Application of Duhamel's convolution integral in computer measurement systems

Abstract

The paper is a new approach to the Duhamel's convolution integral. It contains a brief description of the Duhamel's convolution integral and an overview of applications of this integral. The scientific novelty presented in the work is the original algorithm for determining the frequency characteristic, together with its mathematical justification as well as with hardware and software implementation. The proposed algorithm was used in computer measurement systems enabling the determination of Bode and Nyquist characteristics of objects used in automation. The measurement system was built by the authors on the basis of the proposed algorithm. Measurements were carried out using it. During the measurements of the selected automation object, actual results were obtained and referenced to theoretical results. Then their correctness was assessed using the theory of measurement errors. In this way, the correctness of the mathematical considerations concerning the application of the Duhamel's convolution integral in computer measurement systems enabling the determination of the frequency characteristics of objects used in automation was confirmed.

High-level noise load identification based on Chebyshev polynomial piecewise fitting

“…At present, load identification is mainly divided into two categories : time domain and frequency domain [1] . One of the main research directions in the time domain is based on the Duhamel integral [5][6] . The discrete system equation is obtained by discretization using Duhamel integral.…”