прикладной химии. 1997. Т. 70, Вып. 10. С. 1631-1637.</mixed-citation><mixed-citation xml:lang="en">Литовка Ю. В. Математическое описание изменения концентрации электролита в гальванической ванне // Журнал прикладной химии. 1997. Т. 70, Вып. 10. С. 1631-1637.</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>
