**2. Modelling of piezoelectric stick-slip actuators**

The piezoelectric stick-slip actuator is a type of actuator that uses the inverse piezoelectric effect and the friction principle to realize the stepping displacement. Its motion process is more complex and influenced by more factors. Therefore, the establishment of a piezoelectric stick-slip actuator model needs to reflect as many motion laws as possible. By analyzing the principle of stick-slip drive and establishing a comprehensive representative model of piezoelectric stick-slip drive based on a simplified model. On the one hand, the influence of each factor on the system can be analyzed by simulation. On the other hand, for the control method containing the system model, the establishment of the model is the theoretical basis for control, and the accuracy of its model directly affects the performance of the control system.

A typical piezoelectric stack-frictional rod type consists of four principal parts the fixed part, the piezoelectric stack, the frictional rod, and the slider. The

## *A Review of Modeling and Control of Piezoelectric Stick-Slip Actuators DOI: http://dx.doi.org/10.5772/intechopen.103838*

piezoelectric element elongates and contracts under the action of a sawtooth wave drive signal driving the friction rod into a corresponding reciprocating motion. The slider is displaced forward by the frictional force with the friction rod and its own inertia. The basic drive principle of a piezoelectric stick-slip actuator is illustrated in **Figure 1**. The drive process is divided into a stick phase and a slip phase within one cycle, and its force analysis is shown in **Figure 1b**. In the sticky stage, when a slowly increasing voltage is added to the piezoelectric element, the piezoelectric element slowly extends to drive the friction rod to the right. At this time, the friction force between the slider and the friction rod is greater than the inertia force. The slider and the friction rod remain relatively stationary and move together with the right *S*0. At the slip stage, the voltage loaded on the piezoelectric element disappears quickly, and the piezoelectric element contracts quickly to the initial position. At this time, the inertia force between the slider and the friction rod is more important than the friction force and drives the slider to produce a backward displacement *S*<sup>1</sup> to the left. The effective step in each cycle is *ΔS*. The drive can achieve continuous motion to the right by continuously repeating the motion process.

Research shows that the modeling accuracy of piezoelectric stick-slip actuators is mainly determined by the following aspects—the hysteresis effect of the piezoelectric stack, the relationship between the driving voltage and the driving force, the model of the mechanical structure of the piezoelectric stick-slip actuator, and the friction model between the slider and the friction rod. Therefore, a representative integrated model of piezoelectric stick-slip actuators is discussed based on these factors in this paper.
