Nonlinear Analysis for Influence of Parametric Uncertainty on the Stability of Rotor System With Active Magnetic Bearing Using Feedback Linearization

Abstract

Active magnetic bearing (AMB) is the device to support and control rotating shaft. Feedback linearization is one of the methods to compensate the system nonlinearity, and it is often used in the control of AMB. Some parameters in the electromagnetic force model have often been ignored or their parametric uncertainty from the nominal values has been calibrated; however, their influence on the stability has not been investigated. In this paper, the influence of the parametric uncertainty in the electromagnetic force model on the stability of AMB is investigated. The equilibrium positions and their stability are investigated and clarified analytically. Furthermore, the choice of the parameter value for improving the stability of AMB with feedback linearization is proposed, and its effectiveness is explained analytically. It is shown that the proposed choice of the parameter value also reduces the remained nonlinearity significantly. The validity of theoretical results and proposed choice of the parameter value are confirmed by experiment.

A state-of-the-art review on uncertainty analysis of rotor systems

“…However, the variabilities of the natural characteristics, critical dynamic responses and any other important findings should be also experimentally verified and it is mandatory to demonstrate the various techniques proposed are reliable. Some works present good results that are validated experimentally, for example, the analyses of measurement uncertainty [88], the parameter identification of faults or bearings [166,256], characterizing the influence of uncertainty in rotor balancing [44,175], control problems [225] and validations of nonlinear FRFs [298]. However, the number of experimental studies on this topic is limited and it is far from sufficient because standard strategies and mature experiment methods are still missing.…”

“…The research on nonlinear rotordynamics under uncertainty is more difficult than the linear studies since there are interactions between nonlinearities and uncertainties. Some papers investigated the nonlinear dynamics of the rotor-AMBs systems [64,225,226] and cracked rotor systems [47,75,76,115,227,228]. Nonlinear analysis techniques, such as the alternating frequency/time technique (HB-AFT), orthogonal polynomial approximation and linearization, are used to deal with nonlinearities.…”

“…17(c). Considering leakages in the magnetic circuit and the non-flat shape of the magnetic circuit at the gap in electromagnets, Kato et al [225] revealed the effects of parametric uncertainties in the electromagnetic force model on the equilibrium positions and their stability. In addition, the stability of the AMB was improved by choosing the proper parameter value based on feedback linearization.…”

Mechanism of Low Frequency Vibration Caused by Actuator Saturation for AMB based Motor and Its Compensation Strategy

“…The results showed that the AMB based rotor exhibit amplitude hopping and multi frequency vibration under the action of the nonlinear electromagnetic force, and the nonlinear dynamic response of the system could be effectively affected by changing the magnitude of the external excitation. Literature [23] studied the influence of the uncertainty of electromagnetic force parameters on the stability of the AMB control system, and proved that when the electromagnetic force parameters contained the uncertainty of parameters, additional equilibrium points would appear in the case of feedback linearization, and these additional points would seriously affect the stability of the system, causing the system to diverge due to initial conditions or disturbances. The above results have a more thorough explanation of the nonlinear electromagnetic force its influence, but there is no internal relationship between it and the low frequency vibration of the rotor.…”

Research on Dynamic Modeling and Parameter Influence of Adaptive Gun Head Jet System of Fire-Fighting Monitor

“…Methods like sensitivity analysis [24], numerical simulation [25], and feedback linearization etc. [26] have been applied by scholars in studying the influence analysis of dynamic system parameters. In terms of parameter optimization, multi-factor design optimization has become the major research direction.…”