# Identification Approach for Nonlinear MIMO Dynamics of Closed-Loop Active Magnetic Bearing System
## 3 Experimental Setup for Identification of Rotor/RAMB Dynamic Model
### Parallel Amplitude-Modulated Pseudo-Random Binary Sequence (PAPRBS) Generator  
Numerous types of excitation signals can be applied for system identification, e.g., pseudo-random binary sequence (PRBS), chirp signal, multi-sine signal, and stepped sinusoidal wave [30]. It is noted that the rated rotational speed of the TMP rotor is pretty high, e.g., 30,000 RPM for the TMP studied by this work, and the rated speed is higher than the first bending frequency of the TMP rotor. Consequently, the chirp signal is not suitable for system identification upon the rotor/AMB dynamics since the levitated rotor could collide with the auxiliary bearings as the frequency of the perturbation signal is close  
Figure 11: Photograph of summer module. Figure 10: Layout of summer module. to/or across the resonance frequencies of the rotor/AMB unit. Among these commonly employed perturbation signals, PRBS, namely maximum length sequence or M-sequence, possesses the merits of deterministic, lowest crest factor and white-noise-alike properties. Therefore, the accuracy of system identification by PRBS can be guaranteed to some extent. In addition, since the system to be identified, i.e., the rotor/RAMB (rotor/radial active magnetic bearing) dynamics, is a MIMO system, the correlation degree between any two perturbation signals has to be reduced as much as possible. Fortunately, once the parallel PRBS generator is well-designed, the aforesaid correlations can be almost eliminated. In this study, hence, the parallel PRBS is adopted as the perturbation signal to identify the MIMO rotor/RAMB dynamic system. Generally, the number of amplitude types of a PRBS is 2, i.e., +V and \(-\)V. However, to explore the nonlinear dynamic properties of the rotor/RAMB unit, the amplitude of the perturbation signal has to vary so that the nonlinearities of the studied system, e.g., saturation, hysteresis, or high-order modes, can be appropriately excited. Therefore, in this study, the conventional parallel PRBS generator is extended to a parallel \"**amplitude-modulated**\" PRBS (PAPRBS) generator by multiplying a random number sequence. The proposed PAPRBS is designed and realized via the commercial software, Simulink. The layout of the Simulink code for the PAPRBS generator is shown in Figure 12. The order of the PAPRBS is set as 15. As a result, the maximum length of the 15 th-order PAPRBS is \(2^{15}-1=32767\). Four separated sets of perturbation signals can be generated by the PAPRBS generator simultaneously to identify the rotor/RAMB dynamics. To make the four sets of the perturbation signals uncorrelated, the start points of the four sets of perturbation signals are set at: (i) the beginning, (ii) the one-fourth, (iii) the one-half, and (iv) the three-fourth of the 15 th-order PRBS, respectively. The length of each perturbation signal sequence is made up by 8000 points such that the correlation between any two perturbation signals can be almost eliminated. The first 200 points of these four perturbation signal sequences are shown in Figure 13. It can be observed that the patterns of these four signals are quite different. To be more specific, the correlations of these four perturbation signals are evaluated and shown in Figure 14. From Figure 14, no cross-correlation between any two of these four perturbation signals is found. It is noted that the bit duration of PAPRBS has to be properly chosen so that the bandwidth of the perturbation signal can cover the operational range of the object/system to be identified.