Dynamic Design of Optimal Stochastic Stabilization System of Cutting Power on a Band Saw Machine

Abstract

The article is devoted to the development of methodological foundations for constructing an optimal system of stochastic stabilization of cutting power based on the results of structural identification of models of the dynamics of the system '' woodworking machine-cutting process '' and uncontrolled disturbance. In order to solve the problem of structural identification of the '' woodworking machine-cutting process ' system and the disturbance acting in the process of wood-cutting, the article proposes a special technology, the use of which made it possible to determine the transfer function of the '' woodworking machine-cutting process '' and estimate the spectral density of the disturbance acting during the processing. It has been established that when the physical and mechanical properties of wood and the state of the cutting tool change, the structure of the transfer function and spectral density does not change, but only the parameters change.As a result of solving the synthesis problem, the structure and parameters of the optimal controller are determined, which ensures the specified quality of the processed surface with minimal energy consumption. To assess the quality of control, it is proposed to use a quadratic criterion, which is the sum of two weighted variances of the stator current deviation of the main motion motor (characterizes energy costs) and the variance of the feed drive speed control signal.Studies of the robust stability of the optimal system with the obtained controller under the influence of unstructured disturbances made it possible to determine the class and estimate the maximum norms of unstructured disturbances at which the system maintains stability and a given control quality. The use of the proposed approach to the construction of an optimal system of stochastic stabilization of cutting power makes it possible to achieve a reduction in energy costs by 12% for a given quality of the processed surface by increasing the stabilization accuracy by two orders of magnitude.