A Fractional-Order Normalized Bouc–Wen Model for Piezoelectric Hysteresis Nonlinearity

This article 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 fact that classical BW (CBW) is only efficient for symmetric rate-independent description, FONBW devoted characterizing behaviors in PEAs by adopting an $N$ th-order polynomial input function two fractional operators, respectively. Different from traditional modified models, proposed also eliminates redundancy parameters CBW via normalization processing. By this way, developed has relatively simple mathematic expression with fewer simultaneously characterize PEAs. Model are identified self-adaptive differential evolution algorithm. To validate effectiveness model, series verification inverse-multiplicative-structure-based feedforward control experiments carried out on PEA system. Results show superior modeling accuracy compensation.