## 4 Experimental Research
### Experimental Results  
The dynamic performance of the motor system represents the advantages and disadvantages of the motor control performance. In this study, the step signal tracking test was firstly carried out. During the movement process, the multilevel EMA works under variable load conditions. The test used a spring device to simulate variable load loading of multistage EMA. After the system was powered on, the upper computer gave a step displacement command when the lateral spring gave a constant force of 150 N. Since the spring of the loading device had a maximum deformation constraint, the load step displacement command could not exceed the maximum deformation range. Here, the amplitudes were set to 100 mm, 200 mm, 400 mm, and 800 mm, respectively. The control algorithm adopted traditional PID and adaptive inversion method, respectively, to read the feedback signal of the displacement sensor. The test results are shown in Table 2.  
The analysis shows that, under the step displacement command of 100 mm, 200 mm, 400 mm, and 800 mm, the adaptive inversion control had a significant decrease in the average adjustment time compared with the traditional PID, and the decrease rates were 21.2%, 26.2%, 23.5%, and 21.7%, respectively. In terms of the average overshoot, the reduction ranges reached 72.7%, 80%, 66.7%, and 83.3%, which verifies that the adaptive inversion control method designed in this paper can significantly improve the fast response of the loading system, reduce the system overshoot, and improve loading accuracy.  
Afterwards, the sinusoidal signal tracking experiment was carried out. The sinusoidal test can effectively test the followingability of the controlled target to the command and measure the control effect of the adaptive inversion strategy. The output end of the multilevel electromechanical servo system was connected to a spring load, the system was powered on, the host computer gave a sinusoidal displacement command, and set the corresponding offset, so that the EMA ran in the range of 1100-1900 mm, 1300-1700 mm, 1400-1600 mm, 1420-1580 mm, respectively. Inside, the corresponding frequencies were 0.05 Hz, 0.1 Hz, 0.2 Hz, and 0.5 Hz, respectively. Figure 9 shows the comparison of the traditional PID and the adaptive inversion method at a frequency of 0.5 Hz, and the comparison data at different frequencies are summarized in Table 3.  
The analysis shows that, when the system displacement closed loop adopts the adaptive inversion control strategy, the multilevel electromechanical servo system has better follow-up performance. Under the same command, its lag time and amplitude decay are better than the traditional PID strategy.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Step Displacement** & \multicolumn{2}{c}{**Traditional PID Control**} & \multicolumn{2}{c}{**Adaptive Inversion Control**} \\ \cline{2-5}
**Command** **(mm)** & **Average Adjustment Time** **(s)** & **Average Overshoot** **(mm)** & **Average Adjustment Time** **(s)** & **Average Overshoot** **(mm)** \\ \hline
100 & 3.3 & 1.1 & 2.6 & 0.3 \\ \hline
200 & 4.2 & 2 & 3.1 & 0.4 \\ \hline
400 & 6.8 & 1.2 & 5.1 & 0.4 \\ \hline
800 & 11.5 & 1.8 & 9.0 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Time domain indicators of multistage electromechanical servo system.