*2.2. Test Results*

The experimental system was built using a laser interferometer, nanopositioning platform, reflection mirror, controller, and computer software, as shown in Figure 3a. The laser interferometer used is the Renishaw XL-80 series achieves an accuracy of ± 0.5 ppm. The selected driver was the HVA-150D.A3 instrument from Harbin Xinmingtian Company, whose voltage input variable range is 0 V-150 V. Figure 3b shows the actual experimental system.

(**a**) 

(**b**) 

The user performs the following steps to test the output displacement characteristics of the nanopositioning stage in the x-direction motion, under single-ring linear voltage and under reciprocating linear voltage:

(1) Adjust the laser interferometer so that its light signal intensity is within the confidence range. Connect the computer, controller, and laser interferometer via the USB interface data cable. Data is collected on the computer by the corresponding software of the controller and laser interferometer.

(2) The controller matching software loads the electrical signal to the driving controller. The initial driving voltage is 0 V. Experiment 1 is carried out to give a linear voltage rise signal from 0 V to 150 V. The displacement is measured and recorded by laser interferometer for every 7.5 V. Next, a linear voltage reduction signal is sent from 150 V to 0 V. The displacement is measured and recorded every 7.5 V. A single-ring linear voltage signal is shown in Figure 4a.

(3) Similarly, experiment 2 is carried out. The reciprocating linear voltage signal is recorded, as shown in Figure 4b.

(4) Record several measurements.

(5) Check the instrument and turn it <sup>o</sup>ff. Process experimental data.

Through the above experiment, two sets of data can be obtained: a single-ring linear voltage–displacement characteristic curve, as shown in Figure 5a; and a reciprocating linear voltage–displacement characteristic curve, as shown in Figure 5b.

**Figure 4.** Experimental loading voltage: (**a**) single-ring linear voltage (**b**) and reciprocating linear voltage.

**Figure 5.** Voltage–displacement experimental curves: (**a**) single-ring linear voltage (**b**) and reciprocating linear voltage.

The expected voltage displacement curves should be linear. Analysis of the experimental data established the nonlinearity of the experimental curve. The voltage displacement curve at the single-ring linear voltage has a hysteresis characteristic. The voltage displacement curve at the reciprocating linear voltage has the same hysteresis characteristics as the single-ring voltage's, while the reciprocating voltage's hysteresis loop conforms to the Madelung principle [30]. Therefore, in order to solve the hysteresis characteristics of the piezoelectric ceramic under single-ring linear voltage and reciprocating linear voltage, an effective compensation method is needed.
