## 4 Movement Control Algorithm Using Eccentricity  
Assuming that the attachment position of the non-contact encoder is correct, the X-Y axis movement distance through movement control has the same meaning as the control that generates eccentricity through control. Therefore, in order to generate the movement control of the magnetic levitation system, it is possible to artificially generate X-Y axis eccentricity by distributing the rotation torque of each stator part. In the vector control technique of the surface-mounted permanent magnet motor, as described above, the current component can be separated by \(i_{d}\) and \(i_{q}\), and the \(i_{q}\) component generates a rotational force as a torque equivalent current. Equation (3) is the equation of the interior permanent magnet motor torque and the current vector. It is composed by using the values for d, q-axis inductance (\(L_{d}\), \(L_{q}\)), number of poles (\(P\)), and flux linkage (\(\Phi_{f}\)) required for torque of a permanent magnet motor [16; 17; 18; 19]. \[T=\frac{P}{2}\frac{3}{2}\Big{[}\Phi_{f}i_{q}+\big{(}L_{d}-L_{q}\big{)}i_{d}i_{ q}\Big{]} \tag{3}\]  
However, since the surface-mounted permanent magnet synchronous motor has the feature of non-saliency, \(L_{d}\) and \(L_{q}\) can be treated as the same. Therefore, as shown in Equation (4), the torque equation of SPMSM without reluctance torque component can be expressed. \[T=\frac{P}{2}\frac{3}{2}\Phi_{f}i_{q}(L_{d}=L_{q}) \tag{4}\]  
As shown in Equation (4), the d-axis current \(i_{d}\) does not contribute to the rotation torque generation. As shown in Equation (4), the q-axis current command of the four stator parts of the magnetic levitation system is proportional to the rotation torque command. \(F_{rotation}\) refers to the rotational force (torque) of the rotor and is equal to the average of the rotational force of each stator (parts A, B, C, D). Since four stars share one rotor, the current equation for rotation control of the magnetic levitation system can be expressed as Equation (5). \(I_{rotation}\) is the average rotational current command (\(I_{q}\)) of the rotor, and \(I_{qA}\), \(I_{qB}\), \(I_{qC}\), \(I_{qD}\) are the \(i_{q}\) current command applied to each stator. \[F_{rotation}*=\frac{F_{qA}+F_{qB}+F_{qC}+F_{qD}}{4}\simeq I_{rotation}*=\frac{I_ {qA}+I_{qB}+I_{qC}+I_{qD}}{4} \tag{5}\]  
When a rotational current command is applied as shown in Equation (5), each stator applies a constant \(i_{q}\) current and the rotor performs a constant rotational motion. The centrifugal force at this time is generated for each rotational direction, as shown in Figure 12 and Equation (6), cancels each other, and converges to zero. \[ \begin{array}{c}F_{\rm C}=F_{qA}+F_{qB}+F_{qC}+F_{qD}=0\\ \big{(}F_{qA}=-F_{qC},\ F_{qB}=-F_{qD},\ F_{qC}=-F_{qA},\ F_{qD}=-F_{qB}\big{)} \end{array}  \tag{6}\]  
Figure 12: The centrifugal force is canceled by the constant rotational force of each stator. Therefore, in order to generate eccentricity using centrifugal force as shown in Figure 7, the command of the rotational force in the direction that is offset from each other must be distributed differently. If the rotation direction is set clockwise as shown in Figure 12, the direction of the centrifugal force can be divided by the X-Y axis to be expressed as Equation (7). \(X_{translation}\) is movement in the positive direction of the X axis, and \(F_{XtransC}\) is the centrifugal force in the direction of the X axis. \[ \begin{array}{l}F_{XtransC}=F_{qA}-F_{qC}(X_{translation}>0)\\ F_{YtransC}=F_{qB}-F_{qD}(Y_{translation}>0)\end{array}  \tag{7}\]  
Eccentricity can be caused by generating centrifugal force in the X-Y axis direction using each \(i_{q}\) current command. It can be seen that the magnitude of the force generated on each axis is proportional to the velocity by the relational equation in Equation (1), and for movement control, a difference in velocity must be placed on each pair of stators.