The topic of hierarchical control of technological machines is one of the most relevant in mechanical engineering technology. The most difficult issue in this area is the organization of interactions between different control levels, on the one hand, and the choice of automatic control methods for each of these control levels (control by deviation, control by disturbance, mixed control, etc.), on the other. In this article, in relation to machining technology, a method and corresponding device are proposed that make it possible to implement the control of cutting force parameters (axial cutting force and cutting torque) in an automatic control system for the deviation of cutting torque by changing the axial cutting force (lower level of control). The lower-level control ensures the required quality of the surface layer (surface integrity) of the machined parts. At the same time, the required dimensional accuracy of parts is ensured at the upper level of control, which is implemented by the CNC system of the machine. At the upper level, automatic control is carried out based on the deviation of the kinematic parameters of the movement of the working parts of the CNC machine (acceleration, speed, displacement). Control switching from upper to lower level and back is carried out without using a spindle linear axial movement sensor. Instead of this expensive sensor, a limit switch (a closed and opened pair of contacts) is used, which fixes the lowest axial position of the spindle (and cutting tool). Based on the signal of closing the specified contacts of the limit switch, a transition from the lower control level to the upper one is carried out. Thus, the upper-level system operates only when these contacts are closed, and the lower-level system operates only when they are open. In relation to the upper-level system, the lower-level control system implements the control “by disturbance” principle, also known in control theory as the “disturbance compensation principle”.