# Identification Approach for Nonlinear MIMO Dynamics of Closed-Loop Active Magnetic Bearing System
## 2 System Identification on Controllers for Radial Magnetic Bearings  
The system to be identified in this work is the rotor/radial active magnetic bearing (rotor/RAMB) module of the commercial turbo-molecular pump (TMP), _OSAKA K701_, produced by Osaka Vacuum, Ltd. (Chuo-ku, Osaka). This section is aimed at identifying the controller embedded in the closed-loop TMP system. The control structure of the TMP is depicted in Figure 1. Since the control loop of TMP has integrated: (i) controller, (ii) power amplifier, (iii) shaft/rotor, and (iv) gap sensors, the following steps are to be undertaken so that the transfer function of the controller, \(G_{\text{C}}(s)\), can be obtained. The identification procedure of the controller is depicted in Figure 2.  
**Step #1**. Measure the upper and lower bounds of the control circuit's input and output signals.  
**Step #2**. Disconnect the control circuit from the control loop of the TMP, but the power is still supplied to the control circuit.  
**Step #3**. Excite the control circuit with the 'chirp' perturbation signals and record the corresponding responses.  
**Step #4**. Construct the dynamic model of the controller via the aid of the commercial software, _MATLAB_.  
Figure 1: Control structure of rotor/AMB unit.  
The internal view of the electronic control unit (ECU) for TMP, _Osaka TD700/1100_, is shown in Figure 3. The detailed structures of the control circuit of AMBs are depicted in Figure 4. The notations, e.g., **S1**, **S3**,..., **S9**, **CP2**, **CP4**,..., **CP8** and **CP10** are referred to as test points. Embedded in the control circuits, we employ the notch filters to lower down the control force under critical speeds and make the shaft of TMP to spin around its inertia axis instead of its centroidal axis. By applying the notch filters, vibrations induced by the unbalance mass of the rotor can be, to some extent, suppressed.  
Figure 3: Internal view of ECU for TMP (Model: _Osaka TD700/1100_).  
Figure 2: Identification procedure of controller.  
The individual control circuit for AMBs, composed of resistors, capacitors, and operational amplifiers (Op-Amps), is of the analog type. As a result, the controller can be identified by a linear system approach. In addition, because these five sets of control circuits are not connected to each other, the scheme by linear single-input-single-output (SISO) system identification is employed.  
The block diagram of system identification on the controller is depicted in Figure 5. As to the rotor/AMB unit, the load to the power amplifiers is nothing but the AMB coils. Moreover, the AMB coil is of inductive load whose dynamic behavior can be expressed by a first-order equation. To identify the dynamics of the controller, the AMB coils are replaced by resistors whose resistance values are the same as those of the AMB coils. Furthermore, an anti-aliasing filter, i.e., a second-order Butterworth filter, is cascaded ahead of the ADC (analog-to-digital converter) to restrict the bandwidth of the signal to satisfy the Nyquist-Shannon sampling theorem over the band of interest [29]. The test rig for system identification on the controller is shown in Figure 6. To identify the controller, the input signal is the type of chirp in a sinusoidal waveform whose frequency is increased exponentially. The initial frequency of the chirp signal is 0 Hz, and the final frequency is 5000 Hz. The time duration of the chirp signal is set as 10 s, and the sampling period of _DS1104_, \(T_{\text{S}}\), is set as 0.5 ms.  
Figure 4: Detailed structures of the control circuit of AMBs.  
Figure 5: Block diagram of system identification on commercial controller.