Mathematical Model of a Nonlinear Electromagnetic Circuit Based on the Modified Hamilton–Ostrogradsky Principle

Andriy Chaban, Andrzej Popenda (), Tomasz Perzyński, Andrzej Szafraniec () and Vitaliy Levoniuk
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Andriy Chaban: Faculty of Transport, Electrical Engineering and Computer Science, Casimir Pulaski Radom University, 26-600 Radom, Poland
Andrzej Popenda: Faculty of Electrical Engineering, Czestochowa University of Technology, 42-201 Czestochowa, Poland
Tomasz Perzyński: Faculty of Transport, Electrical Engineering and Computer Science, Casimir Pulaski Radom University, 26-600 Radom, Poland
Andrzej Szafraniec: Faculty of Transport, Electrical Engineering and Computer Science, Casimir Pulaski Radom University, 26-600 Radom, Poland
Vitaliy Levoniuk: Department of Electrical Systems, Lviv National Environmental University, 80381 Dubliany, Ukraine

Energies, 2024, vol. 17, issue 21, 1-21

Abstract: This paper presents a mathematical model of a typical lumped-parameter electromagnetic assembly, which consists of two subassemblies: one includes a magnetic circuit and the other with selected elements of electric circuits. An interdisciplinary research approach is used, which assumes the use of a modified integral method based on the variational Hamilton–Ostrogradsky principle. The modification of the method is the extension of the Lagrange function by two components. The first one reflects the dissipation of electromagnetic energy in the system, while the second one reflects the effect of external non-potential forces acting on the electromagnetic system. This approach allows for the avoidance of the inconvenience of the classical theory, which assumes the decomposition of the entire integrated system into individual electrical subsystems. The state equations of the electromagnetic subassembly are presented solely on the basis of the energy approach, which in turn allows taking into account various latent motions in the system, because the equations are derived based on non-stationary constraints between subsystems. The adopted theory allows for the formulation of the model of the system in a vector form, which gives much more possibilities for the analysis of higher-order electromagnetic circuits. Another important advantage is that the state equations of the considered electrical object are given in Cauchy normal form. In this way, the equations can be integrated both explicitly and implicitly. The results of computer simulations are presented in graphical form, analysed, and discussed.

Keywords: magnetic circuits; Hamilton’s principle; Lagrange’s equations; mathematical modelling; nonlinear electromagnetic circuits (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: 2024
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