МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ В ЗАДАЧЕ ПОИСКА ОПТИМАЛЬНОГО УПРАВЛЕНИЯ ПРОЦЕССОМ ПОЛУЧЕНИЯ СПЛАВОВ ДЛЯ ДЕТАЛЕЙ МАШИН В УСЛОВИЯХ НЕОПРЕДЕЛЁННОСТИ (Mathematical Modeling in the Problem of Searching for the Optimal Control of the Process of Producing Alloys for Machine Parts Under Uncertainty Conditions)

Ukrainian abstract: Описані результати досліджень, присвячених матема-тичному моделюванню в задачах пошуку оптимального за кінцевим станом керування процесами отримання сплавів для відповідальних деталей енергетичного машинобудування. Запропоновано матема-тичний опис об'єкта керування і показано, які з параметрів мате-матичної моделі підлягають оцінці для реалізації відомих методів пошуку оптимального керування в лінійно-квадратичної задачі і за-дачі пошуку оптимального за кінцевим станом керування. Наведено алгоритм оцінювання параметрів математичної моделі досліджу-ваного процесу в умовах дворівневої невизначеності.English abstract: The aim of research is to develop a principle for constructing a mathematical description of a control object, a characteristic feature of which is a two-level uncertainty in the estimation of its parameters, for the choice of optimal control. The object of research is the process of electric arc melting.Regression analysis and methods of fuzzy mathematics are chosen as research methods. A procedure for evaluating the structure and parameters of mathematical models describing the processes of obtaining alloys for parts of power engineering in electric furnaces is proposed, which allows one to bypass the fundamental difficulties associated with the presence of two-level uncertainty and the complexity of the mathematical description of the controlled melting process. It is shown which of the parameters of the mathematical model are to be estimated for the implementation of the known methods of finding optimal control in the linear-quadratic problem and the problem of finding the optimal control in the final state. An algorithm for estimating the parameters of a mathematical model of the process under study in conditions of two-level uncertainty is presented.Implementation of the proposed procedure for evaluating the structure and parameters of mathematical models, based on obtaining an analytical description of the relationship between output and fuzzy input variables in the form of a regression equation and the subsequent use of this description in the structural diagram of the control system, makes it possible to obtain a stable chemical composition and microstructure of the alloy, which determine its high mechanical properties. In this case, the concept of stability assumes that the values of the parameters of the alloy fall within the specified range throughout the entire melting process. Thus, the results obtained suggest the possibility of increasing the parametric reliability of the melting process. The given algorithm for estimating the parameters of the mathematical model of the process under study in conditions of two-level uncertainty can be used to solve the issues of technical implementation of control systems for the alloy production process in the process control system, since it allows calculating in real time those parameters that are not subject to direct control during the technological process