Application of Fractional-Order Calculus to Improve the Mathematical Model of a Two-Mass System with a Long Shaft

Andriy Lozynskyy, Andriy Chaban, Tomasz Perzyński, Andrzej Szafraniec and Lidiia Kasha
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Andriy Lozynskyy: Institute of Power Engineering and Control Systems, Lviv Polytechnic National University, 79-013 Lviv, Ukraine
Andriy Chaban: Faculty of Transport, Electrical Engineering and Computer Science, University of Technology and Humanities in Radom, 26-600 Radom, Poland
Tomasz Perzyński: Faculty of Transport, Electrical Engineering and Computer Science, University of Technology and Humanities in Radom, 26-600 Radom, Poland
Andrzej Szafraniec: Faculty of Transport, Electrical Engineering and Computer Science, University of Technology and Humanities in Radom, 26-600 Radom, Poland
Lidiia Kasha: Institute of Power Engineering and Control Systems, Lviv Polytechnic National University, 79-013 Lviv, Ukraine

Energies, 2021, vol. 14, issue 7, 1-15

Abstract: Based on the general theory of fractional order derivatives and integrals, application of the Caputo–Fabrizio operator is analyzed to improve a mathematical model of a two-mass system with a long shaft and concentrated parameters. Thus, the real transmission of complex electric drives, which consist of long shafts with a sufficient degree of adequacy, is presented as a two-mass system. Such a system is described by ordinary fractional order differential equations. In addition, it is well known that an elastic mechanical wave, propagating along a drive transmission with a long stiff shaft, creates a retardation effect on distribution of the time–space angular velocity, the rotation angle of the shaft, and its elastic moment. The approach proposed in the current work helps to take in account the moving elastic wave along the shaft of electric drive mechanism. On this basis, it is demonstrated that the use of the fractional order integrator in the model for the elastic moment enables it to reproduce real transient processes in the joint coordinates of the system. It also provides an accuracy equivalent to the model with distributed parameters. The distance between the traditional model and the model in which the fractional integral is used for the elastic moment modelling in a two-mass system, with a long shaft, is analyzed.

Keywords: electric drive; fractional calculus; two-mass system; Caputo-Fabrizio operator; mathematical model; synthesis of control system; full state vector control (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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