# Identification Approach for Nonlinear MIMO Dynamics of Closed-Loop Active Magnetic Bearing System
## 3 Experimental Setup for Identification of Rotor/RAMB Dynamic Model
The relation between the maximum frequency of the identified model, i.e., \(f_{\rm max}\), and the bit duration of PAPRBS, i.e., \(\Delta\), has to satisfy the following condition [31]:  
\[2\pi/3\Delta>f_{\rm max} \tag{21}\]  
Since the maximum frequency of the identified model of rotor/AMB unit is set as 2000 Hz, the bit duration of PAPRBS signal has to meet the following inequality:  
\[\Delta<2\pi/(3*2000)=1.047\ {\rm ms} \tag{22}\]  
Finally, the bit duration is selected as 0.5 ms, and the corresponding period of each PAPRBS as four seconds (i.e., 8000 \(\times\) 0.5 ms). ### Parallel Amplitude-Modulated Pseudo-Random Binary Sequence (PAPRBS) Generator  
The test rig for the system identification on the multi-input-multi-output (MIMO) rotor/RAMB dynamic system is shown in Figure 15. The corresponding schematic diagram is depicted in Figure 9. In the experiments, the perturbation signals, i.e., PAPRBS signals, are imported to the input points of the controller, i.e., S3, S5, S7 and S9 shown in Figure 4, as the rotor is fully levitated by the commercial controller. Afterwards, the perturbation signals and their corresponding responses, i.e., position deviations of the rotor, are recorded and will be used later. Figure 12: Layout of _Simulink_ code for PAPRBS generator. Figure 10:0 First 200 points of PAPRBS. To construct the rotor/RAMB dynamic model by experiments, the input signals to the plant and the corresponding responses of the rotor/RAMB unit, i.e., _Point B_ and _Point C_  
Figure 10:1 Correlations between perturbation signals. Figure 10:2 Test rig for system identification on rotor/AMB dynamics. shown in Figure 9, respectively, are necessary to be recorded initially. The plant is referred to as the rotor/RAMB unit in this study. In order not to introduce the noises to the power amplifier directly, the input signals to the plant are not recorded at _Point B_ but at _Point A_. The detailed steps to generate the corresponding responses at _Point B_, shown in Figure 9, by applying the perturbation signals recorded at _Point A_, as shown in Figure 9, to the dynamic model of controllers of AMBs are summarized as:  
1. Four perturbation signals are imported at the input points of the controllers, as the TMP rotor is fully levitated. 2. Meanwhile, record the four perturbation signals imported at the input points of the controller, i.e., at _Point A_, shown in Figure 10:3
3. Import the recorded four perturbation signals to the dynamic model of the controllers of AMBs, i.e., Equation (5), Equation (10), Equation (15) and Equation (20), respectively. 4. Record the corresponding responses of the plant model with the controllers. The flowchart of responses generation with perturbation signals is depicted in Figure 10:4 The sampling period, \(T_{\text{S}}\), is set as 0.05 ms. The input signals imported to the dynamic model of the controllers and the corresponding responses are shown in Figure 10:5 As the input signals to the rotor/RAMB dynamics and the corresponding responses, i.e., _Point B_ and _Point C_, shown in Figure 9, respectively, are obtained, the rotor/RAMB dynamic model can therefore be identified.