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.

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 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.

Steelmaking is one of the most energy-intensive industries, so improving control efficiency helps to reduce the energy used to produce a tonne of steel. Mutual influences between the phases of an electric arc furnace in available electrode movement control systems cause unproductive electrode movements as a reaction to the redistribution of currents among the phases of a three-phase power supply system due to changes in arc length in one of the phases. The nonlinearity of the characteristics of an electric arc furnace significantly complicates the ability to provide autonomous electrode movement control. The approach proposed in this paper, based on the formation of a matrix of mutual influences with variable coefficients, significantly improves the per-phase autonomy of the electrode movement control system. Nonlinear dependences of the mutual influence coefficients as a function of the current increment in the phase in which the disturbance occurred are obtained. Thus, it is possible to practically eliminate unproductive electrode movements in existing control systems by avoiding the traditional use of a dead zone, which reduces the control quality in the zone of small disturbances. The complex of experiments performed using the mathematical model demonstrate that the mutual influence improves the dynamic properties of the electrode movement system in certain operating modes.

To stabilize the electrical mode of an arc steelmaking furnace in the initial stages of melting, it is advisable to use a high-speed current-limiting system, in addition to the traditional electrode movement control system. This system is implemented by including the primary winding of the furnace transformer choke, controlled by thyristors. The use of such a system, on the one hand, reduces the negative impact of the arc steel furnace on the the power supply network operation and, on the other, affects the operation of the electrode movement system, built on the principle of an impedance regulator. In order to analyze the mutual influences between such systems, a mathematical model for the power supply and control system of the arc steelmaking furnace was created. The developed model can work in real time, which corresponds to the world trends of modern control system synthesis for complex technological objects. In the created model, the work of the combined control system with different approaches to the formation of the control effect in the high-speed circuit and the effect of the combined control system on the power supply system of the ASF are analyzed.