Browsing by Author "Tryputen, Maksym"
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Item The Generalized Chaotic System in the Hyper-Complex Form and Its Transformations(Springer, Cham, 2022) Voliansky, Roman; Volianska, Nina; Kuznetsov, Vitaliy V.; Tryputen, Mykola; Kuznetsova, Alisa; Tryputen, MaksymENG: The paper deals with the development of the mathematical backgrounds to design the novel chaotic systems by transforming existent ones. These backgrounds are based on using well-known shift, rotation, and scale transformations and we offer using hyper-complex numbers to simplify these transformations and represent the transformed chaotic system by using the one 1st order ordinary differential equation. In such form all well known, newly discovered and unknown chaotic systems have the similar mathematical models that are differs only by used nonlinear function of hyper complex variable in the right hand expression. That is why the consideration chaotic system dynamic in the hyper-complex domain allows us to simplify initial system definition as well without applying any transformations. This fact simplifies mathematical definition of chaotic systems and their modeling and simulation. The right-hand expression of the transformed equation in this case are defined as the combination of transformation hyper-complex numbers and source system nonlinearity which is given in the hyper-complex domain. We offer to use variable transformation factors to improve the performance of the considered chaotic system. Since the above-mentioned variable factors can be produced by other chaotic systems, we suggest designing the novel chaotic system by combining existed ones with the linear transformations. As an example, we consider the transformation of the well-known Lorenz system and show the differences between the source system and target one.Item Improving the Reliability of Simulating the Operation of an Induction Motor in Solving the Technical and Economic Problem(Springer, Cham, 2020) Tryputen, Mykola; Kuznetsov, Vitaliy; Kuznetsova, Alisa; Tryputen, Maksym; Kuznetsova, Yevheniia; Serdiuk, Tetiana M.ENG: The article is devoted to the control of the statistical laws of linear voltages reproduced on a computer during computational studies on an energy-economic model when solving the problem of choosing protection tools for induction motors operating in workshop electric networks of industrial enterprises with low-quality electricity. Simultaneous and continuous estimation of average values, variances, autocorrelation and cross-correlation functions of harmonics of linear voltages is based on the adaptive approach. The article presents mathematical expressions for correcting the values of statistical quantities with the accumulation of information and proposes structural schemes for a comprehensive analysis of the results of reproduction of random variables and functions on a computer. The results of checking the values of the average values and dispersions of six harmonics of simulated linear voltages supplying an induction motor with a power of 7.5 kW are shown for the conditions of the rolling shop No. 1 of Dneprospetsstal LLC.Item Mathematical Model of Dynamics of Homomorphic Objects(Petro Mohyla Black Sea National University, Mykolaiv, 2019) Kuzenkov, Olexandr; Serdiuk, Tetiana M.; Kuznetsova, Alisa; Tryputen, Mykola; Kuznetsov, Vitaliy; Kuznetsova, Yevheniia; Tryputen, MaksymENG: Abstract. The paper concerns topical problem of mathematical modeling of dynamics of heterogeneous groups with a logistic function as a basic one. Joint use of mathematical models of biological systems and computer-based simulation makes it possible to minimize time and save material resources while determining general tendencies of subpopulation progress; and to forecast state of the system as well as possible consequences of artificial intervention in the environment. Among other things, it concerns forecasting of genetic abnormalities. The paper proposes a model of dynamics of progress of a population consisting of n subpopulations. The model is represented in the form of differential equations with transition coefficients within their right sides. The transition coefficients mirror the share of species getting from ith subpopulation to jth one. The proposed system is not Voltairian one since its phase trajectories may cross coordinate axes. It has been proved that the system of differential equations is degenerated in the neighbourhood of equilibrium points. Analysis of the system of differential equations for n=2 has demonstrated a potential for three bifurcations. It has been proved that nine bifurcation types are possible for n=3. Numerical computer-based experiments have shown that the proposed model is stable as for the disturbance of its coefficients, and the obtained characteristics of the degenerated system are close to real ones.Item Model for a Direct Torque Control System of an Alternating Current Electric Drive for Urban Transport Rolling Stock Tasks(Springer, Cham, 2022) Stopkin, Vasyl V.; Tryputen, Mykola; Nikolenko, Anatoliy V.; Kuznetsov, Vitaliy V.; Tryputen, MaksymENG: A mathematical model has been developed in the paper of the direct torque control (DTC) system of an alternating current (AC) electric drive for the tasks of the urban electric transport rolling stock, as an alternative to the existing types of frequency control of an induction motor, taking into account its relevance, principles of operation and causes of occurrence. During the research on the mathematical model of direct torque control of an induction motor on the MATLAB platform, its main disadvantages have been revealed, which limit the scope of its application. The main task of the DTC system is to identify the stator flux linkage, which is solved by integration with a certain accumulation of errors. The source of accumulated errors is the inaccuracy when determining the stator active resistance and its change during the induction motor operation. The DTC system is characterized by the disadvantage of torque pulsation occurrence and rotor speed fluctuations at low loads. The main advantage of the DTC system has been determined – high static and dynamic speed accuracy. The results of mathematical modeling and the presented sequence of studies are of practical value in the development and adjustment of complete electric drives with a DTC control system for railway transport mechanisms. New is a technical solution that acts as an alternative to a complex vector control system - this is the use of the DTC system for the tasks of the rolling stock of urban transport.Item One Approach to Quasi-Optimal Control of Direct Current Motor(IEEE (Institute of Electrical and Electronics Engineers), 2019) Tryputen, Mykola; Kuznetsov, Vitaliy; Serdiuk, Tetiana M.; Kuznetsova, Alisa; Tryputen, Maksym; Babyak, Mykola O.ENG: The article presents the calculation of the transfer function of the DCM-30-N1-0.2 micromotor DC, obtained a transcendental system of equations for determining the duration of the quasi-optimal control intervals and the dependence of the first control interval on the specified overshoot. The obtained dependence can be used in the engineering methodology for the synthesis of quasi-optimal control and the choice of actuators of the automatic control system.