An improved parametric model for hysteresis loop approximation.

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.