Development and Research of the Method of Static Systems Identification by Hysteresis

The paper considers methods for constructing and numerical realization of a hysteresis model for engineering systems. Mathematical models based on the analytical representation of the hysteresis characteristics of linear systems obtained by specifying piecewise linear signals at their input with different velocities of both signs on linear sections are proposed. For a more accurate description of the hysteresis characteristics of static systems that actually occur in practice, in a number of cases, differential equations of higher order are used, in particular, equations of the second order. The use of differential equations of higher order makes it possible to simulate cyclically unstable hysteresis, when the shape and slope of the hysteresis curves can change from a cycle to a number of cycles. For some systems, this process ends after a certain number of cycles (there is a so-called transient process in the phenomenon of hysteresis, in electrical engineering, it is called accommodation in relation to magnetic elements), for other systems this process of cyclic instability of hysteresis can be observed for any length of time. Methods for identifying static objects by hysteresis were developed and investigated.

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