Research and Development of Electrostatic Accelerometers for Space Science Missions at HUST

Using DWS Optical Readout to Improve the Sensitivity of Torsion Pendulum

In space gravitational wave detection missions, a drag-free system is used to keep the test mass (TM) free-falling in an ultralow-noise environment. Ground verification experiments should be carried out to clarify the shielding and compensating capabilities of the system for multiple stray force noises. A hybrid apparatus was designed and analyzed based on the traditional torsion pendulum, and a technique for enhancing the sensitivity of the torsion pendulum system by employing the differential wavefront sensing (DWS) optical readout was proposed. The readout resolution experiment was then carried out on an optical bench that was designed and established. The results indicate that the angular resolution of the DWS signal in optical readout mode can reach the level of 10 nrad/Hz1/2 over the full measurement band. Compared with the autocollimator, the sensitivity of the torsional pendulum is noticeably improved, and the background noise is expected to reach 4.5 × 10-15 Nm/Hz1/2@10 mHz. This method could also be applied to future upgrades of similar systems.

A method for high-precision measuring differential transformer asymmetry

The differential transformer is an important component in the front-end electronics of high-precision capacitive position sensing circuits, which are widely employed in space inertial sensors and electrostatic accelerometers. The position sensing offset, one of the space inertial sensors' most critical error sources in the performance range, is dominated by the differential transformer asymmetry and requires a high-precision evaluation. This paper proposes a method to assess differential transformers' asymmetry and realize a prototype circuit to test a transformer sample. The results show that the asymmetry measurement precision can achieve 0.6 ppm for the transformer with an asymmetry level of about -278.2 ppm.

Robust Control Allocation for Space Inertial Sensor under Test Mass Release Phase with Overcritical Conditions

This paper proposes a robust control allocation for the capture control of the space inertial sensor's test mass under overcritical conditions. Uncertainty factors of the test mass control system under the overcritical condition are analyzed first, and a 6-DOF test mass dynamics model with system uncertainty is established. Subsequently, a time-varying weight function is designed to coordinate the allocation of 6-DOF generalized forces. Moreover, a robust control allocation method is proposed to distribute the commanded forces and torques into individual electrodes in an optimal manner, which takes into account the system uncertainties. This method transforms the robust control allocation problem into a second-order cone optimization problem, and its dual problem is introduced to simplify the computational complexity and improve the solving efficiency. Numerical simulation results are presented to illustrate and highlight the fine performance benefits obtained using the proposed robust control allocation method, which improves capture efficiency, increases the security margin and reduces allocation errors.

Analysis of a Capacitive Sensing Circuit and Sensitive Structure Based on a Low-Temperature-Drift Planar Transformer

In space gravitational-wave-detection missions, inertial sensors are used as the core loads, and their acceleration noise needs to reach 3×10−15 ms−2/Hz at a frequency of 0.1 mHz, which corresponds to the capacitive sensing system; the capacitive sensing noise on the sensitive axis needs to reach 1 aF/Hz. Unlike traditional circuit noise evaluation, the noise in the mHz frequency band is dominated by the thermal noise and the 1/f noise of the device, which is a challenging technical goal. In this paper, a low-frequency, high-precision resonant capacitor bridge method based on a planar transformer is used. Compared with the traditional winding transformer, the developed planar transformer has the advantages of low temperature drift and low 1/f noise. For closed-loop measurements of capacitive sensing circuits and sensitive structures, the minimum capacitive resolution in the time domain is about 3 aF, which is far lower than the scientific measurement resolution requirement of 5.8 fF for gravitational wave detection. The capacitive sensing noise is converted to 1.095 aF/Hz in the frequency band of 10 mHz−1 Hz. Although there is a gap between the closed-loop measurement results and the final index, the measurement environment is an experimental condition without temperature control on the ground; additionally, in China, the measurement integrity and actual measurement results of the capacitive sensing function have reached a domestic leading level. This is the realization of China’s future space gravitational wave exploration.

