Hybrid static and dynamic model for hysteretic piezoelectric stack actuator and its application for hysteresis compensation

This paper aims at proposing a novel nonlinear model for piezoelectric stack actuators (PSAs) applied in vibration control systems. Piezoelectric stack actuator with its advantages in nano resolution positioning, large actuating force and rapid response, exhibits exceptional potential in active structural vibration suppression and noise reduction. However, PSA generally shows nonlinear hysteretic behavior between the applied electric field and the output displacement or force, which may compromise the control efficiency. In the present work, a nonlinear model combined with Bouc-Wen model and an innovative static operator is introduced to simulate the hysteretic phenomenon of the PSA including dynamic behavior. The static operator is established by a butterfly-shaped function, which is approximately and analytically inspired from hysteresis loops observed in piezoelectric actuator characteristic tests. Model predictions show good agreement with experimental results performed on a unipolar unloaded PSA. Both the transient loop behavior for the initial electrical loading and the stable dynamic hysteresis loops are accurately simulated, demonstrating the ability of the model for efficiently tracking the dynamic response as the input voltage changes. Then, in the purpose of compensating the nonlinear hysteretic characteristics of the actuator, feedforward compensation scheme using the proposed model is designed. In the control scheme, the feedforward compensator is constructed directly by employing the identified hysteresis model. Experimental results show great improvement for linearizing the relationship between actuator output and input reference signal, thanks to the accuracy of the hysteretic modeling proposed.