Electrostatic Levitation Bearing Rotor Unbalance Vibration Control Method

As the key component of electrostatically suspended gyroscope (ESG), the spherical rotor with mass unbalance would cause unbalance vibration. Therefore, it's very important to carry out research on the suppressing rotor vibration for ESG with high precision. The thesis describes a method used to suppress the unbalance vibration with notch filter, and focuses on illustrating the methods of choosing the notch filter parameters and researching into the change of the closed-loop system stability, dynamic stiffness and dynamic response of the system after the notch filter is introduced into the system. The main contents of this research are the following:The mathematical models between displacement of the geometric center of rotor, electrostatic force and frequency characteristics of electrostatic suspension system are derived. It is shown that the change of active stiffness of the system would result in the change of displacement of the geometric center of rotor and electrostatic force. The analysis further indicates that the notch filter could alter the active stiffness of the system, which would decrease to zero near the center frequency of notch filter. Therefore rotation axis of the rotor would locate near mass center, and then the displacement of the geometric centre of rotor and electrostatic force would decrease. For the system including feedback linearization, rotation axis of the rotor is consistent with the mass center completely, that is to say, the rotor revolves round principal axis of inertia, and electrostatic force drops to zero.The characteristics of conventional notch filter and generalized notch filter and the methods of choosing its parameters are respectively presented in this thesis. Their impacts on the system are compared through simulation and experiment as well. It is shown that when the center frequency of notch filter is larger than the gain-crossing frequency of the system, the system's stability would not be destroyed; therefore the selection of its center frequency is limited by the system's parameter. However, the position of zero and pole of the generalized notch filter could be adjusted flexibly through T matrix, thus the system keep stable regardless of the suspension system parameters.In order to realize the digitization of the notch filter on DSP, the continuous notch filter must be converted into a set of difference equations that can be programmed directly into a control computer. Two key questions, selection of sampling period and phenomenon of frequency aberrance, must be considered when the continuous notch filter is discretized. Considering the combined impact of all kinds of factor, the sampling period is chosen to be 40 ^s. And the discretization method with frequency prewarping is presented based on a MATLAB function in the thesis.Simulating experiment of electronic circuit shows that after the notch filter being introduced into the system, the close-loop bandwidth and resonant peak of the system alter little. However, its dynamic stiffness changes greatly near the center frequency of the system. For the system with lower bandwidth, dynamic stiffness increases near center frequency, and for the system with higher bandwidth, dynamic stiffness decreases at the left near side of center frequency and enhance at the right near side of center frequency. The dynamic response of system appears a "worm crawling' phenomenon. Its magnitude is relative to attenuation coefficient of the notch filter and square wave frequency. If the attenuation coefficient reduces, the magnitude could do so. And if the rotor spin frequency is even times of frequency of square wave, the magnitude is lower, and if odd times or no integer times, the magnitude is larger.Computing results demonstrated that after the notch filter is introduced into the system, electrostatic disturbance force and torque arose by unbalance vibration of the rotor had reduced by 75.51 percent and 88 percent respectively, and rotor displacement had decreased by 51 percent. The rotors rotate almost round mass center. For the system including feedback linearization, the corresponding electrostatic disturbance force and torque drop to near zero, and rotor displacement decreases by 61 percent. The research results in this thesis arrive at anticipatable aims, and laid the firm foundations for further engineering applications of ESG.