# Identification Approach for Nonlinear MIMO Dynamics of Closed-Loop Active Magnetic Bearing System
###### Abstract  
A systematic identification approach for the rotor/radial active magnetic bearing (rotor/RAMB) system is presented in this study. First, the system identification of the controller of commercial TMP is undertaken, and the corresponding linear dynamic models are constructed. To perfectly excite the nonlinearities of the rotor/RAMB system, a parallel amplitude-modulated pseudo-random binary sequence (PAPRBS) generator, which possesses the merits of no correlation among the perturbation signals, is employed. The dynamics of the rotor/RAMB system is identified with a Hammerstein-Wiener model. To reduce the difficulty of the identified two nonlinear blocks, the output nonlinear characteristics are estimated prior to the recursive process. Two conventional nonlinear model structures, i.e., NARX and NARMAX, are employed for comparison to verify the effectiveness of the identified Hammerstein-Wiener model. The averaged fit values of the Hammerstein-Wiener model, NARX model, and NARMAX model are 93.25%, 88.36%, and 76.91%, respectively.  
system identification; closed-loop system; magnetic bearing; multi-input multi-output (MIMO); nonlinear dynamics +
Footnote †: journal: Applied  
On the other hand, scholars have proposed various identification procedures to identify the overall rotor/AMB dynamics. [PERSON] investigated the nonlinear dynamics of rotor levitated by the passive-active magnetic bearing [22]. [PERSON] et al. established a 2 \(\times\) 2 MIMO system identification procedure. The resulted model is the combination of both rigid-mode and flexible-mode models [23]. [PERSON] and [PERSON] proposed a two-stage identification approach with the continuous subspace method to model the MIMO magnetic-bearing system [24]. [PERSON] and [PERSON] proposed an identification approach to model the linear MIMO dynamics of the radial-magnetic-bearing system [25]. To identify more appropriate behaviors of a real rotor/AMB system, the nonlinear auto-regressive methods are applied. [PERSON] et al. identified the model of zero-bias axial magnetic bearing with the NARX (nonlinear autoregressive with external input) neural network [26]. [PERSON] and [PERSON] estimated the coefficients of SISO (single-input, single-output) NARMAX (nonlinear auto-regressive moving average with exogenous variables) polynomial model of radial magnetic bearing [27]. [PERSON] et al. proposed a genetic algorithms (GA) identification for AMB which can get the global optimum estimation [28].  
Since the dynamics of an open-loop active magnetic bearing (AMB) system is inherently unstable, a controller is essential for an AMB system. However, the performance and the dynamics of the AMB system are dominated by the controller. As a result, the accuracy of the identified model employed to design the controller is important. That is, the more informative the system model is, the more suitable the model-based controller can be designed. However, few papers presented identification procedures for nonlinear MIMO dynamics of the closed-loop rotor/AMB system. Moreover, many nonlinear models of AMBs are identified with black-box identification approaches. It is hard to interpret the information from the black-box models. As most of the controllers for AMBs are model-based controllers, this study aims to propose an identification approach to estimate a high-accuracy dynamic model from a MIMO closed-loop system for controller design.