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The article proposes representation of crushing and grinding complex in form of a system with distributed parameters of the reducing function of the processed raw materials size in order to increase the energy efficiency of entire ore preparation process. Despite the fact that many different automated control systems for domestic and foreign production technological process are now used in the ore preparation processes, there is still a need to solve the problems of optimal control of such objects in order to both reduce energy costs and improve the quality of the final product. In terms of energy consumption, grinding processes are superior to crushing processes, so it is necessary to consider the crushing and grinding complex as a whole to increase the whole process energy efficiency. Since the processes of crushing, grinding and classification are purely random and at any time are characterized by transient probabilities, and the crushing and grinding complex occupies a large area and is geographically distributed in space, it should be considered as a system with distributed parameters of raw material size reduction, recyclable. Redistribution of loads between the individual components of this complex in accordance with the current characteristics of processed ore and the state of process equipment allows to reduce the load on the final stage - it is grinding, which in turn contributes to the overall reduction of energy consumption. The peculiarity of this approach is the need for the formation of spatial-temporal controls on basis of spatially distributed control of the object, the use of appropriate feedback signals and regulators with spatially distributed control effects.

The subject of the research is automatic control system modeling features for tensioning of stands roughing group, which takes into account changes in the rolling speed at exit of the previous stand and entrance to the next stand. Control systems for high-speed rolling on section mills are the most critical systems, since the trouble-free operation of rolling mill largely depends on their work. Rolling speed control is understood to mean tension regulation in the roughing group of stands and stabilization of the rolling loop in the finishing groups. The influence of such technological factors as uneven heating of blanks, change in the crimping mode in stands, etc. leads to the appearance of tension or back-up forces, deviation of rolled loop from the specified values. Tension rolling, in contrast to loop rolling, is a stable rolling mode. However, (at significant values of tension in the rolled products) such a rolling mode leads to different thicknesses of the finished product. The loop rolling mode is an unstable mode and is impossible without automatic control systems. Both in the tension rolling mode and in the free rolling mode with a loop, it is necessary to study automatic control systems in order to determine the possibilities of compensating for disturbing influences and obtaining rolled products of the given accuracy. Therefore, the main task of the automatic control system is to maintain the rolling mode with the lowest possible tension. To achieve this goal, direct control of the tension of the rolled strip with modern technical means is rather difficult, and the operation of tension control systems is based on indirect methods of measuring it, and the study of the system efficiency is reduced to modeling the process itself. The developed model consists of three stands and two inter-stand spaces, since it takes into account changes in rolling speed at the exit of previous stand and the entrance to the next stand. It is due to this that adequate simulation results are obtained that are close to the real rolling process. Keywords: automation, rolls, stand, inter-stand spacing, modeling, loop tension, rolling mill, roughing group.

The subject of the article is a variant of an efficient algorithm for synthesizing a dual discrete model and controller for tracking a given trajectory of a dynamic nonlinear, nonstationary black box object, using standard procedures for diagonalizing the state matrix, which makes it possible to simplify obtaining control values in numerical form and reduce the number of calculations. The current article presents one the possible solutions to the problem of regulator synthesis to ensure stable development of a given trajectory of motion of a nonlinear, non-stationary object of "black box" type using the concept of dual control. The task was set to simplify the previously proposed synthesis algorithm for the adaptive control of dynamic nonlinear, non-stationary objects using the example of first-order object of the "black box" type, using standard procedures for the diagonalization of the state matrix. An extended state matrix is the basis for obtaining a control model and predicting the behavior of a nonlinear non-stationary object, which in turn makes it possible to effectively use the concept of dual control. Methods used in the work are based on concept of dual control, nonlinear dynamic models, matrix theory, difference equations. Obtained results of this work consist of the development of a version of a dual nonparametric controller of nonstationary nonlinear processes, which has adaptive properties, does not require knowledge of the physics of functioning of the control object, is presented in the form of a simple algebraic formula that does not contain coefficients that require adjustment. Conclusion. Scientific novelty lies in the application of each interval matrix operator control for the diagonalization of the state submatrix. This operator is used for subsequent calculation of the control action. This approach enables the use of a standard diagonalization procedure using mathematical applications. The results are presented in the form of a final formula that does not require use of matrix operations during control, which makes it possible to simplify the synthesis of the controller using standard mathematical procedures.