Parametrization of electromechanical systems must acknowledge Newton and Maxwell
DOI:
https://doi.org/10.5540/03.2021.008.01.0459Keywords:
Lagrangian, Energy, Co-energy, Electromechanical system, Galvanometer.Abstract
Electromechanical systems are an interesting type of coupled systems. They are com- posed by two subsystems with different nature: mechanical and electromagnetic. The subsystems interact. To represent the dynamics of a coupled system, it is necessary to properly characterize their interaction. The dynamics of an electromechanical system is given by an initial value prob- lem (IVP) comprising a set of coupled differential equations involving, necessarily, mechanical and electromagnetic variables. Despite the ubiquity of electromechanical systems, a few authors do not parametrize them properly. Frequently, by some artífice, strange to the problem, the coupled system is uncoupled disregarding the electromagnetic subsystem. Hence, the uncoupled system has a different dynamics, resulting a reduced IVP with only a mechanical equation. This paper discusses this uncoupling using as example a galvanometer, a well-known measuring device. To analyze the effects of the decoupling, numerical simulations of the two IVP, complete and reduced, are performed.
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References
Jeltsema, D. and Scherpen, J. M. A. Multidomain modeling of nonlinear networks and systems. IEEE Control Systems, volume 29, no. 4, pages 28-59, 2009. DOI: 10.1109/MCS.2009.932927.
Hirschfeldt, N., Lima, R. and Sampaio, R. Coupling in electromechanical systems, Encontro Regional de Matemática Aplicada e Computacional (ERMAC-MS), 2020.
Hirschfeldt, N., Lima, R. and Sampaio, R. Electromagnetic loudspeaker: an energetic approach, XIV Encontro Acadêmico de Modelagem Computacional, 2021.
Lima, R. and Sampaio, R. Two parametric excited nonlinear systems due to electromechanical coupling. Journal of the Brazilian Society of Mechanical Sciences and Engineering, volume 38, pages 931-943, 2016.
Lima, R. and Sampaio, R. Pitfalls in the dynamics of coupled electromechanical systems. CNMAC 2018, Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2019.
Lima, R., Sampaio, R., Hagedorn, P. and Deü, J. Comments on the paper “On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chãos control taking into account parametric errors” published in this journal. Journal of the Brazil ian Society of Mechanical Sciences and Engineering, volume 41, page 552, 2019.
Manhães, W., Sampaio, R., Lima, R., Hagedorn, P. and Deü, J. Lagrangians for electrome chanical systems. Mecânica Computacional, volume XXXVI, pages 1911-1934, 2018.
Manhães, W., Sampaio, R., Lima, R. and Hagedorn, P. Two coupling mechanisms compared by their Lagrangians. DINAME 2019, Proceedings of the XVIII International Symposium on Dynamic Problems of Mechanics, 2019.
Madhu. Moving Coil Meter. Codrey Electronics, 26, June, 2020. Available: <https://www.codrey.com/electrical/moving-coil-meter/>. Access in: 13, March, 2021.
Preumont, A. Mechatronics: dynamics of electromechanical and piezoelectric systems, volume 136, G.M.L. GLADWELL, University of Waterloo, Canada, 2006.
Sampaio, R., Lima, R. and Hagedorn, P. One alone makes no coupling. Mecânica Computacional, volume XXXVI, pages 931-944, 2018.
Wells, D. A. Schaum’s outline oftheory and problems of Lagrangian dynamics with a treatment of Euler’s equations of motion, Hamilton’s equations and Hamilton’s principie, New York: McGraw-Hill, 1967.
