静电悬浮加速度计伺服控制分析

Servo-control Analysis of Electrostatically Suspended Accelerometer

根据广义相对论原理选定的坐标系参照物为理想情况下在轨道上自由飘浮的卫星,据此讨论静电悬浮加速度计检验质量块的运动和电极笼的运动,得到检验质量在电极内运动的动力学方程,证明以往相关文献提供的公式存在明显缺陷;在此基础上分析了伺服控制电路,给出了电阻尼系数、闭环自然谐振的角频率(或称为加速度计的基础角频率)、受静电负刚度等非受控刚度制约的角频率、来自于静电悬浮的加速度、检验质量的相对位移等一系列表达式,从而提出必须有足够的增益以提供适度的闭环自然谐振角频率.给出了位置噪声引起的加速度噪声表达式,证明当伺服回路的增益足够大时,在悬浮频带内检验质量的相对位移几乎为零.

According to the principle of general relativity, in this paper the reference frame is chosen as the satellites, which levitate freely in the orbit under ideal circumstance, The movement of the test mass and the electrode cage of the electrostatically suspended accelerometer are discussed and the dynamics equation of test mass motion, inside the electrode cage is obtained. It is beared out, that the visible lacunan is in the similar expression offered by references [1], [2]. The servo-control circuitry of the electrostatically suspended accelerometer is analyzed and the expressions of the electric damp coefficient, the closed loop natural angular frequency （i.e. the basic angular frequency of the accelerometer）, the angular frequency dominated by the uncontrolled stiffness, such as the electrostatic negative stiffness, the acceleration from electrostatically suspending and the relatively displacement of the test mass etc are presented. It is put forward that the gain of the servo-control circuitry must be sufficient to provide the appropriate closed loop natural angular frequency. The expressions of the acceleration noise caused by the position noise are offered. It is proved, that the relatively displacement of the test mass is nearly naught in the frequency bandwidth of the suspension, when the gain of the servo-control circuitry is sufficient.