Dear Colleagues!
There were several questions related to building hysteresis loops. Recently, I have published the article “An improved parametric model for hysteresis loop approximation” that deals with the problem.
Abstract
A number of improvements have been added to the existing analytical model of hysteresis loops defined in parametric form. In particular, three phase shifts are included in the model, which permits us to tilt the hysteresis loop smoothly by the required angle at the split point as well as to smoothly change the curvature of the loop. As a result, the error of approximation of a hysteresis loop by the improved model does not exceed 1%, which is several times less than the error of the existing model. The improved model is capable of approximating most of the known types of rate-independent symmetrical hysteresis loops encountered in the practice of physical measurements. The model allows building smooth, piecewise-linear, hybrid, minor, mirror-reflected, inverse, reverse, double, and triple loops. One of the possible applications of the model developed is linearization of a probe microscope piezoscanner. The improved model can be found useful for the tasks of simulation of scientific instruments that contain hysteresis elements.
R. V. Lapshin, An improved parametric model for hysteresis loop approximation, Review of Scientific Instruments, vol. 91, iss. 6, no. 065106, 31 pp., 2020 (DOI: 10.1063/5.0012931)
The article can be downloaded at https://doi.org/10.1063/5.0012931
Take attention to the “Supplementary material” that accompanies this article:
1. r.v.lapshin_hysteresis_loop_mathcad_2001i_worksheets_ver.03.01.2020.zip (34 MB)
https://aip.scitation.org/doi/suppl/10.1063/5.0012931/suppl_file/r.v.lapshin_hysteresis_loop_mathcad_2001i_worksheets_ver.03.01.2020.zip
2. r.v.lapshin_hysteresis_loop_readable_mathcad_2001i_worksheets_ver.03.01.2020.pdf (76 MB)
https://aip.scitation.org/doi/suppl/10.1063/5.0012931/suppl_file/r.v.lapshin_hysteresis_loop_readable_mathcad_2001i_worksheets_ver.03.01.2020.pdf
The supplementary material includes zip archive with Mathcad 2001i worksheets, where all aspects of the original and the improved parametric models of hysteresis loop are considered in detail (definitions, proofs, illustrating graphs, comments, notes). Due to restriction on the length of the article, it presents only the most common hysteresis loops. If the required loop is absent in the article, it makes sense to search in the supplementary material.
Best regards,
Rostislav Lapshin
Rostislav V. Lapshin, Ph. D.
Institute of Physical Problems
