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Electrical drive systems are commonly applied for the mechanisms of precise movement, where having a high-quality position and high-quality speed control is especially valuable. Very often, the mechanical part of these systems reveals resonant properties that are related to the limited stiffness of the interconnection between subsequent parts of the mechanism. In most cases, this sort of system may be described as a model of several linked masses. If only the structure of the mechanical part is known and the corresponding parameters are constant and identified, the demanded control quality may be obtained using a properly tuned ADRC or PID controller equipped with appropriate anti-resonance filtration. However, if the parameters of the mechanical part are variant, adaptive control may be considered as a solution. In this paper, artificial neural network (ANN) is considered to be a speed controller and its training method assures adaptation to the unknown mechanical parameters. The paper is particularly focused on a three-mass system, which possesses, due to its structure, two resonant frequencies. The unique property of the analyzed system is the application of drive units at both ends of the system, so that the controller has the ability to influence the resonant system from both sides. The coordination of the drive unit is performed by the aforementioned ANN, from which two outputs affect the drive units independently. The derivation of the mathematical model is followed by its implementation in a computer simulation and finally the evaluation in a dedicated laboratory setup, the construction of which is also presented in the paper. [ABSTRACT FROM AUTHOR]