Modeling the dynamic sandwich system with hysteresis using NARMAX model

A systematic design procedure for the identification of dynamic sandwich system with hysteresis (DSSH) is proposed. The nonlinear auto-regressive and moving average model with exogenous input (NARMAX) is utilized to describe the behavior of DSSH based on the input space expansion. Since the input–output characteristic of DSSH is usually a distorted dynamic hysteresis, a hysteretic operator is developed to act as a coordinate to specify the change tendency of the distorted dynamic hysteresis so as to transform its multi-valued mapping into a one-to-one mapping without dependence on the gradient of the output of DSSH with respect to its input, as the non-differentiable feature of the distorted dynamic hysteresis can not ensure the gradients of the extrema to be obtained. Both the modified akaike's information criterion (MAIC) and the recursive least squares (RLS) algorithm are employed to estimate appropriate structure and parameters of the model in the range of the assumed model structure. The simulations and experiment on X–Y ultra-precision micro-moving stage (UPMMS) are carried out to demonstrate the effectiveness of the proposed modeling approach.