Bias Stability Investigation of a Triaxial Navigation-Compatible Accelerometer with an Electrostatic Spring

The bias stability performance of accelerometers is essential for an inertial navigation system. The traditional pendulous accelerometer usually has a flexible connection structure, which could limit the long-term bias stability. Here, based on the main technologies employed in previous space missions of our group, we developed a terrestrial triaxial navigation-compatible accelerometer. Because there is no mechanical connection between the inertial test mass and the frame, the bias performance relies on the stability of the equivalent electrostatic spring, where further sources are analyzed to get the optimal electrostatic force scheme. To investigate the bias stability under different ranges, the vertical and horizontal measurement ranges are designed at 5 g and ±10 mg, respectively. A low-noise high-voltage levitation scheme is adopted to extend the vertical measurement range from sub-mg to more than earth's 1-g gravity. Finally, the experimental validation results show that the 24-h bias stability of vertical and two horizontal directions come to 13.8 μg, 0.84 μg, and 0.77 μg, respectively.

Study on the Method of Charge Accumulation Suppression of Electrostatic Suspended Accelerometer

Electrostatic suspended accelerometers (ESAs) are widely used in high accuracy acceleration measurement. However, there exist accumulated charges on the isolated mass which damage the accuracy and the stability of ESAs. In this paper, we propose to apply actuation voltage with a combined waveform to suppress the acceleration noise due to deposited charge. A model of the electrostatic force on the mass is established and the deviation voltage is found to be the dominant source of charge noise. Based on the analysis of disturbance electrostatic force under DC and AC signals, actuation combined with DC and AC voltage is designed and the disturbance force due to charge can be suppressed through adjustment towards the duty cycle of different compositions. Simulations and experiments are carried out and the results indicate that the disturbance due to charge can be suppressed up to 40%, which validates the efficiency of the scheme.

GRACE Accelerometers Sensitive to Ionosphere Plasma Waves: Similarities between Twangs and Whistlers

Electrostatic space accelerometers are high-precision instruments used in gravity and magnetic fields and in fundamental physics missions. From their first use in space, these instruments show disturbances around the read-out frequency. In recent missions like Swarm and GRACE-FO, these instruments are seriously compromised. Their capability cannot be fully exploited or, in the worst case, not used for science data processing at all. We currently neither understand the mechanism nor the cause of the disturbance. For that reason, every correlation, direct or indirect, between signatures in the accelerometer data and other phenomena in the satellite environment is very important to study. In the GRACE mission, some of the disturbances relate to onboard current switching processes, such as switching of heater and torquer currents. In this paper, we examine the phenomena called twangs. The shape of these disturbances is responsible for their name, because they look like a decaying tone. Some of these twangs seem to relate to changing currents, too. They occur when sunlight hits surfaces of the satellite. This can cause the discharging of satellite parts. Here, we focus on special twangs, which we call cloud-related twangs, as recent investigations related them to cloud coverage. How can clouds in the troposphere influence a satellite, orbiting in the ionosphere? We investigated the troposphere–ionosphere coupling and found that the only coupling which can be responsible for disturbances on satellites and which may affect the accelerometers, are electromagnetic waves traveling in the so-called whistler mode at frequencies in the very-low-frequency (VLF) domain. This special propagation mode is a coupled electromagnetic and electrostatic mode. There, the electric field vector has a component in the direction of propagation due to the interaction with ions and the magnetic field in the ionosphere and magnetosphere. This led us to investigate the similarities between whistlers and twangs. The hypothesis that they are related is very important in our further understanding of disturbances on satellite instruments sensible to electromagnetic pulses in the range of very low frequencies and below.

Estimation and Error Analysis for Optomechanical Inertial Sensors

A sensor model and methodology to estimate the forcing accelerations measured using a novel optomechanical inertial sensor with the inclusion of stochastic bias and measurement noise processes is presented. A Kalman filter for the estimation of instantaneous sensor bias is developed; the outputs from this calibration step are then employed in two different approaches for the estimation of external accelerations applied to the sensor. The performance of the system is demonstrated using simulated measurements and representative values corresponding to a bench-tested 3.76 Hz oscillator. It is shown that the developed methods produce accurate estimates of the bias over a short calibration step. This information enables precise estimates of acceleration over an extended operation period. These results establish the feasibility of reliably precise acceleration estimates using the presented methods in conjunction with state of the art optomechanical sensing technology.

Highly precise in-plane displacement sensor based on an asymmetric fiber Fabry-Perot interferometer

An in-plane displacement sensor based on an asymmetric extrinsic fiber Fabry-Perot interferometer (EFPI) is proposed and demonstrated. The asymmetric EFPI composed of a step-shaped external reflector and a cleaved fiber end face can be equivalent to two parallel FPIs with slightly different cavity lengths. By calculating the peak intensity difference of the two FPIs, the in-plane displacement can be demodulated with enhanced sensitivity and suppressed common mode noise. Both theoretical analyses and experimental results show that the sensitivity and the linear range of the in-plane displacement sensor are dependent on the cavity length. A displacement resolution of 5 nm and a linear range of ±7µm under the cavity length of 250 µm are achieved in the experiment. The proposed in-plane displacement sensor with a nanometric resolution and compact size can be widely used in the fields of metrology, accelerometers, and semiconductor manufacture.

