  This paper presents a new fractional-order normalized Bouc-Wen (BW) (FONBW)
model to describe the asymmetric and rate-dependent hysteresis nonlinearity of
piezoelectric actuators (PEAs). In view of the fact that the classical BW (CBW)
model is only efficient for the symmetric and rate-independent hysteresis
description, the FONBW model is devoted to characterizing the asymmetric and
rate-dependent behaviors of the hysteresis in PEAs by adopting an Nth-order
polynomial input function and two fractional operators, respectively. Different
from the traditional modified BW models, the proposed FONBW model also
eliminates the redundancy of parameters in the CBW model via the normalization
processing. By this way, the developed FONBW model has a relatively simple
mathematic expression with fewer parameters to simultaneously characterize the
asymmetric and rate-dependent hysteresis behaviors of PEAs. Model parameters
are identified by the self-adaptive differential evolution algorithm. To
validate the effectiveness of the proposed model, a series of model
verification and inverse-multiplicative-structure-based feedforward control
experiments are carried out on a PEA system. Results show that the proposed
model is superior to the CBW model and traditional modified BW model in
modeling accuracy and hysteresis compensation.
