Hysteresis modeling of piezoelectric actuators with the frequency-dependent behavior using a hybrid model

In order to overcome the problem of positioning inaccuracy caused by nonlinear hysteresis of piezoelectric actuators, a hybrid model based on least-squares support vector machine and Bouc–Wen model is proposed to model the rate-dependent hysteresis of piezoelectric actuators. A rate-independent Bouc–Wen model and its parameters identification method is established as the basis of least-squares Bouc–Wen model. Least-squares support vector machine, which is optimized by particle swarm optimization, is introduced to improve the Bouc–Wen model into a rate-dependent model by adjusting parameters of Bouc–Wen dynamically. Experiment is carried out to validate both Bouc–Wen model and the proposed least-squares Bouc–Wen model. The results show that the proposed least-squares Bouc–Wen method is a valid and a more precise method compared to the rate-independent Bouc–Wen model.