# Optimal Control of Electric Smelting Process Copper Concentrate

In accordance with the decomposition process control of electric smelting of copper concentrates selected tasks of control of technological and energy regime of the process. The solution of these problems is connected with the development of the mathematical description of the relevant object of management, selection and justification of criteria of optimal control and restrictions on the variables of management and the state of the object, the mathematical formulation of the problem of optimal control, the choice of method the decision and develop a flowchart of algorithms of control, definition of structure and software of the control system.

The purpose of the mathematical model of technological mode is to establish the dependencies between the input and output of qualitative and quantitative variables electric smelting process: between quantity and chemical composition popravljeno shty and the quantity and chemical composition of the products. The possibility of considering the influence of the Converter slag is due to the inclusion in the model of balance equations with coverage Converter redistribution.

A necessary condition for solution of research tasks and optimal management of such complex object, as electroplasma, is his mathematical description as a set of relations that describe the quantitative relations between the physical variables of the process (chemical compounds, costs, temperature and so on); generalized technical-economic indicators characterizing the quality of the process (performance, cost, the degree of extraction, unit costs of materials and energy, specific losses and the like); the variables are not available direct control, and their indirect indicators (model of indirect control), extrapolated values of variables in discrete moments of time (predictive models).

The problem of determining the optimal chemical composition of the pile is formulated as follows: find the chemical composition of the pile, minimizing the concentration of copper in dump slags electric furnace Department, with restrictions on quality indices of products of fusion - matte and slag. Optimization of chemical composition of the pile is the task of top-level and solved once in 4-6 days (for the period bookmarks).

Mathematical model of the problem of determining the composition of the stack installs the dependencies between the input and output of qualitative and quantitative variables technological complex "shihtopodgotovki - electroplate" - between the quantity and chemical composition popravljeno charge and quantity and chemical composition of the products. The possibility of considering the influence of the Converter slag stipulates the inclusion in the model equations with coverage Converter perdel. Mathematical model of technological process of electric smelting constructed in the class of models deterministic structures, taking into account the carrying ratios for individual substances and products melting.

The solution is based on the mathematical models of complex " charge - blister copper" taking into account the influence of BOF slag that defines the relationship of quality characteristics smelting products for the separation with the charge, and is formalized as a problem of nonlinear programming. Mathematical statement of the problem of determining the optimal chemical composition of the pile charge includes: the criterion of optimization, mathematical model of the process of electric smelting and limitations. As an optimization criterion in the determination of the optimal chemical composition of the pile accepted the content of copper in otvorenom the slag, which is a function of the number popravljeno charge and Converter slag content in otvorenom slag CaO, SiO and Fe.

In the result of the work describes the process of electric smelting of sulphide copper concentrates on Stein in ore-smelting electric furnaces. Produced calculations of material and heat balance of the process. An analytical review of the determination of the optimal composition of the pile of copper concentrates produced by technological processes of electric smelting, a mathematical model is constructed for systems management processes blending and melting of copper concentrate smelting ensure the reduction of losses of metal and energy consumption.

The optimal management of energy regime of electric smelting process based on the use of a mathematical model constructed in the class of experimental and analytical models and descriptive in relation to the consumption of electric power (output variable) with quantitative and qualitative characteristics downloads, phase voltages, and attenuation of electrodes.

Conclusions: the characteristic of the process of melting of copper concentrates as a management object. The analysis of existing practice management process, the development of mathematical models and control systems of processes of melting. Taking into account features of the object of management, modern approaches and methods for mathematical description and control of technological processes selected principle, and the generalized structure of the management of the smelting process, formulated the problem of research. Implemented mathematical modeling of energy regime of the smelting process.

The structure of the tasks of process automated control system of electric smelting of copper concentrates with respect to the system of relations of the process in the structure of copper-smelting production. Defined management objectives and levels in the control system, formulated preliminary management tasks, reflecting the interdependence of tasks in the system.

The study of the basic technological regularities of the process of electric smelting copper sulphide concentrates, which revealed that the qualitative indicators of the process of electric smelting mainly determined by the ratio of components in the mixture, the cost pyrite concentrate, limestone.

Formulated substantive and formal statement of the problem of determining the optimal composition of the charge, the optimal distribution of material flows, optimal control of technological and power mode of the furnace.

The selected method of parametric identification of a control object and the main stages of development of mathematical description. With account of the kinetics of chemical reactions, processes of heat exchange interacting substances developed basic mathematical model of the process of conversion.

The mathematical model allows to:

- to carry out the calculation of basic temporal and weight characteristics of the Converter heats when drafting the plan-schedule of Converter section;

- selection of operational parameters in the Converter melting;

- to simulate the Converter redistribution in the study and the adjustment of the control algorithm area and a separate fuse;

Built semiotic model of Converter Department, which is a set of predicates, which provides a choice of governors impact on the Converter Department for each current market condition;

The algorithm of forming of schedule of work of the Converter Department, which together with the semiotic model forms the system of formation of the optimal schedule of work of the convective section.

Development of algorithm of operative control of Converter Department involves the testing of the control algorithm in conjunction with the control object, in this regard, built simulation of the Converter Department of metallurgical plant.

Imitation modeling of management system showed the efficiency of the system and the possibility of a significant increase of efficiency of technological processes of metallurgical plant during its implementation.

Considered meaningful and mathematical formulation of the problem of control of the heat, and the algorithm of formation of the optimal schedule of the heat.