CHOICE OF THE OPTIMAL CONTROL STRATEGY FOR THE DUPLEX-PROCESS OF INDUCTION MELTING OF CONSTRUCTIONAL IRON
To find effective control of the duplex process of induction melting in conditions of uncertainties, a method was suggested that made it possible to obtain optimal controls for both stages: melting and thermal treatment.
It is shown how the search for an optimal melting control strategy can be performed using the theory of statistical games. At the same time, it is selected which of the melting regimes will be the best with the existing provision of the shop with charge materials. The costs of melting are the total costs, consisting of:
– costs for the selected technological mode of melting (including costs for materials),
– costs from the potential rejection of castings due to the non-conformity of the chemical composition of the alloy to the specified – due to the incorrectly chosen melting mode,
– costs from the downtime due to the fact that the necessary amount of metal from the furnace is not delivered to the conveyor.
The choice of an optimal control strategy in accordance with the proposed procedure can remove uncertainty in the evaluation of input process variables if they are taken as indicators of the charge quality.
To find the optimal control at the stage of the heat treatment, a multialternative description of the final state is proposed on the basis of solving the problem of ridge analysis. This makes it possible to remove the uncertainty in the estimation of the final state, which allows a lot of optimal solutions in the sense of achieving a given quality. It is shown that such approach makes it possible not only to synthesize the optimal controller of the temperature regime on the basis of an analysis of the system of differential equations describing the control object, but also the application of the Pontryagin maximum principle to search for optimal control of the thermal treatment.
The proposed method allows to determine the optimal control in the sense of stabilization for a given process parameter of the duplex process of induction melting. The resulting solutions form the necessary logical conditions for the logic control unit for the control system of the duplex induction melting process.
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