Development of the method for creating explicit integral dynamic models of measuring transducers

Alexander Sytnik,Konstantin Klyuchka,Sergey Protasov

doi:10.15587/1729-4061.2017.111444

Abstract

Increasing requirements to measuring transducers lead to the need to improve and propose alternatives of their mathematical description. The application in this case of differential equations of various types testifies to great computational complexity of the given problem statement. In this regard, constructively relevant are the methods for creating integral dynamic models of measuring transducers that enable expansion of the tools for computer simulation. The method considered in present paper implies determining a pulse transient characteristic and leads to the formation of the operators (cores) of measuring transducers in the form of integral mathematical dependences, that is, explicit integral dynamic models. The method of obtaining an analytic expression of the pulse transition function of measuring transducers with lumped parameters is represented as a solution to the homogeneous differential equation that corresponds to the specified non-homogeneous differential equation. This technique is easily illustrated on the examples of measuring transducers of the first and second order. The principle of determining a pulse transient characteristic for measuring transducers with distributed parameters by the assigned equations in partial derivatives is the same as for the case with lumped parameters.

Highlights

According to the systems approach, widely applied for examining many classes of objects, measuring transducers (MT) are the devices that serve for the perception and primary conversion of information on a physical magnitude to be measured [1,2,3].Dynamic models of stationary and non-stationary measuring transducers are typically very different
The reaction of stationary MT does not depend on the moment of application of the measured impacts, and depends only on the difference between the current time and the moment of application of the measured impacts
We shall note that integral dynamic models (IDM) have a number of such positive attributes as high universality

Summary

Introduction

According to the systems approach, widely applied for examining many classes of objects, measuring transducers (MT) are the devices that serve for the perception and primary conversion of information on a physical magnitude to be measured [1,2,3]. The inputs of measuring transducers with lumped parameters can be represented by points Dynamic properties of these MT are typically described by ordinary differential equations (DE) [5, 6]. The inputs of measuring transducers with distributed parameters are continuously distributed along a certain line or a surface Dynamic properties of such MT are most often described by DO with partial derivatives or, in a generalized form, by functional equations. We shall note that IDM have a number of such positive attributes as high universality (the structure of the model is unchanged for different classes of MT; the properties that are assigned by a single function ‒ the core of the integral operator).

Literature review and problem statement

The aim and objectives of the study

Conclusions