Exploration and Innovation in Static System Identification through Hysteresis

Abstract

This paper explores techniques for designing and numerically modeling of hysteresis behavior in engineering systems. It presents mathematical models that analytically represent the hysteresis behavior in linear systems. These models are derived by applying piecewise linear signals with varying velocities and signs to the system's linear sections. To better capture the hysteresis characteristics found in practical static systems, higher-order differential equations, particularly second-order, are sometimes employed. These equations enable the simulation of cyclically unstable hysteresis, where both the shape and slope of hysteresis curves can change over multiple cycles. In some systems, this process stabilizes after a certain number of cycles, known as the transient phase (referred to accommodation in magnetic components in electrical engineering). In other systems, the hysteresis instability may persist indefinitely. Furthermore, methods for identifying static systems based on hysteresis behavior are developed and analyzed.