Convergence Analysis of the Dynamic Accuracy Assessment Procedure for Transducers Used in the Energy and Electromechanical Industry

This paper presents an analysis of the convergence of a numerical procedure used to evaluate the dynamic accuracy of measurement transducers, with particular emphasis on their application in energy and electromechanical systems. The main objective of the study is to assess the effectiveness of a fixed-point algorithm designed to determine test signals that satisfy time and amplitude constraints while maximizing an integral quality criterion of the “energy-optimal” type. The analysis employs numerical modeling of two types of temperature transducers: an NTC-type resistance temperature transducer and a K-type thermocouple. These models are based on a polynomial approximation method, enabling the estimation of the upper bound of the dynamic error—a key parameter in applications involving rapid changes in physical conditions, typical of energy and electromechanical systems operating under variable loads, such as industrial drives, clutches, bearings, and cooling systems, as well as in automation systems, control loops, and diagnostic frameworks. From the perspective of theoretical mechanics, temperature transducers can be modeled as a dynamic system characterized by thermal inertia, whose behavior is governed by first-order differential equations analogous to the equations of motion of a mass in a mechanically damped system. The results are presented graphically, illustrating the algorithm’s convergence behavior and computational stability. The practical application of the proposed approach can contribute to improving the accuracy of temperature transducers, enhancing error compensation algorithms, and optimizing the design of measurement systems in the energy sector and electromechanical industry, as well as in mechanical and electrical systems, especially where fast and reliable measurements under variable thermal loads on machine components are crucial.