vmaitComputational Mathematics and Information TechnologiesComputational Mathematics and Information Technologies2587-8999Донской государственный технический университет10.23947/2587-8999-2020-1-1-47-55vmait-7Research ArticleСтатьиАлгоритм анализа устойчивости решения многокритериальной оптимизации каталитических процессов к малым возмущениям в параметрах, через кинетическую модельAlgorithm for catalytic processes multicriteria optimization solution stability analysis to small perturbations in the parameters, through the kinetic modelКолединаК. Ф.KoledinaK. F.

Камила Коледина, кандидат физико-математических наук, доцент кафедры математики

ул. Космонавтов, 1, Уфа

Kamila F. Koledina, Cand.Sci. (Phys.-Math.), associate professor, researcher, associate professor of the Mathematics Department Institute of Petrochemistry and Catalysis of RAS

Kosmonavtov St., Ufa

koledinakamila@mail.ruКолединС. Н.KoledinS. N.

Сергей Коледин, кандидат физико-математических наук, доцент кафедры математики

ул. Космонавтов, 1, Уфа

Sergey N. Koledin, Ph.Dr. (Phys.-Math.), associate professor of the Mathematics Department

Kosmonavtov St., Ufa

koledinsrg@gmail.comГубайдуллинИ. М.GubaydullinI. M.

Ирек Губайдуллин, доктор физико-математических наук, профессор кафедры технологии нефти и газа

ул. Космонавтов, 1, Уфа

Irek M. Gubaydullin, Dr.Sci. (Phys.-Math.), associate professor, senior researcher, professor of the Oil and Gas Technology Department

Kosmonavtov St., Ufa

IrekMars@mail.ruИнститут нефтехимии и катализа УФИЦ РАН; Уфимский государственный нефтяной технический университетРоссияInstitute of Petrochemistry and Catalysis of RAS; Ufa State Petroleum Technological UniversityRussian FederationУфимский государственный нефтяной технический университетРоссияUfa State Petroleum Technological UniversityRussian FederationУфимский государственный нефтяной технический университетРоссияInstitute of Petrochemistry and Catalysis of RAS; Ufa State Petroleum Technological UniversityRussian Federation202020022023414755Copyright © Коледина К.Ф., Коледин С.Н., Губайдуллин И.М., 20232023Коледина К.Ф., Коледин С.Н., Губайдуллин И.М.Koledina K.F., Koledin S.N., Gubaydullin I.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.cmit-journal.ru/jour/article/view/7

Многокритериальное оптимальное управление сложными каталитическими реакциями на основе кинетической модели актуально как для промышленных, так и лабораторных процессов. Для задач химической кинетики при анализе устойчивости многокритериальной оптимизации необходимо определить радиус устойчивости по каждому параметру, с целью возможного изменения рассчитанных значений с заданной погрешностью.Приведена постановка задачи многокритериальной оптимизации (МКО) условий проведения каталитической реакции на основе кинетической модели. Дано определение устойчивости решения задачи МКО и радиуса устойчивости.Разработан алгоритм расчета радиуса устойчивости решения МКО-задачи. Для каталитической реакции метилирования первичных аминов диметилкарбонатом решена задача МКО условий проведения на основе кинетической модели и рассчитан допустимый интервал изменения оптимальных значений температуры и времени реакции для недопущения сильного изменения значений критериев оптимальности.Многокритериальное оптимальное управление сложными каталитическими реакциями на основе кинетической модели актуально как для промышленных, так и лабораторных процессов. Однако, является недостаточным только расчет всех эффективных траекторий, значений варьируемых параметров и критериев оптимальности. Для применения на практике рассчитанных режимов для лица принимающие решение (ЛПР) важным является информация о допустимом интервале изменения оптимальных режимов. В работе для каталитической реакции метилирования первичных аминов диметилкарбонатом решена задача МКО условий проведения на основе кинетической модели и рассчитан допустимый интервал изменения оптимальных значений температуры и времени реакции для недопущения сильного изменения значений критериев оптимальности.

The multicriteria complex catalytic reactions optimal control based on the kinetic model is relevant for both industrial and laboratory processes. It is necessary to determine the stability radius for each parameter, for the chemical kinetics problems in the analysis of multicriteria optimization stability, with the aim of possible change in the calculated values with a given error.The multicriteria optimization problem statement (MCO) for the catalytic reaction based on the kinetic model is presented. The solution stability definition of the MCO problem and the stability radius is given.An algorithm has been developed for calculating the stability radius of the MCO problem solution. The problem of the MCO conditions was solved on the kinetic model basis for the catalytic reaction of primary amines methylation with dimethyl carbonate, and the acceptable range of changes in the optimal temperature and reaction time was calculated to prevent a strong change in the optimality criteria values.The multicriteria complex catalytic reactions optimal control based on the kinetic model is relevant for both industrial and laboratory processes. However, only the all effective trajectories calculation, the varied parameters values and optimality criteria is insufficient. For the application in practice of the calculated modes for decision makers (DM), information on the acceptable interval for changing the optimal modes is important. In this work, for the catalytic reaction of methylation of primary amines with dimethyl carbonate, the problem of the MCO conditions was carried out on the basis of the kinetic model and the allowable range of changes in the optimal temperature and reaction time was calculated to prevent a strong change in the values of the optimality criteria.

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The authors declare that there are no conflicts of interest present.