High-bandwidth modeling for rate-dependent hysteresis nonlinearity using a standard Prandtl–Ishlinskii model

Rate-dependent hysteresis of piezoelectric stack actuators (PSAs) is known to cause oscillations and instabilities. This paper introduces a novel electro-mechanical coupling model that can accurately characterize the high-bandwidth rate-dependent hysteresis of a PSA. The proposed model contains three components to fully represent the output response of the system, namely, an electric model that is used to describe the electric dynamic behaviors of the PSA and its power amplifier, a hysteresis model that is applied to represent the inverse piezoelectric effect, and a mechanical model that is able to characterize the mechanical dynamic behavior of the PSA. It should be noted that, in the mechanical model, the force generated by the inverse piezoelectric effect of piezoelectric wafers is considered a distributed force and the dynamic model of the PSA is regarded as a longitudinal vibration straight bar with a uniform cross section. Through this proposed model, high modeling accuracy is achieved well with high-bandwidth varying frequencies (1–1000 Hz) as well as varying amplitudes. This paper provides a simple and effective novel method for the high-bandwidth modeling of smart material-based actuators with rate-dependent hysteresis nonlinearity.