Non-symmetrical Bouc–Wen model for piezoelectric ceramic actuators

The existing Bouc–Wen models for piezoelectric ceramic actuators (PCAs) possess the symmetrical characteristic of the hysteretic component and can be categorized as symmetrical Bouc–Wen models. When modeling PCAs with non-symmetrical hysteresis by a symmetrical Bouc–Wen model, large modeling errors will occur. In this paper, a non-symmetrical Bouc–Wen hysteresis operator for modeling the non-symmetrical hysteresis of PCAs is established by introducing a non-symmetrical formula into the Bouc–Wen hysteresis operator. Accordingly, a non-symmetrical Bouc–Wen model for PCAs is proposed and established by modeling the non-symmetrical hysteresis component of PCAs with the non-symmetrical Bouc–Wen hysteresis operator. A corresponding parameter identification method, which can identify the parameters by obtaining analytical solutions with a set of input–output experimental data to and from a PCA with an applied periodic voltage under the zero initial condition, is established. In the parameter identification, the least-squares method is used to reduce external random disturbances. The performance of the non-symmetrical Bouc–Wen model with the corresponding parameter identification method is experimentally verified by the established experimental setup. The research results show that the non-symmetrical Bouc–Wen model can simulate the PCA with the non-symmetrical hysteresis more accurately than the symmetrical Bouc–Wen models, and the modeling errors are decreased by about 30%. In addition, the established parameter identification method can be used to identify the parameters of the non-symmetrical and symmetrical Bouc–Wen models effectively and quickly.