Modeling of Dynamic Systems With Hysteresis Using Predictive Gradient-Based Method

A new modeling method of dynamic systems with rate-dependent hysteresis is proposed in this paper. In this method, a hysteresis model with simple exponential structure is proposed to describe the features of rate-dependent hysteresis. Subsequently, the properties of the proposed hysteresis model are analyzed. Then, a Hammerstein model embedded with the proposed hysteresis model is established to describe the behavior of dynamic systems with rate-dependent hysteresis. Afterward, a predictive gradient-based modeling method is proposed to determine the parameters of the new model. In addition, the convergence analysis of the predictive gradient based modeling method is analyzed. Then, the proposed identification method is applied to modeling of electromagnetic scanning micromirror chips. Finally, the comparison between the proposed novel modeling scheme and other typical nonlinear modeling methods is illustrated. Note to Practitioners—To describe the characteristics of rate-dependent hysteresis in electromechanical systems, both rate-dependent hysteretic operator-based models and non-smooth differential equation-based hysteresis models have complex model structures. However, the exponential-type hysteresis model proposed in this paper not only has a simple structure but can also describe the more complex characteristics of rate-dependent hysteresis. In addition, for rate-dependent hysteresis with multiple local extremes, the proposed modeling method based the predictive gradients can avoid the modeling process being stuck in local extremes, thereby obtaining fast convergence and accurate modeling results.