FEATURES OF THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF THE MODEL ELECTROMECHANICAL SYSTEMS IN SOFTWARE ENVIRONMENT MATLAB
Journal Title: Електромеханічні і енергозберігаючі системи - Year 2017, Vol 2, Issue 38
Abstract
Purpose. The scientific work is devoted to the research of electromechanical systems by means of their modeling using the software environment Matlab. Originality. The features of obtaining a numerical solution in the software environment Matlab are considered. The emphasis has been placed on the features of mathematical models, taking into account for energy converters and methods for their numerical integration. Methodology. The features of modeling and the need to take into account the fundamental laws of electrical engineering of induction motors with parametric dissymmetry are shown, that are not automatically performed. For nonlinear systems, as an example of a two-mass system of a DC electric drive, quantitative and qualitative differences are shown in the solutions, that occur when the numerical method and its parameters are incorrectly chosen, and taken into account nonlinearities and real energetic parameters at the converter output in models. For test differential equations influence of the relative and absolute errors on qualitative character and accuracy of the received solution is analyzed. The character of solutions for electric drive systems with a discontinuous right-hand side is analyzed. The research of solutions of systems of differential equations is carried out, using a method with a constant step of integration for different values of the step, and with variable step - for different values of the calculation accuracy. Results The choice of the integration method must be evaluated from the point of view of applying it for a given system of differential equations. In many cases, much better than other methods, is the classical fourth-order Runge-Kutta method, which provides a given accuracy up to the 5th order inclusive. For systems with discontinuities in the right-hand side of differential equations, the feature of the numerical solution is shown in change of period length of the cyclic solution and step-by-step offset along a numerical axis, reducing thereby solution period length. The result of shift practically does not depend on calculation accuracy. Practical value. General recommendations are presented to reduce the errors, that can arise in solutions when applying universal mathematical packages for modeling. For non-linear systems, if possible, it is necessary to use methods with a constant step of integration. For systems with discontinuous nonlinear functions, stable solutions can be obtained by methods with a constant step of integration with a preliminary estimate of the step size. In a research the general methods of the theory of the electric drive, electrical engineering and mathematical modeling in packet Matlab were used.
Authors and Affiliations
Oleksii Petrovych Chornyi, Evgeniia Burdilna, Oleksandr Romanov, Valerii Kostiantynovych Tytiuk, Olexander Pozigun, Аbdelmajid Berdai
Keywords
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