Pseudo-Hammerstein model based identification for rate-dependent hysteresis

A pseudo-Hammerstein model based identification scheme is proposed for rate-dependent hysteresis. In this strategy, the pseudo-Hammerstein model constituted by a nonlinear moving average model with exogenous inputs(NMAX) in series with an auto-regressive moving average(ARMA) model is presented to describe the dynamic behavior of rate-dependent hysteresis. In view of the multi-valued mapping of hysteresis, a hysteretic operator is introduced to establish an expanded input space for the NMAX model. Based on the key term separation principle, the recursive least squares(RLS) algorithm is employed to accomplish an on-line identification for the auto-regressive(AR) parameters of the ARMA model. The relevant Levenberg-Marquardt (L-M) algorithm is developed to acquire an appropriate structure and the remaining parameters of the pseudo-Hammerstein model. Finally, the numerical results on a Duhem model of the piezoelectric actuators have validated the effectiveness of the proposed model.