The space gravitational wave detection and drag free control requires the micro-thruster to have ultra-low thrust noise within 0.1 mHz–0.1 Hz, which brings a great challenge to calibration on the ground because it is impossible to shield any spurious couplings due to the asymmetry of torsion balance. Most thrusters dissipate heat during the test, making the rotation axis tilt and components undergo thermal drift, which is hysteretic and asymmetric for micro-Newton thrust measurement. With reference to LISA’s research and coming up with ideas inspired from proportional-integral-derivative (PID) control and multi-timescale (MTS), this paper proposes to expand the state space of temperature to be applied on the thrust prediction based on fine tree regression (FTR) and to subtract the thermal noise filtered by transfer function fitted with z-domain vector fitting (ZDVF). The results show that thrust variation of diurnal asymmetry in temperature is decoupled from 24 μN/Hz^1/2 to 4.9 μN/Hz^1/2 at 0.11 mHz. Additionally, 1 μN square wave modulation of electrostatic force is extracted from the ambiguous thermal drift background of positive temperature coefficient (PTC) heater. The PID-FTR validation is performed with experimental data in thermal noise decoupling, which can guide the design of thermal control and be extended to other physical quantities for noise decoupling.

中文翻译：

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在扭力天平中测量的微牛顿推力的热噪声解耦

空间引力波探测和无拖曳控制要求微型推进器具有0.1 mHz-0.1 Hz范围内的超低推力噪声，这给地面标定带来了巨大挑战，因为无法屏蔽任何杂散耦合。扭力平衡不对称。大多数推进器在测试过程中散热，使旋转轴倾斜和组件发生热漂移，这对于微牛顿推力测量是滞后和不对称的。参考 LISA 的研究和从比例积分微分 (PID) 控制和多时间尺度 (MTS) 中获得灵感的想法，本文提出扩展温度状态空间以应用于基于精细树回归 (FTR) 的推力预测，并减去通过 z 域向量拟合 (ZDVF) 拟合的传递函数过滤的热噪声。结果表明，温度昼夜不对称的推力变化与 24 μN/Hz 解耦^1/2至 4.9 μN/Hz ^1/2在 0.11 mHz。此外，从正温度系数 (PTC) 加热器的模糊热漂移背景中提取了静电力的 1 μN 方波调制。PID-FTR 验证是用热噪声解耦中的实验数据进行的，它可以指导热控制的设计并扩展到其他物理量以进行噪声解耦。