Optimization of two-stage methanogenesis regime based on the Pontryagin’s maximum principle ***
Introduction. The solution to the problem of optimal control of the biogas process under its conversion in two digesters is considered. The work objectives are to propose a mathematical model of this process and to develop an optimal control algorithm.Materials and Methods. The developed mathematica...
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| Format: | Article |
| Language: | Russian |
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Don State Technical University
2019-06-01
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| Series: | Advanced Engineering Research |
| Subjects: | |
| Online Access: | https://www.vestnik-donstu.ru/jour/article/view/1520 |
| _version_ | 1797881296357163008 |
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| author | S. A. Korolev D. V. Maykov |
| author_facet | S. A. Korolev D. V. Maykov |
| author_sort | S. A. Korolev |
| collection | DOAJ |
| description | Introduction. The solution to the problem of optimal control of the biogas process under its conversion in two digesters is considered. The work objectives are to propose a mathematical model of this process and to develop an optimal control algorithm.Materials and Methods. The developed mathematical model describes the biomethanation from animal waste through the downstream processing of the substrate in two digesters. Cases of the same and different temperature media (mesophilic and thermophilic) are considered. An optimal control problem is defined as a Lagrange problem for this model. Its modifiers are the rates of substrate entry into the digesters. The algorithm for solving this problem is proposed; it is based on the numerical implementation of the Pontryagin maximum principle. When optimizing, a hybrid genetic algorithm was used with an additional search in the neighborhood of the best solution through the conjugate gradient method.Research Results. A new mathematical model is developed. It describes the biomethanation during the downstream processing of the substrate in two digesters. A numerical algorithm for solving an optimal control problem is proposed and software-implemented. The numerical studies have shown that the biogas production rate is nearly twice as high for a thermophilic medium as for a mesophilic one. It is established that the downstream processing of the substrate in two digesters with the same temperature medium allows the biogas production rate to be doubled. If the temperature media in the digesters are different, then in the first of them, the mesophilic medium should be used, and in the second - the thermophilic medium. At this, the biogas formation rate is somewhat lower compared to the case when there is a mesophilic medium in each of the digesters; however, the degree of the substrate processing is by 10-15% higher.Discussion and Conclusions. The results obtained can be used for the calculation and design of biogas plants, as well as in the development of appropriate software. |
| first_indexed | 2024-04-10T03:17:56Z |
| format | Article |
| id | doaj.art-8d6c9dad4c934a09b81b235c3971c0ab |
| institution | Directory Open Access Journal |
| issn | 2687-1653 |
| language | Russian |
| last_indexed | 2024-04-10T03:17:56Z |
| publishDate | 2019-06-01 |
| publisher | Don State Technical University |
| record_format | Article |
| series | Advanced Engineering Research |
| spelling | doaj.art-8d6c9dad4c934a09b81b235c3971c0ab2023-03-13T07:31:28ZrusDon State Technical UniversityAdvanced Engineering Research2687-16532019-06-0119219520310.23947/1992-5980-2019-19-2-195-2031420Optimization of two-stage methanogenesis regime based on the Pontryagin’s maximum principle ***S. A. Korolev0D. V. Maykov1Ижевский государственный технический университет им. М.Т. КалашниковаИжевский торгово-экономический техникумIntroduction. The solution to the problem of optimal control of the biogas process under its conversion in two digesters is considered. The work objectives are to propose a mathematical model of this process and to develop an optimal control algorithm.Materials and Methods. The developed mathematical model describes the biomethanation from animal waste through the downstream processing of the substrate in two digesters. Cases of the same and different temperature media (mesophilic and thermophilic) are considered. An optimal control problem is defined as a Lagrange problem for this model. Its modifiers are the rates of substrate entry into the digesters. The algorithm for solving this problem is proposed; it is based on the numerical implementation of the Pontryagin maximum principle. When optimizing, a hybrid genetic algorithm was used with an additional search in the neighborhood of the best solution through the conjugate gradient method.Research Results. A new mathematical model is developed. It describes the biomethanation during the downstream processing of the substrate in two digesters. A numerical algorithm for solving an optimal control problem is proposed and software-implemented. The numerical studies have shown that the biogas production rate is nearly twice as high for a thermophilic medium as for a mesophilic one. It is established that the downstream processing of the substrate in two digesters with the same temperature medium allows the biogas production rate to be doubled. If the temperature media in the digesters are different, then in the first of them, the mesophilic medium should be used, and in the second - the thermophilic medium. At this, the biogas formation rate is somewhat lower compared to the case when there is a mesophilic medium in each of the digesters; however, the degree of the substrate processing is by 10-15% higher.Discussion and Conclusions. The results obtained can be used for the calculation and design of biogas plants, as well as in the development of appropriate software.https://www.vestnik-donstu.ru/jour/article/view/1520метаногенезбиогазметантенкпереработка отходов животноводстваматематическая модельсистема дифференциальных уравненийчисленное решениеметоды оптимизацииоптимальное управлениепринцип максимума понтрягина |
| spellingShingle | S. A. Korolev D. V. Maykov Optimization of two-stage methanogenesis regime based on the Pontryagin’s maximum principle *** Advanced Engineering Research метаногенез биогаз метантенк переработка отходов животноводства математическая модель система дифференциальных уравнений численное решение методы оптимизации оптимальное управление принцип максимума понтрягина |
| title | Optimization of two-stage methanogenesis regime based on the Pontryagin’s maximum principle *** |
| title_full | Optimization of two-stage methanogenesis regime based on the Pontryagin’s maximum principle *** |
| title_fullStr | Optimization of two-stage methanogenesis regime based on the Pontryagin’s maximum principle *** |
| title_full_unstemmed | Optimization of two-stage methanogenesis regime based on the Pontryagin’s maximum principle *** |
| title_short | Optimization of two-stage methanogenesis regime based on the Pontryagin’s maximum principle *** |
| title_sort | optimization of two stage methanogenesis regime based on the pontryagin s maximum principle |
| topic | метаногенез биогаз метантенк переработка отходов животноводства математическая модель система дифференциальных уравнений численное решение методы оптимизации оптимальное управление принцип максимума понтрягина |
| url | https://www.vestnik-donstu.ru/jour/article/view/1520 |
| work_keys_str_mv | AT sakorolev optimizationoftwostagemethanogenesisregimebasedonthepontryaginsmaximumprinciple AT dvmaykov optimizationoftwostagemethanogenesisregimebasedonthepontryaginsmaximumprinciple |