# Decoupling Control of Multi-DOF Supporting System of MLDSB
## 6 Experimental Result of Decoupling
### Analysis of Experimental Results  
According to Figures 6 and 7, the magnetic circuit coupling between each magnetic pole of the stator can reduce the control accuracy of the channel and the stable suspension of the MLDSB. 1. Magnetic circuit coupling characteristics between channel \(x\) and channel \(y\). In order to explore the magnetic circuit coupling characteristics between channel \(x\) and channel \(y\) of the stator, only channel \(x\) or channel \(y\) is opened to achieve single-channel electromagnetic suspension. The steady-state displacement of the rotor is tested as shown in Figure 18.  
According to Figure 16, the rotor can be stably suspended by channel \(x/y\), the displacement is within the range of \((-1,1)\) um, and the requirements of engineering practice can be met. When channel \(x\) and channel \(y\) are opened, the steady-state displacement is obtained by the test as shown in the blue curve in Figures 19 and 20. According to Figures 19 and 20, the rotor moves irregularly, and its displacement increases greatly. It is basically limited within the range of \((-40\)-\(40)\) um and reached the design value of oil film thickness, and then, the rotor cannot be suspended stably. The coupling phenomenon in the rotation state is more obvious than with no rotation, and the peak fluctuation phenomenon of the steady-state displacement appears at the same frequency. By comparing Figures 18-20, it can be seen that the magnetic circuit coupling between the magnetic poles is large, and the control accuracy and stability of channel \(x\) and channel \(y\) is greatly reduced. (2) Magnetic circuit decoupling between channel \(x\) and channel \(y\). Based on the coupling characteristics of the magnetic circuit and the above decoupling theory, channel \(x\) and channel \(y\) are decoupled and controlled to obtain the decoupling displacement of the rotor as shown in the red curve of Figures 19 and 20. Figure 19: Displacement of the rotor without rotation. Figure 18: Steady-state displacement under single suspension. According to Figures 19 and 20, the rotor returns to the equilibrium position after decoupling, and it vibrates regularly in the \(y\)-direction and \(x\)-direction. There is minimal interference between the \(y\)-direction and \(x\)-direction. Compared to before the decoupling, the steady-state displacement is significantly reduced from (\(-40\)-\(40\)) \(\upmu\)m to (\(-20\)-\(20\)) \(\upmu\)m, and the decoupling effect of channel \(y\) is greatly improved. (3) Regulation characteristics of channel \(x\) and channel \(y\) after decoupling. In order to further study the regulation characteristics of each channel after decoupling, the sinusoidal signal (amplitude is \(5\)\(\upmu\)m and period is \(10\) ms) is given in the \(x\)-direction and \(y\)-direction respectively, and the following curves are obtained as shown in Figures 21 and 22. Figure 20: Displacement of the rotor with rotation. According to Figures 21 and 22, the rotor displacement before decoupling in the input channel presents the sinusoidal motion law with high-frequency oscillation as shown in the blue curve of Figures 21a and 22b. After decoupling, the decoupling controller effectively eliminates the oscillation and greatly improves the displacement with the characteristics as shown in the red curve of Figures 21a and 22b. Due to the coupling characteristics of the magnetic circuit, the rotor displacement before decoupling in the non-input channel is also affected by the coupling of the input channel, and it shows a small sinusoidal motion with the same frequency as shown in the blue curve of Figures 21b and 22a. After decoupling, the decoupling controller effectively eliminated the rotor high-frequency oscillation and greatly improved the zero-retaining characteristic of rotor displacement, and then the decoupling effect of channel \(y\) is greatly improved as shown in the red curve of Figures 21b and 22a. The theoretical correctness of the decoupling controller can be effectively proven.