Hybrid Adaptive Controller Design with Hysteresis Compensator for a Piezo-Actuated Stage

Piezo-actuated stage (P-AS) has become the topic of considerable interest in the realm of micro/nanopositioning technology in the recent years owing to its advantages, such as high positioning accuracy, high response speed, and large output force. However, rate-dependent (RD) hysteresis, which is an inherent nonlinear property of piezoelectric materials, considerably restricts the application of P-AS. In this research paper, we develop a Hammerstein model to depict the RD hysteresis of P-AS. An improved differential evolution algorithm and a least-squares algorithm are used to identify the static hysteresis sub-model and the dynamic linear sub-model for the Hammerstein model, respectively. Then, a hysteresis compensator based on the inverse Bouc–Wen model is designed to compensate for the static hysteresis of the P-AS. However, the inevitable modeling error presents a hurdle to the hysteresis compensation. In addition, external factors, such as environmental noise and measurement errors, affect the control accuracy. To overcome these complications, a hybrid adaptive control approach based on the hysteresis compensator is adopted to increase the control accuracy. The closed-loop system stability is analyzed with the help of the Lyapunov stability theory. Finally, experimental results indicate that the raised control approach is effective for the accurate positioning of P-AS.