In many automatics and mechatronics systems accurate modeling of several physical processes is needed. In power system, one of these is the process of control of angular velocity of power blocks during their connection to parallel operation. This process is extremely dynamic and the response of control system results from continuous changes in many physical parameters (temperature, pressure and flow of the working medium, etc.). An accuracy of modeling this process influences int. al. on: quality of the automatic synchronizer diagnostic tests in the laboratory, as well as the possibility of evaluation of prospects for connection process in the power system, without the automatic synchronizer [. Automatics systems used for research and diagnosis of automatic synchronizers are known in the literature as and simulators [2, . To impose similar to real working conditions, it is required to implement an appropriate models of control systems. One of such models, representative for the larger population of objects, is model of control systems of angular velocity. Currently used models, e.g. [3, 4, 5, , allow to approximate the response of real object, or to impose higher restricted conditions of work, for example: related to the angular acceleration dω/dt, the size of overshoots and decay time of transitional characteristics, while accurate modeling the real working conditions using them is not possible. Furthermore, their use requires knowledge of the (often difficult to access) object parameters and time-consuming selection of manual procedure of certain substitute settings, occurring in these models. To eliminate inconveniences mentioned above, in the paper the proposal and mathematical modeling procedure is presented, which allow to obtain much more accurate transitional characteristics of real objects.