It is now the most widely used the multilayer piezoelectric actuators polarized by series of mechanical and electrical parallel. When adding constant pressure on the drive, the piezoelectric equation can be expressed as △L-Nd33V. N is the number of laminated ceramic; d33 is the piezoelectric constant; the V is the applied voltage; △L is the displacement generated in the thickness direction.

 

Figure following is the actual measured piezoelectric ceramic voltage - displacement curve of tungsten bronze series piezoelectric actuators under open-loop control. It can be seen that when the voltage begins to decrease from the maximum value, the displacement is not returned from the rising displacement curve , but there has been a large displacement hysteresis, particularly in the control voltage of 50V, the input voltage is the same as the corresponding displacement hysteresis has reached 0.231μm.

 

This hysteresis relationship between voltage and the displacement is the hysteresis characteristics of piezoelectric actuators. Which is because d can only be constant only when the material is a single crystal of single domain state and in a weak field. But for a piezoelectric ceramic material constituted by polycrystalline, because there are a lot of electricity domains on its composition crystal, when there is a strong electric field, steering motion of electricity domains make the d no longer a constant, but the with the function changing with electric field strength E. Thus, the amount of displacement generated by the driver is not only related to the voltage, but also to the changing piezoelectric constant. When the electricity domain is angle of 180 °, the drive will not produce displacement hysteresis when it is reversed; but when the electricity domain is angle of 90 °, when the voltage drops, 90 ° domain inversion will make the displacement of the drive in parallel or perpendicular in the direction of the electric field a non-linear increase, which will lead to voltage - displacement hysteresis of piezoelectric actuators.