**2.3 Compensation of hysteresis in piezoelectric actuator**

According to Eqs. (6–7), under ideal conditions, the output displacement of the piezoelectric actuator is proportional to the driving voltage, as shown by the red solid line in **Figure 4**. But, in fact, due to the difference in structure and the complexity of its working mechanism, piezoelectric actuators have the inherent characteristics of hysteresis [17], which leads to the fact that the voltage rise and drop curve of the output displacement do not overlap, as shown by the green and blue lines in **Figure 4**. This affects the control accuracy of the piezoelectric actuator to a certain extent. In general engineering applications, the displacement error is relatively small, and the piezoelectric actuator can be used approximately linearly. However, in some applications that require high control accuracy, it is necessary to perform hysteresis compensation [18–21]. The hysteresis in the piezoelectric actuator can be compensated by the hysteresis inverse compensation method. The specific compensation control block diagram is shown in **Figure 5**. This method can avoid complex modeling and parameter identification of the piezoelectric actuator, and the error output can be directly used for compensation control to achieve the effect of eliminating hysteresis and improve the control accuracy of the piezoelectric actuator.
