Modeling rate-dependent hysteresis in piezoelectric actuators

Hysteresis of a piezoelectric actuator is rate dependent. Most hysteresis models are based on elementary rate independent operators and are not suitable for modeling actuator behavior across a wide frequency band. This work proposes a rate dependent modified Prandtl-Ishlinskii (PI) operator to account for the hysteresis of a piezoelectric actuator at varying frequency. We have shown experimentally that the relationship between the slope of the hysteretic loading curve and the rate of control input can be modeled by a linear function. The proposed rate-dependent hysteresis model is implemented for open-loop control of a piezoelectric actuator. In experiments tracking multi-frequency nonstationary motion profiles, it consistently outperforms its rate-independent counterpart by a factor of two in maximum error and a factor of three in rms error.