State machine based nonlinear hysteresis model

A wide range of systems are characterized by nonlinear hysteresis effects. This especially appears in moving or deforming mechanical systems. In an effort to model these effects, a novel approach is presented in this work. The proposed model is based on a state machine imposing very few restrictions on the modeled system and therefore allowing a wide range of applications. The state machine represents the memory of the system. The size of the hysteresis loop and the local dependence is described by envelop functions while the shape of the loop is affected by the transition function. In this work we use polynomial functions as the envelop function and a hyperbolic tangent function to model the transition. The separation of these two parts and hence the free choice of functions allows a very good and easy fit to real system behavior. The identification of two exemplary mechanical systems with hysteresis is described and the results are presented.