**4. Conclusions**

Piezoelectric stick-slip actuators have great potential in the field of precision operation. However, whether at the experimental level or in the application, the hysteresis nonlinearity of the piezoelectric stick-slip actuator, the complex friction motion relationship in the driving mechanism, its vibration and external disturbance will have a great impact on its motion control accuracy, so that the piezoelectric stick-slip actuator cannot achieve the ideal output performance. In this paper, the modeling and control of piezoelectric stick-slip actuators are summarized and studied.

In the aspect of modeling, the existing mathematical models describing the hysteresis characteristics of piezoelectric stick-slip actuators and the mathematical models of complex friction relationships in the structure are introduced. Hysteresis models mainly include Prandtl-Ishlinskii (PI) model, Krasnosel'skii-Pokrovskii (KP) model, Preisach model, Bouc-Wen model, and Rayleigh model. In terms of the friction model, the existing dynamic friction and static friction models are mainly introduced. The model of piezoelectric stick-slip actuators usually includes the hysteresis model and friction model. In the modeling part, the mathematical model of piezoelectric stick-slip actuators proposed by people is summarized and studied, which provides a reference for the control and model analysis of piezoelectric stick-slip actuators.

In terms of control, according to open-loop control and closed-loop control, this paper summarizes and studies the efforts made by people to make up for control accuracy, and summarizes many control cases, such as feedforward control, sliding mode control, PID control, neural network control, and so on. In the future development of piezoelectric stick-slip actuators, opportunities and difficulties coexist. The control mode can effectively make up for the output performance of piezoelectric stick-slip actuators and make them meet the actual need in various complex environments.

Based on this paper, a more comprehensive dynamics model can be developed in the future by analyzing the characteristics of piezoelectric viscous-slip actuators indepth to extend to actuators of different mechanical structures. By combining various control methods to eliminate system nonlinearity, higher accuracy and precision motion can be achieved. With the combination of intelligent control field and piezoelectric actuators, piezoelectric stick-slip actuators will be applied to more fields in the future.
