Sytnyk O. Methods of mathematical and computer modeling of dynamics of measuring transducers based on integral equations

The dissertation is adressed to solving the scientific and technical problem of creation and development of mathematical and computer modeling of dynamics in a wide class of modern measuring transducers. The aim of research is to increase the efficiency of methods and means of mathematical modelling of dynamic processes in measuring transducers on the basis of application of dynamic models in the form of Volterra integral equations and operators, creating algorithmic bases and software means of their computer realization. As improvement the integral method of mathematical modelling of processes in measuring transducers was introduced, proved and researched. This method involves application of mathematical models in the form of integral operators and Volterra equations. Formation methods of explicit and implicit non-parametric dynamics models of stationary measuring transducers with concentrated and distributed parameters, including macro models, were developed. Identification method of non-stationary measuring transducers is suggested. It is based on the solution of algebraic system, obtained by approximation of integral operator, which has potential high speed and noise resistance. The properties of non-parametric dynamical models are analyzed in the form of integral operators and Volterra equations, which define their functional possibilities in the study of different classes of measuring transducers. The method of numerical solution of integral Volterra equations of the I kind is offered in the incorrect problem of restoring the input signal of measuring transducer with distributed parameters; the method provides a stable solution based on the internal regularization by using the method of model experiments. On the basis of the proposed algorithms for the first time a complex of application programs was developed to simulate a wide class of measuring transducers with the implementation of linear and nonlinear integrated models and their systems. The method of application of the complex for solving specific problems is worked out.A number of the following applied problems were solved with the help of proposed algorithms and developed software: formation of integral dynamic models of measuring transducers of gas humidity, flow rate, angle of rotation, acceleration, losses, pressure, temperature, chemotronic measuring transducers; construction of models of gradient receivers of thermal flows; obtaining by the experimental data of the integral models of gas analyzers, film thermoreceiver, piezoelectric pressure sensor etc. The results of the dissertation are implemented at Cherkassy city REN (regional electric network) PJSC Cherkasyoblenergo (Cherkasy c.), LTD SICAME Ukraine (Kyiv c.) SE (state enterprise) Cherkasystandartmetrologia (Cherkasy c.), PJSC AZOT (Cherkasy c), PJSC Ternopilskiuj radiozavod (Ternopyl radio plant) Orion (Ternopyl c.), LTD Navis-Ukraine (Smila c.), into the educational process of Cherkasy State Technological University.