# Suppression of Harmonic Current in Magnetic Bearing-Rotor System with Redundant Structure
## 4 Suppression of Harmonic Current in AMB with Redundant Structures
### Simulation Verification and Analysis  
In order to verify the effectiveness of the proposed control strategy, simulations on the magnetic bearing-rotor system with redundant structures were carried out on Matlab/Simulink. The repetitive controller was designed according to the loop model of the equivalent control system shown in Figure 7. The currents of the coils were determined by the \(x\) and \(y\) control loops in the maglev bearing-rotor system. On the basis of the  
Figure 11: Phase–frequency curve of \(F(s)\) (black line) and \(C(s)F(s)\) (red dotted line). closed-loop equivalent control schematic diagram of the entire system shown in Figure 5, we established the control structure shown in Figure 13. \(G_{xRC}(\mathrm{s})\) and \(G_{yRC}(\mathrm{s})\) represent the repetitive controllers applied to the \(x\)- and \(y\)-directions, respectively. Considering the symmetry of the magnetic bearing, we defined the structure of \(G_{yRC}(\mathrm{s})\) as the same as \(G_{xRC}(\mathrm{s})\), and that of \(G_{cx}(\mathrm{s})\) as the same as \(G_{cy}(\mathrm{s})\). However, there was a phase lead link \(z\) in the zero-phase LPF, and it could not be used directly in the Simulink platform. To solve this problem, we took an approximate approach to replace \(z\). For this paper, the continuous model of \(z\) was \(e^{0.0002s}\), which could be approximately expressed as  
\[e^{0.0002s}\approx 1+0.0002s+\frac{1}{2}(0.0002)^{2}s^{2}. \tag{52}\]  
The phase frequency characteristic curves of \(e^{0.0002s}\) and \(1+0.0002s+\frac{1}{2}(0.0002)^{2}s^{2}\) are expressed by red line and dotted blue line, respectively, in Figure 14, revealing a very small error between the two curves for frequencies below the cutoff frequency. Therefore, we used \(1+0.0002s+\frac{1}{2}(0.0002)^{2}s^{2}\) to replace \(e^{0.0002s}\) in the Simulink platform. In order to ensure the validity of the disturbance signal, we obtained the date of the displacement sensor from the experimental platform as shown in Figure 15.  
As shown in Figure 15, perturbation information can be considered within the sixth harmonic, and the parameters of mass unbalance and sensor runout are given in Table 2. Additionally, we assumed that the mode of sensor runout \(y_{d}(\mathrm{s})\) was the same as \(x_{d}(\mathrm{s})\). In order to demonstrate the advantages of introducing the repetitive controller to effectively suppress the harmonic disturbance of the system, the transient response of currents in the time domain in each coil before and after applying the repetitive controller is displayed in Figure 16. It should be noted that the positive and negative currents result in the poles of the magnetic bearing producing different magnetic field (NSN... NS), which is a typical characteristic of a heteropolar magnetic bearing with redundant structures when no coil fails. Figure 12: Structure of proposed repetitive controller in this paper. Figure 13: Control block diagram of the entire system with repetitive controllers. Figure 14: Phase–frequency characteristics of \(e^{0.0002\mathrm{s}}\) and \(1+0.0002\mathrm{s}+\frac{1}{2}(0.0002)^{2}\mathrm{s}^{2}\). Figure 11:0 Frequency characteristics of displacement sensor in \(x\)-direction. By analyzing Figure 16, we can draw some conclusions. When the repetitive controllers were applied at 1 s, there was a short magnitude pulse in each coil. However, after the pulse, the current amplitude of each magnetic pole began to decay gradually until zero. Since the two repetitive controllers together determine the current characteristics of each coil and there are strongly coupling characteristics in the magnetic bearing with redundant structures, the frequency-domain characteristics of the entire system changed when the repetitive controllers acted at 1 s, causing the current to oscillate at 1 s, as shown in Figure 11:1 As shown in Figure 16, at time = 0-1 s, the current amplitude in the coil was approximately \(\pm\)0.5 A. After 1 s, the current amplitude gradually decayed from \(\pm\)1 A to 0 A.