STATEMENT OF THE PROBLEM OPTIMAL CONTROL THE HARDNESS OF THE STEEL PRODUCED BASED ON THE MODEL OF TAKAGI-SUGENO-KANG

Abstract

This study discusses the problem of mathematical modeling of complex technological systems under uncertainty to obtain the most optimal parameters in the management of the production process in the applied field – metallurgy. In the offered approach one of the most important tasks of management of technological process of steel smelting is considered: maintenance of the set hardness (calcification) of the steel distributed on depth of the smelted product. To minimize the inevitable errors associated with the expert choice of chemical composition, improve the management efficiency and the quality of the produced steel, it is proposed to apply the system of fuzzy production rules Takagi-Sugeno-Kanga (model TSK), based on the modeling of the dependence "composition-hardness". Application of this model will also allow to optimize the choice of the chemical composition of the steel in the conditions of stochasticity of the parameters of the regression models. In addition, in the study of the steel production process there is a need to solve the inverse problem – the determination of the chemical composition of the steel produced at a given hardness value. The proposed model of TSK based on fuzzy production rules for steel smelting prediction and control is presented in matrix form, so one of the possible ways to solve the control problem is to solve the corresponding matrix equation. At the same time, on the basis of experimental data, a significant shift in the estimates of the values of chemical elements was revealed. Therefore, governance must be based on an optimization approach. The proposed formulation of the optimization problem will develop an algorithm for solving the problem of optimal hardness control on the basis of the TSK model, characterized by the ability to automatically determine the required chemical composition of steel by a given distribution of its hardness. In addition, the developed model TSK using the optimal control problem will eliminate errors in determining the calculation model, as well as to determine the hardness of steel for the chemical composition does not fully correspond to a certain set of allowable intervals of changing the mass fractions of chemical elements.

Keywords

• Modeling
• optimization problem
• hardness of steel
• metallurgy
• intelligent control
• Takagi-Sugeno-Kang