This study addresses the issue of forecasting active and reactive power consumption at a mining and processing plant, aiming to improve the efficiency of energy resource management. It explores existing approaches to modelling and analysing electricity consumption, including methods for forecasting active power to accurately assess the energy needs of industrial enterprises, as well as methods for estimating reactive power required to compensate for reactive components and stabilize grid parameters. Using real electricity consumption data from an industrial enterprise, the completed training and research demonstrates the potential to forecast energy consumption for the next 24 to 48 hours using artificial neural networks with nonlinear autoregressive architecture. It also provides rationale for pre-processing initial data to enhance forecast accuracy. These approaches contribute to reducing capital and operating costs, improving the reliability and stability of energy systems, and optimising operating efficiency.

This article is an integrated study conducted to develop a learning model which would make it possible to identify the students’ changes of knowledge, abilities and skills acquisition over time as well as the formation of special features of their individual background. Authors have justified the application of the cybernetic model based on fractional equations for the description and evaluation of the student’s learning process. Learning is dealt as a transformation of young people’s knowledge, abilities and skills into a complex background, which envisages its implementation in the future professional activity. The advantage of the suggested model is better approximation characteristics which allow the consideration of a wide range of factors affecting the learning process including the youth’s neurodynamic and psychological nature. The research has employed both mathematical modeling methods and psychodiagnostic techniques (surveys, questionnaires). As a result of the findings, students who assimilate the content of teaching information and form personal experience in different ways have compiled different groups; the learning curve constructed on the basis of the heterogeneous differential equation of second order with integer powers has been compared with the set of models with equations of fractional order of aperiodic and fractional power components. The prospect of the issue to explore is the improvement of the suggested model considering special characteristics of cognitive processes aimed at the formation of an individual path of the student’s learning.

Control systems with a fractional order which provide better dynamic and static indicators for many technical objects in comparison with systems with integer order of astaticism were studied. Based on the analysis of frequency characteristics, transient processes and a modified criterion for quality assessment, optimal relationships between parameters of the desired transfer function were obtained. Normalized transition functions of closed systems with the order of astaticism from 1 to 2 were presented with overregulation less than 2...5 % on the basis of which parameters can be chosen and the controller structure determined. The process of stabilizing cutting power was analyzed for a milling machine as an example of the systems with nonlinear parametric and structural dependences in control and perturbation channels. It was shown that fractional integral-differentiating controllers make it possible to provide the order of astaticism from 1.3 to 1.7 and permissible level of overregulation in a wide range of external perturbing influences. A method for approximate calculation of fractional integrals based on the approximation of the highest coefficients of expansion in a series of geometric progressions was developed. It provides reduction of the memory capacity required to store the coefficient arrays and the history of the input signal and requires significantly less CPU time to calculate the controller signal. For example, for controllers based on the Intel® Quark ™ SoC X1000 or FPGA Altera Cyclone V, the quantization period is 6...15 μs and several milliseconds for Atmega328. This makes it possible to implement fractional integral-differentiating controllers based on widely used modern processors and apply fractional-integral calculus methods for synthesis of high-speed automatic control systems. The proposed methods can be used in the control of the objects both with fractional and integer orders of differential equations.

Synthesis and implementation of fractional-order controllers in a current curcuit of the motor with series excitation

Application of high-voltage frequency converters is one of the most prospective trends in the development of current powerful electric drives, i.e. in high-speed trains. In terms of such converters, a multilevel cascaded H-bridge converter is becoming the most widespread one owing to its increased reliability, survival in terms of one or more damaged cells, and quick repairability due to its modular structure. The research proposes a control method, which provides maximum possible linear voltage in case of one or several damaged cells owing to the shift of zero point and turning of phase voltages. It is also demonstrated how turning angles of phase voltages should be set to preserve spatial position of the linear voltage vectors which provides the least complicated electromagnetic transients in terms of nominal rotation frequency; in case of low or middle frequencies, damage of the cells may have no effect on the motor operation. Fast algorithm to calculate turning points of phase voltages is proposed; the algorithm may be applied in the industrial microprocessor control systems. Algorithm of the operations, which provides implementation of the method, is described.

This work is aimed at developing a stand for tuning the fuel system of an internal combustion engine based on two electromagnetic retarders connected to the driving wheels of a car to simulate a load, and a microprocessor-based torque control system for each brake. In accordance with the terms of reference from the specialists of the automotive service center, such a stand should provide two main modes of operation: (1) stabilization of the speed of the drive wheels in the entire range of loads (fuel supply); (2) engine acceleration and deceleration according to linear tachograms in the range from minimum to maximum speed to determine the dependence of engine power and torque on speed. The purpose of this research is the synthesis of controllers, testing, the choice of the structural scheme, and the parameters of the control and data processing system in the stand for the precision tuning of internal combustion engines. Based on a preliminary analysis of the system, taking into account the mechanical connection of the wheels through the main gear and the car differential, the nonlinear dependence of the electromagnetic torque on the current and retarder speed, and subsequent experimental results, we obtained two types of controller—a third-order aperiodic transfer function and a fractional aperiodic transfer function of order 1.6. This made it possible to synthesize a family of controllers that ensure the operation of the stand in the required modes: synchronization of wheel speeds during engine acceleration; stabilization of the reference speed when the engine torque is changed from minimum to maximum due to fuel supply; measurement of the maximum power and torque of the internal combustion engine during the formation of a triangular tachogram with a given acceleration to compensate for the dynamic component of the torque due to mechanical inertia. The system with the PID controller configured in MATLAB in the “Tune” package has the best performance, but the smallest overshoot and the best dynamic accuracy are ensured by the PIDI^γI^µ fractional–integral controller, where the system is characterized by a fractional order of astaticism 1.6. Such a controller for each electromagnetic retarder serves as the basis of the microprocessor-based control, data acquisition, processing, graphical display system, and will also be used to develop a similar bench for tuning four-wheel-drive vehicles.