Методи математичного та комп’ютерного моделювання динаміки вимірювальних перетворювачів на основі інтегральних рівнянь

Abstract

Thesis work solved the problem of scientific and technical creation and development of mathematical and computer modeling of dynamics of a wide class of modern measuring transducers. As improvements, the cumulative method of mathematical modeling of processes in the measuring transducers is suggested, grounded and examined, which consists in the application of mathematical models in the form of operators and Volterra equations. Methods for formation of explicit and implicit nonparametrical models of the dynamics of the stationary measuring transducers with concentrated and distributed parameters, including macromodels are developed. The properties of nonparametrical dynamic models in the form of integral Volterra equations are analyzed, that determine their functionalities in the study of various classes of measuring transducers, as well as features are formulated that influence the choice of methods and the development of algorithms for the numerical solution of equations and creating software for their computer realization. Algorithmic fundamentals of fast computing processes of implementation of integrated models are developed that are based on the account of the properties of separable nuclei. The method of formation is developed based on two-dimensional transient features of integrated dynamic models of non-stationary measuring transducers with concentrated and distributed parameters. The method of identification of non-stationary measuring transducers is suggested based on algebraic system solution, obtained by approximation of the integral operator that has potentially high performance and is interference-free.