The article describes an experimental model of stabilization of a mechanized system. The following are shown: a skate; an element of the program code; an algorithm for stabilizing a proportional-integral-differential controller (PID). The experimental model uses the calculation and adjustment of the regulator according to the Ziegler-Nichols method. For the case of applying the neural network approach to the search for equilibrium, the Hopfield neural network is used. The technology of calculating the balancing of the values of the coefficients: proportional, integral, differential components are described. The design of the rolling system is described. The experimental model is designed to identify the balancing range of the rolling system of small-diameter balls. The experimental module balances the ball at a distance of 4.5 to 7 cm (SW-range). The shortcomings of the experimental model of stabilization of the mechanized system are revealed. The analysis of experimental studies of spacecraft stabilization is carried out. It is determined that it is advisable to use the mathematical tools of the sixth-order Butterworth polynomial in the training of a neural network. Complex neural network calculations make it possible to calculate the stabilization coefficients of the spacecraft when the coordinate system does not coincide with the axes of inertia. An overview of the authors ' research on the use of intelligent quality control systems for the production of medicines is given. An overview of neural network solutions for stabilizing the turning angle of high-speed cars is given. The expediency of selecting the stabilization coefficients of a proportional-integral-differential regulator by a trained neural network for various rolling ranges is proved.
