Thermal Noise Decoupling of Micro-Newton Thrust Measured in a Torsion Balance

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.

Microgravity Decoupling in Torsion Pendulum for Enhanced Micro-Newton Thrust Measurement

“…Generally, when the thrust measurement period is short, the relationship between and is constant. However, when the measurement period is long, because of the thermal strain of the structure [17], the installation base of the torsion pendulum is no longer fixed, the tilt caused by thermal expansion and cold contraction, the center of mass of the pendulum frame deviates from the rotating axis, so that the quasi-static balance relationship of the torsion pendulum becomes:…”

Synchronization of dynamical systems on Riemannian manifolds by an extended PID-type control theory: Numerical evaluation

“…Introduction. Proportional-integral-derivative control (PID) is a well-known control theory widely utilized in engineering practice and in applied sciences [1,6,9,19,26,31,32,35,36]. The general idea to control a dynamical system into approaching a desired state trajectory is to define an error field and to take a driving signal as a linear combination of the error field, of the time-derivative of the error field and of a time-integral of the state-to-state error field.…”