The object of the dissertation research is the processes in electromechanical systems of cranes and mine skip hoists with electric drives with variable parameters and elastic connections. The purpose of the dissertation research is to increase the accuracy and efficiency of electromechanical systems of cranes and skip hoists with electric drives with variable parameters and elastic connections. During the work on the dissertation research methods were used, which were based on: the theory of automatic control, the theory of control systems of electric drives, the theory of modeling of dynamic systems, the theory of differential equations and methods of mathematical physics. Theoretical results: a method of identification of a mathematical model of one class of linear dynamical systems with variable parameters is proposed, which, in contrast to existing solutions, takes into account the time variability of the moment of inertia of flywheels and the time variability of the traction motor during lifting and lowering. mechanism. By comparative analysis it is proved that the use of the classical equation of dynamics of the electric drive system, which contains a constant moment of inertia and a constant moment of loading, leads to significant errors; for the first time a system mathematical model was synthesized and an algorithm for modeling the process of moving a crane was created, using a synthesized model that, unlike existing solutions, takes into account changes in the parameters of the mathematical model of this process over time due to changes in the inertia of the drive system. and the effect of longitudinal oscillations that occur in the cable on which the load is suspended; on the basis of the synthesized mathematical model of the process of cargo movement by a crane, computer modeling of the dynamics of the electric drive system during acceleration, braking, steady speed was carried out. By comparing the obtained modeling results with the results of experimental studies of the same class of dynamical systems obtained by other authors, the adequacy of the synthesized mathematical models is proved; for the first time the law of optimal control of one class of objects with parameters variable in time and space was synthesized, the realization of which is to achieve such characteristics of the cargo movement process that prevent destruction of both cargoes and sites where these cargoes are installed; It is proved for the first time that the static characteristic of a current transformer is not simply nonlinear with saturation, as previously thought, but nonlinear with initial linear increase and subsequent decreasing section, as a result of which two different values of current in its secondary correspond to the same current. winding, to which none of the scientists who studied the processes in current transformers, previously did not pay attention. The practical results are to develop a law of optimal control of one class of objects with parameters variable in time and space, and to apply it in control systems for electric drives for lifting equipment to achieve characteristics of the process of moving goods that prevent the destruction of both cargo and sites which these loads are installed, because the process of moving the load is carried out without their impact contacts caused by the occurrence of longitudinal oscillations in the cable to which the load is suspended. The obtained results also complemented the programs of such disciplines as "Mathematical methods of identification and optimization of dynamical systems", taught to undergraduate students, and "Methodology and organization of research", taught to master's students. It is these results of the dissertation research, which are aimed at solving specific problems of development and use of equivalent process models in real electric drives of lifting equipment, transferred for implementation in JSC "Khmelnitskoblenergo", "Starokostiantynivsky Forestry", LLC "Shpon Shepetivka" and «Veles-Agro LTD».