In this paper the usage of the artificial neural networks instruments for the positioning systems development and for studying its dynamics are described. The described transition from linear differential dynamic equation to architecture of neural network, which reproduces it, ensures the applicability of functional analogy between the structure of linear neuron and the structure of digital filter. These methods are applicable for the many kind of controlled systems, both the homogenous and hybrid type regarding mixing mechanical, electrical, end other types of parts used. In currently researched systems a good reliability of the simulation results are achieved. The described methods are implemented mostly by means of MATLAB environment with the aid of CAD software.