Mathematical modeling in problem of searching optimal control of alloys obtaining for machine parts under uncertainty conditions

D. Demin
2013 Zenodo  
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
more » ... btaining 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 co [...]
doi:10.5281/zenodo.4133684 fatcat:zlhq3qlzczaglixkantbbt3ilu