  A number of improvements have been added to the existing analytical model of
hysteresis loop defined in parametric form. In particular, three phase shifts
are included in the model, which permits 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.
