静电悬浮轴承转子不平衡振动控制方法的研究

【作者】 李振杰；

【导师】 侯伯杰； 韩丰田；

【作者基本信息】 郑州大学 ， 机械电子工程， 2005， 硕士

【摘要】 球形转子是静电陀螺仪的核心部件,其质量不平衡将引起与转子同频的振动,开展抑制球形转子不平衡振动的研究是研制高精度静电陀螺的关键。本文提出了采用陷波滤波器来抑制转子振动的方法,文中重点阐述了陷波器参数的选取方法,并研究了引入陷波滤波器后陀螺支承系统的闭环稳定性、动态刚度和动态响应的变化,其主要内容和成果包括: 推导出了描述偏心转子的球心位移、静电干扰力与静电支承系统频率特性之间关系的数学模型。理论分析表明,系统主动刚度的变化会影响转子的球心位移和静电干扰力。进一步分析显示,陷波器能够改变系统的主动刚度,在其中心频率附近,主动刚度会降至零,转子旋转轴迹点位于质心附近,球心位移和静电干扰力都会减小。对于反馈线性化后的系统,转子旋转轴迹点则完全和质心重合,转子绕惯性主轴旋转,静电干扰力降至零。 分别研究了传统陷波器和通用陷波器的特性及其参数的确定方法,通过仿真与实验比较了二者对陀螺支承系统的影响。结果显示,当传统陷波器的中心频率大于系统的剪切频率时,支承系统的稳定性不被破坏,因此其中心频率的选择受到系统参数的限制;而通用陷波器通过T矩阵,可以灵活调整零极点的分布,因此易于保证系统稳定性,陷波器的参数选取不受支承系统特性的限制。 为了在DSP上实现给出的陷波器算法,需要将连续域中设计的陷波器离散化。本文讨论了离散化时需重点考虑的两个问题:采样周期的选取和频率畸变。综合各方因素,最终选定采样周期为40μs,并给出了基于matlab函数进行频率预畸变的离散化方法。 电模拟实验表明,引入陷波器后,系统闭环带宽和谐振峰基本没有改变,而系统的动态刚度在中心频率附近有显著变化,对于低带宽系统,动态刚度在中心频率附近提高了,而对于高带宽系统,动态刚度在靠近中心频率左侧下降,在右侧上升;系统的动态响应表现出“蠕形”现象,“蠕形”的幅值与陷波器衰减系数和方波激励信号的频率有关。减小衰减系数,“蠕形”幅值就可以减小;当转子频率是方波激励频率的偶数倍时,“蠕形”幅度最小,当奇数倍时,“蠕形”幅度最大。 计算结果表明,加入陷波器后使得转子径向不平衡振动引起的静电干扰力更多还原

【Abstract】 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.更多还原