Based on the general theory of fractional order derivatives and integrals, application of the Caputo–Fabrizio operator is analyzed to improve a mathematical model of a two-mass system with a long shaft and concentrated parameters. Thus, the real transmission of complex electric drives, which consist of long shafts with a sufficient degree of adequacy, is presented as a two-mass system. Such a system is described by ordinary fractional order differential equations. In addition, it is well known that an elastic mechanical wave, propagating along a drive transmission with a long stiff shaft, creates a retardation effect on distribution of the time–space angular velocity, the rotation angle of the shaft, and its elastic moment. The approach proposed in the current work helps to take in account the moving elastic wave along the shaft of electric drive mechanism. On this basis, it is demonstrated that the use of the fractional order integrator in the model for the elastic moment enables it to reproduce real transient processes in the joint coordinates of the system. It also provides an accuracy equivalent to the model with distributed parameters. The distance between the traditional model and the model in which the fractional integral is used for the elastic moment modelling in a two-mass system, with a long shaft, is analyzed.

A numerical one-step method of average voltage values in integration step, which allows to algebraize the differential equations for electric circuits of electromechanical systems with semiconductor converters, was described in the paper. The method is proposed for the creation of digital power circuit real-time models of electrical systems in hybrid models that combine digital and physical components. Digital models in hybrid systems must continuously function over a long time period in conjunction with physical objects. The indicated method provides stability of mathematical models, and is also effective in the sense of the amount of calculations. The article describes the application of the method of average voltage values in the integration step to create a hybrid model of power generation system for a ship's power plant with diesel generator. The digital component of the hybrid model, in this case, is power conversion system that includes a synchronous generator driven by a diesel engine, while the physical part is real excitation controller of generator with automatic voltage regulator. The research results obtained on the hybrid model and their comparison with the results of the physical experiment at the laboratory plant are presented.

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The interconnection between optimal control theory and the theory of energy-shaping control is described in our paper. For linear and nonlinear systems, the application of the theory of optimal control for the synthesis of parameters of energy-shaping control matrices is demonstrated in detail. The use of a Riccati equation allows us to form an optimality criterion and to synthesize the energy-shaping control system that provides the desired transient processes. The proposed approach was applied to the synthesis of control influences for electric vehicle subsystems, such as a two-mass system and a permanent magnets synchronous motor. The results of computer simulation studies, as well as those conducted on real experimental installations, are given in this paper.

The synthesis of a real-time model of the electric mode of an arc steelmaking furnace is shown. This model is based on the method of medium-voltage and can be used to analyze the impact of the arc steelmaking furnace on the supply network at different stages of the melting process at different control systems of the electromechanical electrode movement system, and to create model-predictive control systems of electrode movement, when control using hardware in the loop technology. To implement the chosen method, the dynamic arc resistance was used. The last was obtained on the basis of the averaged experimentally taken volt-ampere characteristics of the arc. In paper was proposed its approximation as a current function and arc length. The simulation results obtained using the created model for different operation modes of the arc steelmaking chipboard for a system with a traditional regulator of the electrode movement system are demonstrated.