Selected issues of the fractional calculus for analysis of dynamic properties of measuring transducers used in transportation facilities

This paper outlines the use of the fractional calculus for dynamic measurements while describing dynamic properties of measuring transducers, which the authors consider to be an original and unique achievement. The aim of this paper is to investigate how models of accelerometers based on the fractional calculus notation convey their dynamic behaviour in comparison to models represented by differential equations of integer orders and to the processing characteristics of their real counterparts. This paper presents state-of-the-art knowledge, simulation and laboratory studies of measuring transducers to measure acceleration (accelerometers), considering them a representative group of the measuring transducers used in transportation facilities. Measurement errors and comparisons of classical and fractional models in terms of dynamic properties were examined. The advantages of fractional calculus in modelling dynamic elements are also indicated. Tests are executed in the MATLAB & Simulink programme.