Minimization of scale formation on the heated ingots in a soaking pit

Abstract

The paper deals with the application of modelling and optimization techniques in the metallurigical process of steel industry. Steel ingots produced by Thomas and Bessmer converters are heated in a soaking pit before rolling, where their characteristics depend on the method of heating.During the heating process a layer develops on the ingots called scale and the purpose of this paper is to develop the necessary control on fuel flow rate to the furnace in order to minimize this scale formation.A mathematical model is obtained for the heating process and the parameters of the model are determined firstly, by simulation of the process on an analogue computer and the parameters determined by trial and error, and secondly, analytically using least square estimation method.The system is then optimized using a performance index which leads to minimization of scale formation. Optimization is also done firstly on the analogue computer, and secondly, analitically using coordinate descent method as a non-linear programming.The results are compared and them a suggestion for their practical implementation is given, also an economical evaluation is made.The Identification Problem.This section deals with the problem of parameter identification of the heating process which is described by a partial differential Eqn.(P.D.E.). Two methods are used:(a) By Simulation of the heating process after describing it as a mathematical problem, then adjusting output results which are as close as possible to the measured one.(b) Analytically by numerical solution of the D.E. describing the process, then estimating the parameters that make this numerical solution approximate to the measured one using least square estimation technique.