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Modelling of Linear Analogue Transducers in Frequency Domain DOI:10.12915/pe.2014.06.039

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The paper presents the method for modelling of linear analogue transducers based on the simultaneous measurement of the amplitude and the phase characteristics in LabVIEW program. The solutions presented are based on the transfer function reparameterisation, which is the basis for the implementation of the weighted least squares procedure [1-3]. The effectiveness of the presented method is verified using an example of the acceleration sensor PCB 338b35 modelling. Streszczenie. Artykuł przedstawia metodę modelowania liniowych analogowych przetworników w oparciu o równoczesny pomiar charakterystyk amplitudowej i fazowej w programie LabVIEW. Przedstawione rozwiązania oparte są na reparametryzacji funkcji przejścia, stanowiącej podstawę do implementacji ważonej metody najmniejszych kwadratów. Efektywność przedstawionej metody została zweryfikowana na przykładzie modelowania czujnika przyspieszenia PCB 338b35. Modelowania liniowych analogowych przetworników w oparciu o równoczesny pomiar charakterystyk amplitudowej i fazowej w programie LabVIEW Keywords Analogue transducer, weighted least squares procedure, reparameterisation of transfer function. Słowa kluczowe: Przetwornik analogowy, ważona metoda najmniejszych kwadratów, reparametryzacja funkcji przejścia. doi:10.12915/pe.2014.06.39 Introduction In measurement practice, the modelling of the transfer function of the measuring transducers, usually defined as an identification process, is most often carried out based on the measurement of the amplitude-frequency characteristic [4-6]. However, the best mapping accuracy of a transducer can be obtained only based on the simultaneous measurement of both the amplitude and phase frequency characteristics. Such an approach to the modelling, requires the implementation of appropriate numerical algorithms, enabling accurate estimation of the parameters as well as the determination of their uncertainty. This paper presents an application of the we[...]

Polynomial Approximation of the Maximum Dynamic Error Generated by Measurement Systems DOI:10.15199/48.2019.06.22

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Introduction Determination of maximum dynamic error [1] first requires the synthesis of a mathematical model for the considered measurement system. This model must be developed in such a way that it allows the associated impulse response to be calculated. This condition is met for models based on differential equations, transfer functions, complex frequency responses or state equations. Mathematical model of most measurement systems (e.g. sensors) have a strictly defined structure and order. The parameters of this structure are determined by parametric identification [2-5] in accordance with the guidelines included in the dedicated standard [6]. This identification consists of two main stages, the first of which involves a practical experiment to determine the measurement of time or the frequency responses of the system. The second stage involves the approximation of this measurement by means of the extended least squares method, and aims to determine the values of particular model parameters [7-11]. The calculations at this stage can be conveniently performed using mathematical software (MATLAB, MathCAD, etc.), due to the necessity of carrying out advanced computations involving vector and matrix calculus. In this method, many procedures are used that are described both in international standards and in the scientific literature [10-13]. These procedures are used in routine calibration tests of measurement systems, which are carried out both in companies and in scientific centres. When a mathematical model of the system has been developed, an appropriate mathematical procedure should be applied to determine the maximum dynamic error that can be generated by this system. The shape of the input signal (both the number and the switching times) is also determined, as is the constraint on its magnitude [14]. In response to this signal, the maximum value of the dynamic error is obtained; any other real signal with switching t[...]

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