Stability analysis and imbalance compensation for active magnetic bearing with gyroscopic effects

Abstract

To reject the influence of gyroscopic effects on system stability and to attenuate the imbalance vibration for active magnetic bearing (AMB) of a magnetically suspended control moment gyro (MSCMG), this paper proposes a controller composed of a complex exponential function feedback and a clean current approach. The AMB is modeled and its dynamic analysis is performed, the complex exponential function feedback can provide proper phase adjustment and effectively suppress the nutation and the precession of the gyroscopic effects, notch filter is adopted to clean the synchronous current and to compensate the imbalance vibration. The stability and parameters of the AMB are analyzed and designed by using the root locus method. Both simulation and experimental results indicate the good effectiveness of the presented approach.

Field Balancing and Harmonic Vibration Suppression in Rigid AMB-Rotor Systems with Rotor Imbalances and Sensor Runout

“…Assuming that the parameters among the four decentralized directions have identical values and the gravity is acting in the Z direction, the dynamics of the rotor in the radial 4-DOF directions can be given based on earlier work [ 30 ]: where M is the mass matrix, G is the gyroscopic matrix, k i is the current stiffness, G w ( s ) is the transfer function of the power amplifier, k v is a coefficient related to the motion induced voltage, T fs , T s , and T ft are coordinate transfer matrices, G s ( s ) is the displacement controller matrix designed in the generalized coordinate, and k x is the displacement stiffness: where m is the rotor mass, J r and J z are the transverse and polar moments of inertia of the rotor, respectively, k s is the coefficient of the displacement sensor, k P and k D are the coefficients of the typical proportional-derivative controller, a pseudo integrator is used to avoid over-restriction, k I and k IM are its parameters, I 4 is a 4 × 4 unit matrix, k rh and k rl are gains of the cross feedback control, ω rh and ω rl are the cutoff angular frequencies of the high-pass and low-pass filters, respectively, ϕ and φ are the cross phases, k w and ω w are the gain and the cutoff angular frequency of the simplified low-pass power amplifier model. The PID controller is employed to stabilize the AMB system with a negative stiffness, while the cross feedback controller is designed to suppress the gyroscopic effect [ 26 ].…”

“…To reduce the synchronous current, a notch filter is widely used and studied owing to its advantages of low computation effort and easy analysis of closed-loop stability [ 24 , 25 ]. However, residual synchronous currents, which are generated by the motion induced voltage, will still remain if the synchronous control voltage is merely cleaned in the AMB-rotor system with voltage-source power amplifiers [ 26 ].…”

Active vibration control of rotor imbalance in active magnetic bearing systems

“…where " and are the amount and initial phase of the static imbalance, and are the amount and initial phase of the dynamic imbalance. Based on previous work (Xu et al, 2012), the fundamental dynamic equations of the rotor for four radial degrees-of-freedom are:…”

Direct Vibration Force Suppression for Magnetically Suspended Motor Based on Synchronous Rotating Frame Transformation

“…Despite their advantages, vibration caused by unbalance mass of rotor and sensor runout is a serious challenge in rotating machinery. Vibration contains Synchronous vibration and multi-frequency vibration [11], [12]. Then mass unbalance coupled with the residual displacement caused by the supported position difference between the balancer and the AMBs lead to the generation of synchronous vibration force.…”