Design and validation of a high-voltage levitation circuit for electrostatic accelerometers

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.

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.

Rotation control of a variable-capacitance electrostatic motor for space equivalence principle tests with rotating masses

Variable-capacitance electrostatic motors are ideal for driving the test mass in ultra-low-noise electrostatic accelerometers. Such devices are essential for testing the new equivalence principle (NEP) with rotating extended masses. However, as the air-film damping is greatly reduced by placing the sensor core assembly in a high-vacuum housing, this synchronous motor may easily fall out of step and suffer spin-up failures with traditional open-loop excitation. In this study, a synchronous electronic phase commutation scheme is proposed by sensing the three-phase position change of the rotor poles and activating the stator electrodes in careful correlation with the instantaneous rotor position. Experiments on a ground-test NEP instrument prototype show that the proposed closed-loop excitation scheme can spin-up the rotor synchronously and maintain stable constant-speed operation of this macroscale variable capacitance motor operated in a high-vacuum environment. This rotation control method is also applicable to the synchronous operation of micromachined variable-capacitance electrostatic motors.

Modeling and compensation of cross-axis coupling in an electrostatic accelerometer for testing the equivalence principle

Electrostatic accelerometers have extremely high sensitivity and are ideal scientific instruments for measuring very weak acceleration. In particular, a single-sensitive-axis electrostatic accelerometer can be used for testing the equivalence principle in space. Sensitive-axis capacitances formed by axial electrodes and a cylindrical proof mass vary with the axial motion of the mass and are also affected by radial motion, which results in cross-axis coupling disturbances. A quantitative model is built to analyze the cross-axis coupling effect on the sensitive axis from the radial suspension loop, including a nonlinear model for large radial motion and a linear model for small radial motion. Frequency response simulation shows that the cross-axis coupling effect for a small signal case arises mostly in the high-frequency range. Experiments are carried out with a ground-based electrostatic accelerometer made of a single, non-rotating test cylinder, and in this case, the experimental results are utilized to verify the mathematical model. Cross-axis coupling for small signal perturbations is virtually removed if the equilibrium position of the proof mass is calibrated to the null position of the sensor cage. In addition, data post-processing can further attenuate the cross-axis coupling disturbances when dealing with large radial motion. The cross-axis coupling disturbances on both the position and the acceleration measurement signals in the sensitive axis are mostly removed in ground-based experiments. The proposed model and compensation can be extended to space equivalence principle instruments and other electrostatic accelerometers with a cylindrical proof mass.

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

High-precision electrostatic accelerometers have achieved remarkable success in satellite Earth gravity field recovery missions. Ultralow-noise inertial sensors play important roles in space gravitational wave detection missions such as the Laser Interferometer Space Antenna (LISA) mission, and key technologies have been verified in the LISA Pathfinder mission. Meanwhile, at Huazhong University of Science and Technology (HUST, China), a space accelerometer and inertial sensor based on capacitive sensors and the electrostatic control technique have also been studied and developed independently for more than 16 years. In this paper, we review the operational principle, application, and requirements of the electrostatic accelerometer and inertial sensor in different space missions. The development and progress of a space electrostatic accelerometer at HUST, including ground investigation and space verification are presented.

Design and Fabrication of a Differential Electrostatic Accelerometer for Space-Station Testing of the Equivalence Principle

The differential electrostatic space accelerometer is an equivalence principle (EP) experiment instrument proposed to operate onboard China’s space station in the 2020s. It is designed to compare the spin-spin interaction between two rotating extended bodies and the Earth to a precision of 10⁻¹², which is five orders of magnitude better than terrestrial experiment results to date. To achieve the targeted test accuracy, the sensitive space accelerometer will use the very soft space environment provided by a quasi-drag-free floating capsule and long-time observation of the free-fall mass motion for integration of the measurements over 20 orbits. In this work, we describe the design and capability of the differential accelerometer to test weak space acceleration. Modeling and simulation results of the electrostatic suspension and electrostatic motor are presented based on attainable space microgravity condition. Noise evaluation shows that the electrostatic actuation and residual non-gravitational acceleration are two major noise sources. The evaluated differential acceleration noise is 1.01 × 10⁻⁹ m/s²/Hz^1/2 at the NEP signal frequency of 0.182 mHz, by neglecting small acceleration disturbances. The preliminary work on development of the first instrument prototype is introduced for on-ground technological assessments. This development has already confirmed several crucial fabrication processes and measurement techniques and it will open the way to the construction of the final differential space accelerometer.

Self-Locking Avoidance and Stiffness Compensation of a Three-Axis Micromachined Electrostatically Suspended Accelerometer

A micromachined electrostatically-suspended accelerometer (MESA) is a kind of three-axis inertial sensor based on fully-contactless electrostatic suspension of the proof mass (PM). It has the potential to offer broad bandwidth, high sensitivity, wide dynamic range and, thus, would be perfectly suited for land seismic acquisition. Previous experiments showed that it is hard to lift up the PM successfully during initial levitation as the mass needs to be levitated simultaneously in all six degrees of freedom (DoFs). By analyzing the coupling electrostatic forces and torques between three lateral axes, it is found there exists a self-locking zone due to the cross-axis coupling effect. To minimize the cross-axis coupling and solve the initial levitation problem, this paper proposes an effective control scheme by delaying the operation of one lateral actuator. The experimental result demonstrates that the PM can be levitated up with six-DoF suspension operation at any initial position. We also propose a feed-forward compensation approach to minimize the negative stiffness effect inherent in electrostatic suspension. The experiment results demonstrate that a more broadband linear amplitude-frequency response and higher suspension stiffness can be achieved, which is crucial to maintain high vector fidelity for potential use as a three-component MEMS geophone. The preliminary performance tests of the three-axis linear accelerometer were conducted under normal atmospheric pressure and room temperature. The main results and noise analysis are presented. It is shown that vacuum packaging of the MEMS sensor is essential to extend the bandwidth and lower the noise floor, especially for low-noise seismic data acquisition.