Adaptive modeling in problems of optimal control search termovremennoy cast iron

Abstract

The aim of research is to develop methods for estimating the parameters of kinetic equations describing the change in time of the content of chemical elements in the melt bath at the stage of thermal treatment of cast iron in electric arc melting.The object of research is the process of heat treatment of cast iron.The methods of adaptive mathematical modeling under non-additive random drift, methods of chemical kinetics, Pontryagin's maximum principle, and ridge analysis were chosen as research methods.An adaptive approach to the estimation of the parameters of mathematical models – kinetic equations, which can be used as a mathematical description of controlled physicochemical processes at the stage of thermal treatment of the alloy is proposed.It is shown that the choice of optimal control of the electrosmelting process at the stage of thermal treatment should be preceded by the procedure for obtaining the parameters of mathematical models describing the state of the object at this stage of electrosmelting and constructing an analytical description of the final state, further implementing the possibility of searching for optimal control of the process of saturation of the bath with carbon using the Pontryagin’s principle. The mathematical description of the electrosmelting process at the stage of thermal treatment is an equation of the rates of chemical reactions, in which the elements of the chemical composition of the cast iron are involved – these are the input variables of the process.Experimental and industrial research with the involvement of the mathematical apparatus of the theory of experiment planning has proved that a method based on an iterative procedure for estimating the coefficients of kinetic equations taking into account the change in process parameters over time can be applied to describe the physicochemical processes occurring in the bath of an electric furnace. This method makes it possible to construct adequate kinetic equations for describing the state of the system at the stage of thermal processing using a limited sample of data. This makes it possible to solve the problem of finding the optimal control of the process of thermal treatment of the melt.The results obtained can be used to solve the problem of finding the optimal control in terms of speed, which also provides the possibility of achieving a given final state by the system.