## 3 Implementation of Dynamic Balance Method
### Influence Coefficient Method  
In this paper, based on the monitoring and control function of the AMB rotor system, the dynamic balance correction of the rotor is carried out by using the ICM.  
ICM is one of the most commonly used dynamic balance correction methods. The essence of the method is to calculate the counterweight mass required to offset the initial imbalance by solving the linear relationship between the test weight and the rotor displacement response (influence coefficient). Mass blocks can be added to the rotor to solve the problem of rotor mass imbalance [22; 23]. The specific implementation process is as follows.  
The rotor is driven to a stable rotational speed \(\omega_{0}\), and the displacement signals at the \(A\) and \(B\) ends of the rotor are collected through the displacement sensor. The improved ANF is used to calculate the amplitude and phase information of the displacement signal, and the initial vibration displacement vectors \(D_{a0}\) and \(D_{b0}\) are obtained.  
We can increase the test weight mass \(M_{A}\) at end \(A\) and drive the rotor to a stable speed \(\omega_{0}\). The displacement signals of the \(A\) and \(B\) ends are collected by the displacement sensor, and the vibration displacement vectors \(D_{a1}\) and \(D_{b1}\) on the two measurement surfaces are obtained.  
Next, we can remove the mass \(M_{A}\), increase the test weight mass \(M_{B}\) at the \(B\) end and drive the rotor to a stable speed \(\omega_{0}\). The displacement signals of \(A\) end and \(B\) end are collected by the displacement sensor and the vibration displacement vectors \(D_{a2}\) and \(D_{b2}\) on the two measuring surfaces are obtained.  
Where \(M_{A}\) and \(M_{B}\) are both vectors. In order to unify the zero phase of the vibration displacement vector and the counterweight vector, a fiber optical sensor is introduced in this paper. Figure 7 is a schematic diagram of the counterweight plate and the fiber optical sensor.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(\lambda\) & 40 \\ \(\xi\) & 0.25 \\ \(\mu\) & 0.001 \\ \(\beta\) & 200 \\ \(N\) & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: ANF parameters.  
Figure 6: Tracking effect of improved ANF algorithm.  
The counterweight plate has a circle of stud holes, which can be counterweighted by inserting studs of different lengths. A stud hole can be selected as the starting position, which is the zero phase of the counterweight vector. The marker can be pasted on the circumference at the same phase as the starting position. The fiber optic sensor encounter marker generates a rising edge signal. During the rotation of the rotor, the fiber optic sensor generates a square wave of the same frequency as the rotational speed. Using the rising edge of the square wave as the zero phase of the displacement vector, the unity of the zero phase of the counterweight vector and the displacement vector is realized.  
The influence coefficient is calculated by using the above displacement vibration vector and test weight mass \(M_{A}\) and \(M_{B}\). The calculation formula is as Equation (16).  
\[\begin{array}{l}K_{A1}=\frac{D_{A1}-D_{A0}}{M_{A}}\\ K_{A2}=\frac{D_{A1}-D_{A0}}{M_{A}}\\ K_{B1}=\frac{D_{A2}-D_{A0}}{M_{B}}\\ K_{B2}=\frac{D_{A2}-D_{A0}}{M_{B}}\\ \end{array} \tag{16}\]  
According to the influence coefficient and the initial vibration displacement vector, the increased counterweight masses \(M_{A0}\) and \(M_{B0}\) at both ends of \(A\) and \(B\) are calculated. The calculation formula is as Equation (17).  
\[\begin{array}{l}K_{A1}M_{A0}+K_{B1}M_{B0}=-D_{A0}\\ K_{A2}M_{A0}+K_{B2}M_{B0}=-D_{A0}\\ \end{array} \tag{17}\]