ВОПРОСЫ АНАЛИЗА УСТОЙЧИВОСТИ, УПРАВЛЯЕМОСТИ И НАБЛЮДАЕМОСТИ ТОНКОГО ПОМОЛА В ПЛАНЕТАРНОЙ МЕЛЬНИЦЕ

The aim of this scientific work is to verify the adequacy of the mathematical model of the designed control system in relation to the physical characteristics of the controlled object, namely the process of fine grinding in a planetary mill. A reliable model serves as the foundation for the development of an effective automatic control system capable of ensuring high accuracy and stability of the technological process. The study analyzes such key properties as controllability and observability, which determine the potential capabilities of the control system under given operating conditions. These characteristics are closely related to the stability and predictability of system dynamics, which is of fundamental importance when working with technogenic raw materials, such as copper-smelting slags. For the analysis, observation methods, theoretical analysis and synthesis, as well as MATLAB and Simulink mathematical modeling tools were used, allowing the reproduction and study of system behavior in various modes. Special attention is paid to the behavior of the system under changes in the characteristics of the controlled process-in particular, when varying the particle size of the ground material at the output. During the experiments, optimal parameters were determined that ensure stable and predictable system response to external disturbances. This confirms the practical applicability of the model for building modern automated grinding process control systems. The obtained results have not only theoretical but also practical significance. They can be used to improve control algorithms, increase the reliability of equipment operation, reduce energy consumption, and enhance the recovery of valuable components from technogenic raw materials. Thus, the presented research lays the foundation for further developments in the field of intelligent control systems and sustainable resource management.