## 9 Experiment and Test of the HCS  
To verify the control effect of the HCS, a horizontal positioning experiment of the MRC was carried out on the MAR system test platform shown in Figure 19.  
The hardware platform comprised an MAR, horizontal control coil, coil driving circuit, sensors, and levitation control system [1]. In the experimental setup, a grating ruler boasting an accuracy of 0.1 \(\upmu\)m and a resolution of 0.01 \(\upmu\)m was employed. It was rigidly connected to the MRC to accurately calibrate the horizontal displacement of the MRC. \(y_{d}\) was captured by measuring coils. The angle sensor is affixed to the MRC using an adhesive. \(\psi\) in Figure 19 was c  
Figure 19: Experimental setup of the MAR system test platform, including the mover core, horizontal control coils, grating ruler, and angle sensor.  
Figure 18: Simulation diagram of the horizontal rotation angle of the MRC.  
Figure 20 shows the measured start-up response curve of the MRC. It can be seen from the curve that the MRC exhibits good response speed and stability during the start-up process. In a very short time, the MRC can quickly reach the preset horizontal position and ensure accurate positioning throughout the process.  
As shown in Figure 20, at \(t\) = 0.5 s, the horizontal position set value of the MRC was adjusted to 1 mm, that is, one step. The horizontal position of the MRC reached the set value within \(t\) = 0.58 s with no obvious overshoot. After \(t\) = 0.75 s, the horizontal position of the MRC stabilized at the set horizontal position value, with an error within \(\pm\)2 \(\upmu\)m. The adjustment speed is slightly slower than that shown in the simulation.  
It can be seen from Figure 21 that the overshoot of the actual HCS is more than twice that of the simulation. The MRC begins to enter a stable state at about \(t\) = 0.72 s, which is 0.02 s more than that in the simulation. After that, there is still an error, but it is less than \(\pm\)2 \(\upmu\)m.  
As shown in Figure 22, at \(t\) = 0.5 s, the deflection angle of the MRC changes. At this time, the horizontal position set value of the MRC also changes suddenly, and the HCS starts to adjust the horizontal position of the MRC. At \(t\) = 0.6 s, the deflection angle reaches its maximum value. Before \(t\) = 0.8 s, the deflection angle returns to zero degrees, and the transition process of the suspension position is also completed. The MRC stabilizes at the new horizontal position.  
Figure 21: Enlarged view of the overshoot part of the displacement response curve during start-up.  
Figure 20: Response curve of displacement during start-up.  
Obviously, there is strong coupling when controlling the horizontal positions of the left and right ends of the MRC. The transition process of the horizontal position will interfere with the deflection angle of the MRC. However, the HCS can eliminate the interference in about 0.22 s, complete one step. The control accuracy can reach \(\pm\)2 \(\upmu\)m under 200 repeated trials, as shown in Figure 23. Therefore, the HCS effectively achieves decoupling control and has excellent robustness.  
The performance comparison among conventional linear active disturbance rejection control (LADRC), PID control methods, and the proposed improved active disturbance rejection control (I-ADRC) method is summarized in Table 3.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Control Method** & **Positioning Accuracy (\(\upmu\)m)** & **Setting Time (ms)** & **Overshoot (\%)** & **Applicability to Nonlinear System** \\ \hline Proposed ADRC & \(\pm\)2 & 580 & 1.2 & Yes (Designed for coupling) \\ PID [8] & \(\pm\)10 & 1200 & 8.5 & No (Linear assumption) \\ LADRC [10] & \(\pm\)5 & 800 & 0.25 & Partial (Limited decoupling) \\ \hline \end{tabular}
\end{table}
Table 3: Comparative performance metrics of control methods in nonlinear and coupled systems.  
Figure 23: Positioning accuracy of the mover core.  
Figure 22: Response curve of angle during start-up.