Multiplicative Approximation Method of Functional Dependencies by Line Segments

Abstract

The article is devoted to the approximation problems of functional dependencies during conversions performed in intelligent measurement devices. Non-linearities are essential parts of most control processes and systems. When using a nonlinear transmitter with a conversion function in measurement information systems used in various fields, it is necessary to perform nonlinear functional conversion operations on numbers in microprocessors/microcontrollers during direct and indirect measurements. For this purpose, various approximation methods are used. The purpose of the approximation is to describe nonlinear functions in a simpler, more convenient way for utilization and calculations, with an insignificantly small loss of accuracy. Existent methods for linearization, although some of them are effective, can be burdensome for implementation in microprocessor-based systems. Here, one of the proposed methods for the approximation of nonlinear functional dependencies by line segments is proposed. In this method, the range of the argument changes in the function is divided into line segments, and the parts of the coordinate system bisector, remaining within the line segments of the function, is swapped to perform approximation. Having involved few simple mathematical operations, the proposed method can be implemented efficiently in microprocessors/microcontrollers to perform approximations in measurement systems.