SYNTHESIS OF CLOSED-LOOP CUTTING POWER STABILIZATION SYSTEMS FOR MILLING MACHINES WITH OPTIMAL DYNAMIC AND STEADY-STATE CHARACTERISTICS

Abstract

The article considers the relevant scientific and applied problem of synthesizing closed-loop systems for automatic stabilization of milling machine cutting power with optimal dynamic and static characteristics. Improving the efficiency of material machining processes requires the creation of high-precision control systems capable of maintaining a specified cutting power level under conditions of changing technological parameters, non-uniformity of the workpiece material, and random external disturbances. Stabilization of cutting power makes it possible to increase machining productivity, improve the quality of the machined surface, reduce energy consumption, and extend the service life of the cutting tool.

The paper proposes an approach to the synthesis of closed-loop control systems based on fractional-integral controllers with an increased astatism order. To evaluate the quality of transient processes, a special optimization criterion is formulated, aimed at achieving maximum speed of response while simultaneously limiting overshoot within a specified corridor of permissible deviations. Unlike traditional mean-square-error criteria, the proposed functional takes into account not only the magnitude of the error but also its position relative to the admissible region, which ensures transient responses without significant short-term overshoots and undershoots.

The search for optimal system parameters was carried out using genetic algorithms implemented in the MATLAB environment. The use of an evolutionary approach made it possible to avoid the local optimization problems typical of gradient-based methods and to determine globally optimal values of the transfer function parameters for a wide range of fractional integration order values. A table of normalized optimal tuning parameters was obtained, and the regularities of their variation depending on the astatism order of the system were established.

Based on the obtained results, fractional-integral controllers were synthesized for the cutting power stabilization system. Several controller structures based on the principles of fractional integration and differentiation were considered. It was shown that the use of fractional-order controllers makes it possible to form desired transient characteristics with significantly better quality indicators compared to classical automatic control systems.

Studies of the dynamic operating modes of the system during start-up, as well as under abrupt load changes simulating variations in the depth of cut, were carried out. The simulation results showed that the proposed controllers provide rapid disturbance rejection and a significant reduction in cutting power deviations. It was established that, when a load change causes a 50% jump in cutting power, the system is capable of reducing the amplitude of the transient deviation from approximately 200 W to 19–39 W depending on the selected astatism order. The transient process duration does not exceed 0.02 s.

Particular attention was paid to the analysis of the properties of systems with a fractional astatism order greater than unity. It was shown that such systems provide a gradual reduction of the velocity error under a linear change of the reference signal, which is an important advantage for the stabilization of technological parameters of the cutting process. It was proved that increasing the astatism order contributes to the reduction of dynamic errors, although it simultaneously complicates the controller structure. Based on the research results, it is recommended to use astatism order values within the range of 1.7–1.8 as a compromise between control accuracy and implementation complexity.

The practical significance of the obtained results lies in the possibility of applying the developed synthesis methods in the creation of modern automatic control systems for metal-cutting machine tools, robotic manufacturing complexes, and other technological installations requiring high-precision regulation of process energy parameters. The proposed approach ensures improved machining quality, technological process stability, and efficiency of production equipment utilization.

Keywords: cutting power, milling machine, automatic control system, fractional-integral controller, fractional order, astatism, genetic algorithm, optimization, transient process, stabilization of technological parameters, MATLAB, electric drive.