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.

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.

The article deals with the application of fractional order desired forms to extend the range of possible fractional controllers adjustment in the synthesis of electromechanical systems loops and to provide better quality of transition processes as compared with integer order controllers. Experimental tests of the fractional order controllers, synthesized by proposed approaches in the control system of frequency converter-induction motor speed, have confirmed the effectiveness in terms of the expansion of adjusting capabilities of PI ^γ D ^μ controller as compared with the classical PID-controller.

From the point of view of the synthesis of control influences, arc steelmaking furnaces are complex nonlinear objects with strongly expressed mutual influences. It has been demonstrated that at a given supply voltage, the distribution of the current values of the phase currents in the quasi-steady-state mode makes it possible to estimate the situation in the arc space of an arc steelmaking furnace and identify the value of arc lengths. This dependence is preserved in transient modes. In order to identify arc lengths from the phase currents, it is proposed to use an approach based on the theory of fuzzy sets. The construction of the fuzzy arc length identifier rule base was carried out in two stages: the first stage used data from quasi-steady-state modes and the Wang–Mendel algorithm; the second stage involved adding a new rule to the database if the activity level of the formed rules was lower than the established level α for the data obtained in the dynamic mode. Further optimization of the parameters of the fuzzy identifier for operation in dynamic modes was carried out using the “back-propagation” algorithm. Based on the identified values of arc lengths, a control system for the movement of electrodes in an arc steelmaking furnace was synthesised. The proposed control system makes it possible to eliminate unproductive electrode movements due to changes in the situation in other phases of the arc steelmaking furnace and simplifies the application of modern methods of synthesising a control system for such complex objects. The results obtained in the mathematical model have confirmed the effectiveness of the proposed control system for the movement of electrodes in an arc steelmaking furnace.

The main advantages of multi-winding (multiphase) induction machines include reducing torque ripple, decreasing rotor harmonics losses, reducing the current per phase without increasing the voltage per phase, reducing the current harmonics of the DC voltage source, and high fault tolerance. The authors propose a theoretical description for the harmonic content of the DC-link current, magnetomotive force, and electromagnetic torque of a multi-winding induction machine (IM), and an account of the interaction of the time harmonics for the power supply and the spatial harmonics for winding functions is presented. The proposed theoretical analysis has made it possible to substantiate supply-winding schemes for the compensation of higher harmonics (6th and 12th in the DC-link current and the IM’s electromagnetic torque) and the improvement of the electromagnetic and electromechanical compatibility of the multi-winding machine, which are justified according to the proposed theoretical description. Further, a schematic solution for the multi-winding induction motor with electronic changing of the pole number is proposed to provide a reduction in speed ripples at low rotation speeds. This decrease is ensured by increasing the number of pole pairs and increasing the frequency of the supply voltage. Mathematical models of multi-winding switch control-based induction machines are developed using the method of average voltages in the integration step for an investigation of electromagnetic and electromechanical processes. It is shown that the developed models are distinguished by high speed of response and accuracy. This is confirmed by the comparative analysis using known methods and models in the Matlab environment, as well as a comparison of the simulation results with the known results of physical experiments. The results of mathematical modeling show that the use of a multi-winding IM with appropriate supply-winding schemes stands to significantly reduce the ripples of the IM’s electromagnetic torque and DC-link current in the case of using six-step voltage source inverters. This makes this type of inverter suitable for use in a frequency-controlled electric drive as an alternative to using a PWM inverter, which has a negative influence on the IM’s state.

The structure of a multiloop system of fuzzy extreme control of modes and optimal stabilization of electric arc furnace coordinates using fuzzy inference systems has been substantiated. A method for calculating integral values of energy efficiency indices is proposed, using which performance curves of electric arc furnace were built. Their analysis showed that fuzzy models of optimal control and control of electric mode coordinates enables comprehensive improvement of indices of electric and technological efficiency of electric arc furnaces and electric power quality.