## 5 Force Imbalance Levitating Motion Control Test
Compared to the 1.0 mm step input, the overshoot of 0.2 mm step length is reduced by 74.9% and the adjustment time is increased by 31.1%. The 2 pairs of 10 sets of repeatability test data meet the 3\(\sigma\) criterion. According to the test data in Tables 2 and 3, plot the change curves of the overshoot and adjustment time of three step inputs in the descending and ascending motion process shown in Figures 12 and 13. The repeatability test results of the descending motion are consistent with the test results shown in Figure 11a, and the repeatability test results of the ascending motion are consistent with the test results shown in Figure 11b. In Figures 12 and 13, \(l_{1}\) represents overshoot of 1.0 mm step input, \(l_{2}\) represents overshoot of 0.5 mm step input, \(l_{3}\) represents overshoot of 0.2 mm step input, \(l_{4}\) represents adjustment time of 1.0 mm step input, \(l_{5}\) represents adjustment time of 0.5 mm step input, \(l_{6}\) represents adjustment time of 0.2 mm step input. Dotted line AVG denotes average value. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No**} & \multicolumn{2}{c}{**1.0 mm**} & \multicolumn{2}{c}{**0.5 mm**} & \multicolumn{2}{c}{**0.2 mm**} \\ \cline{2-7}  & \(\sigma\)\% & **t/s** & \(\sigma\)\% & **t/s** & \(\sigma\)\% & **t/s** \\ \hline
1 & 8.67\% & 0.55 & 5.72\% & 0.71 & 2.41\% & 0.72 \\
2 & 8.57\% & 0.52 & 4.73\% & 0.69 & 2.67\% & 0.81 \\
3 & 7.57\% & 0.51 & 5.03\% & 0.70 & 3.14\% & 0.76 \\
4 & 7.97\% & 0.53 & 5.61\% & 0.76 & 2.41\% & 0.64 \\
5 & 8.57\% & 0.58 & 4.92\% & 0.72 & 3.02\% & 0.75 \\
6 & 8.07\% & 0.59 & 5.72\% & 0.71 & 2.40\% & 0.63 \\
7 & 7.97\% & 0.51 & 5.81\% & 0.70 & 2.43\% & 0.72 \\
8 & 7.99\% & 0.48 & 5.41\% & 0.68 & 2.79\% & 0.76 \\
9 & 8.48\% & 0.52 & 4.76\% & 0.72 & 2.41\% & 0.72 \\
10 & 8.46\% & 0.52 & 5.41\% & 0.74 & 2.53\% & 0.75 \\ \hline AVG & 8.23\% & 0.53 & 5.31\% & 0.71 & 2.63\% & 0.73 \\ \(\sigma\) & 0.35\% & 0.03 & 0.40\% & 0.03 & 0.26\% & 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the dynamic characteristics of the repeatability test of descending motion. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No**} & \multicolumn{2}{c}{**1.0 mm**} & \multicolumn{2}{c}{**0.5 mm**} & \multicolumn{2}{c}{**0.2 mm**} \\ \cline{2-7}  & \(\sigma\)\% & **t/s** & \(\sigma\)\% & **t/s** & \(\sigma\)\% & **t/s** \\ \hline
1 & 8.32\% & 0.66 & 4.41\% & 0.84 & 2.20\% & 0.81 \\
2 & 7.93\% & 0.65 & 5.32\% & 0.82 & 2.76\% & 0.87 \\
3 & 8.71\% & 0.60 & 5.02\% & 0.86 & 2.21\% &When the error band is set to \(\pm\)0.02 mm for more precise levitation, the adjustment time of the 10 sets of test with a step input of 0.2 mm are greatly affected by the adjustment time evaluation standard, which in turn leads to a certain standard deviation of the adjustment time of the 10 sets of test. The analysis results are applicable to descending and ascending motion. For a large displacement of stable levitation motion, the effect of the levitating motion during descending motion is shown in Figure 14. The hall sensor near the permanent magnet ball on the electromagnetic actuator #1 is the coordinate origin. The controllable levitation distance of the active magnetic levitation actuation system in the vertical direction is from \(-\)34.5 mm to \(-\)9.5 mm, and the total levitation range is 25 mm. Figure 12: Change curve of overshoot and adjustment time of repeatability test during descending motion. Figure 13: Change curve of overshoot and adjustment time of repeatability test during ascending motion. Step-by-step actuation control is engaged in for the position control of the permanent magnet ball to realize large displacement motion and step length is set as 0.5 mm. Figure 15 shows the evolution of the tracking trajectory of the permanent magnet ball that responds to some step inputs with predetermined time intervals. Before every step input, values of controller parameters have been already updated.