Abstract
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/Hz1/2 to 4.9 μN/Hz1/2 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.
Highlights
Missions for micro-Newton thruster applications have become prosperous in recent years, and one of the greatest challenges comes from searching for gravitational waves in space [1,2]
A more accurate thrust measurement system is in need to measure the variance of the micro-Newton thrusters on the ground, which is hard for the case of an ultra-low thrust-to-weight ratio (TWR) less than 10−9
In addition to the analytical method to explore the mechanism of temperature action, it is easier to understand the thermal noise in terms of data stream of the system, such as z-domain vector fitting (ZDVF) used to fit the thrust transfer function and filter the thermal noise in the original results
Summary
Missions for micro-Newton thruster applications have become prosperous in recent years, and one of the greatest challenges comes from searching for gravitational waves in space [1,2]. Torsion balances have been widely used in exploring the behavior of gravity for their rotational symmetry across the x-y plane, which is suited for measuring torques while minimizing the impact of gravitational weight. At the University of Washington, a low-frequency torsion pendulum whose angle is measured using a Michelson interferometer was designed, which can be applied to tests of gravity and gravitational wave observation [5]. In the Institute of Mechanics, Chinese Academy of Sciences, a set of sub-micro-scale thrust measurement systems using a torsion pendulum was designed and successfully applied in the radiofrequency ion thruster test for “Taiji-1”, the first experiment satellite for space detection of gravitational waves in China [7]. The Airbus has adopted a double hanging pendulum balance to characterize the LISA dedicated micro-Newton thrusters based on the principle of differential measurement [8]
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