Computer-Oriented Mathematical Modeling of Multiparameter Converters Using Quadratic, Cubic, and N-Dimensional Interpolation

Abstract

The current stage of scientific and technological progress in all areas of industrial production and management is characterized by the introduction of new information technologies that determine the increased integration of all automated equipment types, from sensors and primary measuring transducers (MT) of a wide range of physical quantities to multi-level production control systems and even entire industries. The presence of an adequate MT model that optimally combines such properties as accuracy, universality of structure, and availability for effective computer implementation is the basis for solving problems of synthesizing MT designs and circuits with specified properties, building economical and productive computing devices as components of control, monitoring, identification, and diagnostic systems. The article considers the problem of creating methods and tools for model support of the design processes of multi-parameter MT of devices for monitoring physical quantities, including the creation of adequate mathematical models of processes in MT, oriented toward computer implementation. Methods of quadratic, cubic, and n-dimensional interpolation of multi-parameter transducers based on the theory of simplexes and barycentric coordinates are proposed. Using theorems, the interpolating quadratic form of n variables in the local barycentric coordinate system is determined, the error of the quadratic interpolation method is estimated, and the type of cubic interpolation polynomial is determined. By selecting the approximation method, optimization of the mathematical description is achieved, which allows reducing the cost of experiments, using effective algorithms for processing measurement information, computer implementation. The practical value of the research in this article is determined by the wide possibilities of technological use of the developed methods, algorithms in computer systems for designing MT, the prospects for the implementation and application of the proposed models and devices in highly efficient multi-level distributed control and management systems, as components of complex integrated control systems for technological processes and production.