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Piezoelectric stick-slip actuators with high precision, large actuating force, and high displacement resolution are currently widely used in the field of high-precision micro-nano processing and manufacturing. However, the non-negligible, non-linear factors and complexity of their characteristics make its modeling and control quite difficult and affect the positioning accuracy and stability of the system. To obtain higher positioning accuracy and efficiency, modeling and control of piezoelectric stick-slip actuators are meaningful and necessary. Firstly, according to the working principle of stick-slip drive, this paper introduces the sub-models with different characteristics, such as hysteresis, dynamics, and friction, and presents the comprehensive modeling representative piezoelectric stick-slip actuators. Next, the control approaches suggested by different scholars are also summarized. Appropriate control strategies are adopted to reduce its tracking error and position error in response to the influence of various factors. Lastly, future research and application prospects in modeling and control are pointed out.

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