Noise investigation of an electrostatic accelerometer by a high-voltage levitation method combined with a translation-tilt compensation pendulum bench

A high precision electrostatic accelerometer has widely been employed to measure gravity gradients and detect gravitational waves in space. The high-voltage levitation method is one of the solutions for testing electrostatic accelerometers on the ground, which aims at simultaneously detecting all six-degree-of-freedom movements of the electrostatic accelerometers engineering and flight prototypes. However, the noise performance in the high-voltage levitation test is mainly limited by seismic noise. The combined test of the accelerometer and vibration isolation platform is adopted to improve the detection precision of the high-voltage levitation method. In this paper, a high precision electrostatic accelerometer prototype is developed after designed appropriate mechanical parameters with a test mass weighing 300 g and with an estimated resolution of 2 × 10^-12 m/s²/Hz^1/2 from 0.01 to 0.4 Hz. Such a prototype is tested by the high-voltage levitation method, its measurement noise on the ground is mainly limited by the seismic noise, which is about 5 × 10^-7 m/s²/Hz^1/2 around 0.2 Hz and about 4 × 10^-8 m/s²/Hz^1/2 around 0.1 Hz. A vibration isolation pendulum bench based on the translation-tilt compensation principle is adopted for accelerometer prototype combined tests to suppress the seismic noise, which has a large bench area and the ability to adjust the tilt angle precisely. The measured accelerometer noise of the combined test with the translation-tilt compensation pendulum has reached 3 × 10^-9 m/s²/Hz^1/2 around 0.2 Hz, and it is about two orders of magnitude lower than the measurement noise on the ground. The combined test method provides technical guidance for further improving the noise level of ground test in the future.

Microgravity disturbance analysis on Chinese space laboratory

Many scientific experiments are conducted in space; therefore, it is critical to understand the microgravity environment of a space laboratory. The first Chinese cargo ship, Tianzhou-1 (TZ-1), entered space on 20 April, 2017 and later joined with the Tiangong-2 (TG-2) Chinese space laboratory. TZ-1 carried a high-precision electrostatic suspension accelerometer system (ES-ACC) for measuring the microgravity acceleration on the spacecraft and a microgravity-active vibration system (MAIS), which contained flexible quartz accelerometers (Q-ACC). The ES-ACC was able to provide a reduced-disturbance environment for the MAIS. The purpose of these two instruments was to validate novel technologies and as an opportunity to record the microgravity acceleration of TZ-1 and TG-2 in detail during spacecraft operation in different flight modes, with or without vibration isolation. The acceleration data were analyzed comprehensively in a time–frequency–amplitude spectrogram. Some periodical disturbances with orbital period and irregular signals related to certain in-orbit events were observed. After reducing those disturbances, the microgravity levels on TZ-1 and TG-2 could be resolved to better than 10⁻⁶ m/s² in the root mean square in the frequency of 0.01–10 Hz. These accurate measurements aboard the Chinese space laboratory will provide valuable information to optimize working conditions for scientific experiments.

Identification and compensation of quadratic terms of a space electrostatic accelerometer

The ultra-sensitive space electrostatic accelerometers have been successfully employed in the Earth's gravity field recovery missions and the space gravitational experiments. Since the accelerometer output in the measurement bandwidth can be influenced by the orbital high-frequency disturbances due to the second-order nonlinearity effects, the relevant quadratic term must be accurately compensated to guarantee the accuracy of the electrostatic accelerometer. In this paper, three sources of the quadratic term are studied and formulated. They are the offset of the test mass in the housing due to the bias of the capacitive position transducer, the asymmetry of the electrode area, and the asymmetry of the actuation electronics. Two feasible compensation methods and an identification means are proposed. Compensation is achieved by adjusting the test mass actual working position or the asymmetry factor of the feedback actuation voltage. Identification is conducted by applying a periodic high frequency signal on the electrodes. Finally, the proposed methods are demonstrated, in view of future space applications, by suspending the accelerometer test mass on a torsion pendulum.