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

• Autorzy: Luft M. , Pietruszczak D. , Szychta E. , Szychta L.

Identyfikatory

DOI

10.17402/069

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

accelerometer; ARX identification method; fractional derivative; fractional calculus; MATLAB &Simulink programme; measuring transducer; median relative error; transportation facilities

• Wydawca: Wydawnictwo Naukowe Akademii Morskiej w Szczecinie
• Czasopismo: Zeszyty Naukowe Akademii Morskiej w Szczecinie
• Rocznik: 2015
• Tom: nr 44 (116)
• Strony: 141--147
• Opis fizyczny: Bibliogr. 10 poz., rys., tab.

Twórcy

autor

Luft M.

• Kazimierz Pulaski University of Technology and Humanities in Radom Faculty of Transport and Electrical Engineering 29 Malczewskiego St., 26-600 Radom, Poland

autor

Pietruszczak D.

• Kazimierz Pulaski University of Technology and Humanities in Radom Faculty of Transport and Electrical Engineering 29 Malczewskiego St., 26-600 Radom, Poland

autor

Szychta E.

• Kazimierz Pulaski University of Technology and Humanities in Radom Faculty of Transport and Electrical Engineering 29 Malczewskiego St., 26-600 Radom, Poland

autor

Szychta L.

• Lodz University of Technology, Faculty of Electrical, Electronic, Computer and Control Engineering Institute of Mechatronics and Information Systems 18/22 Stefanowskiego St., 90-924 Łódź, Poland

Bibliografia

• 1. KACZOREK, T. (2011) Selected Problems of Fractional Systems Theory. Berlin: Springer-Verlag GmbH.
• 2. LUFT, M., CIOC, R. & PIETRUSZCZAK, D. (2011) Fractional Calculus in Modelling of Measuring Transducers. Electronics and Electrical Engineering. 4(110).
• 3. LUFT, M., ŁUKASIK, Z., SZYCHTA, E., CIOĆ, R. & PIETRUSZCZAK, D. (2012) Selected issues of fractional calculus in mathematical modelling of measuring transducers used in transportation facilities. Scientific Journals Maritime University of Szczecin. 29(101). pp. 109–116.
• 4. LUFT, M., SZYCHTA, E., CIOĆ, R. & PIETRUSZCZAK, D. (2011) Application of Fractional Calculus in Identification of the Measuring System. Transport Systems and Processes, CRC Press Balkema, Taylor & Francis Group, pp. 63–68. London, UK.
• 5. LUFT, M., SZYCHTA, E. & PIETRUSZCZAK, D. (2015) Some applications of fractional calculus to the analysis of dynamic properties of selected measuring transducer. The 11th European Conference of Young Scientists and Postgraduate Students, Transcom Proceedings 2015, Section 4, Electric Power System, Electrical and Electronic Engineering, pp. 29–34, 22–24 June 2015, Zilina, Slovakia.
• 6. OSTALCZYK, P. (2008) Epitome of the fractional calculus. Theory and its applications in automatics (Published in Polish). Łódź: Wydawnictwo Politechniki Łódzkiej.
• 7. PIETRUSZCZAK, D. (2012) Application of fractional calculus to the analysis of dynamic properties of the measurement systems (Published in Polish). Doctoral dissertation, The Main Library of Kazimierz Pulaski University of Technology and Humanities, Radom, Poland.
• 8. PIETRUSZCZAK, D. & SZYCHTA, E. (2013) Analysis of selected dynamic properties of fractional order accelerometers for application in telematics equipment. Communications in Computer and Information Science. Berlin Heidelberg: Springer-Verlag.
• 9. PODLUBNY, I. (1999) Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications. San Diego-Boston-New YorkLondon-Tokyo-Toronto: Academic Press.
• 10. WALTER, P.L. (2008) Selecting accelerometers for and assessing data for mechanical shock measurements. PCB Piezotronics Technical Note TN-24, USA.