Yanzheng Bai

High resolution space quartz-flexure accelerometer based on capacitive sensing and electrostatic control technology

High precision accelerometer plays an important role in space scientific and technical applications. A quartz-flexure accelerometer operating in low frequency range, having a resolution of better than 1 ng/Hz(1/2), has been designed based on advanced capacitive sensing and electrostatic control technologies. A high precision capacitance displacement transducer with a resolution of better than 2 × 10(-6) pF/Hz(1/2) above 0.1 Hz, is used to measure the motion of the proof mass, and the mechanical stiffness of the spring oscillator is compensated by adjusting the voltage between the proof mass and the electrodes to induce a proper negative electrostatic stiffness, which increases the mechanical sensitivity and also suppresses the position measurement noise down to 3 × 10(-10) g/Hz(1/2) at 0.1 Hz. A high resolution analog-to-digital converter is used to directly readout the feedback voltage applied on the electrodes in order to suppress the action noise to 4 × 10(-10) g/Hz(1/2) at 0.1 Hz. A prototype of the quartz-flexure accelerometer has been developed and tested, and the preliminary experimental result shows that its resolution comes to about 8 ng/Hz(1/2) at 0.1 Hz, which is mainly limited by its mechanical thermal noise due to low quality factor.

Performance measurements of an inertial sensor with a two-stage controlled torsion pendulum

A novel two-stage electrostatically controlled torsion pendulum has been developed to simultaneously investigate the performance of a translational and a rotational degree of freedom of an electrostatic inertial sensor on ground. The motions of the proof mass (PM) relative to the electrode frame are monitored by a high-precision capacitance transducer, and are synchronously controlled by electrostatic actuators. The parasitic stiffness induced by capacitance transducers and the effect of the magnetic field are measured. Both translational and rotational motions of the PM succeed to be simultaneously controlled, and the cross-coupling effect between both controlled degrees of freedom is also preliminary measured. The experiments show that the scheme obviously suppresses the translational to rotational effect of the PM, and then effectively improves the torque resolution compared with the single-stage torsion pendulum. The noise floors of the controlled torsion pendulum come to 1.2 × 10 −11 NH z −1/2 along the translational degree of freedom, and 1.4 × 10 −13 NmH z −1/2 along the rotational degree of freedom, near 30 mHz, which are mainly limited by the back action of the capacitance transducer below 0.1 Hz and by the horizontal seismic noise disturbance above 0.1 Hz.

Resonant frequency detection and adjustment method for a capacitive transducer with differential transformer bridge

The capacitive transducer with differential transformer bridge is widely used in ultra-sensitive space accelerometers due to their simple structure and high resolution. In this paper, the front-end electronics of an inductive-capacitive resonant bridge transducer is analyzed. The analysis result shows that the performance of this transducer depends upon the case that the AC pumping frequency operates at the resonance point of the inductive-capacitive bridge. The effect of possible mismatch between the AC pumping frequency and the actual resonant frequency is discussed, and the theoretical analysis indicates that the output voltage noise of the front-end electronics will deteriorate by a factor of about 3 due to either a 5% variation of the AC pumping frequency or a 10% variation of the tuning capacitance. A pre-scanning method to determine the actual resonant frequency is proposed followed by the adjustment of the operating frequency or the change of the tuning capacitance in order to maintain expected high resolution level. An experiment to verify the mismatching effect and the adjustment method is provided.

A Novel Controller Design for the Next Generation Space Electrostatic Accelerometer Based on Disturbance Observation and Rejection

The state-of-the-art accelerometer technology has been widely applied in space missions. The performance of the next generation accelerometer in future geodesic satellites is pushed to 8×10−13m/s2/Hz1/2, which is close to the hardware fundamental limit. According to the instrument noise budget, the geodesic test mass must be kept in the center of the accelerometer within the bounds of 56 pm/Hz1/2 by the feedback controller. The unprecedented control requirements and necessity for the integration of calibration functions calls for a new type of control scheme with more flexibility and robustness. A novel digital controller design for the next generation electrostatic accelerometers based on disturbance observation and rejection with the well-studied Embedded Model Control (EMC) methodology is presented. The parameters are optimized automatically using a non-smooth optimization toolbox and setting a weighted H-infinity norm as the target. The precise frequency performance requirement of the accelerometer is well met during the batch auto-tuning, and a series of controllers for multiple working modes is generated. Simulation results show that the novel controller could obtain not only better disturbance rejection performance than the traditional Proportional Integral Derivative (PID) controllers, but also new instrument functions, including: easier tuning procedure, separation of measurement and control bandwidth and smooth control parameter switching.

Measurement of the effect of a thin discharging wire for an electrostatic inertial sensor with a high-quality-factor pendulum

In order to suppress the electrostatic and magnetic field effects, ultrathin metal wires are often employed for discharging the proof mass which is used in a high-precision space electrostatic accelerometer or gravitational experiments. This wire introduces a thermal noise limit based on fluctuation–dissipation theory, which depends upon its stiffness and structural loss. In this paper, a simple method for measuring the stiffness and the loss angle of a thin discharging wire is presented by connecting it to a pendulum suspended by a high-quality silica fiber with negligible dissipation. The stiffness and the loss angle of a 10 μm gold wire are measured; the experimental results agree with theoretical estimation. The thermal noise of the pendulum with a thin discharging wire is estimated, and its possible applications in the gravitational experiments are also discussed.

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

A simple high-voltage circuit with a voltage range of 0 to 900 V and an open-loop bandwidth of 11 kHz is realized by using an operational amplifier and a MOSFET combination. The circuit is used for the levitation of a test mass of 71 g, suspended below the top-electrodes with a gap distance of 57 μm, so that the performance of an electrostatic accelerometer can be tested on the ground. The translation noise of the accelerometer, limited by seismic noise, is about 4 × 10(-8) m/s(2)/Hz(1/2) at 0.1 Hz, while the high-voltage coupling noise is one-order of magnitude lower.

Electrostatic-control performance measurement of the inertial sensor with a torsion pendulum

An electrostatic-controlled torsion pendulum was used to simulate the operation of the inertial sensor in flight. The twist motion of the proof mass was monitored by a capacitance transducer and was controlled by an electrostatic actuator. The influences of the parasitic coupling of the capacitance transducer, the magnetic field, and the translation motion coupling were measured. The torque noise of the controlled pendulum came to about 6×10 -13 N m Hz -1/2 from 2 mHz to 0.1 Hz, mainly limited by the translation-rotation coupling and the back action of the capacitance sensor, which could be suppressed by extending the gap of the capacitance sensor.

Self-calibration method of the bias of a space electrostatic accelerometer

The high precision space electrostatic accelerometer is an instrument to measure the non-gravitational forces acting on a spacecraft. It is one of the key payloads for satellite gravity measurements and space fundamental physics experiments. The measurement error of the accelerometer directly affects the precision of gravity field recovery for the earth. This paper analyzes the sources of the bias according to the operating principle and structural constitution of the space electrostatic accelerometer. Models of bias due to the asymmetry of the displacement sensing system, including the mechanical sensor head and the capacitance sensing circuit, and the asymmetry of the feedback control actuator circuit are described separately. According to the two models, a method of bias self-calibration by using only the accelerometer data is proposed, based on the feedback voltage data of the accelerometer before and after modulating the DC biasing voltage (Vb) applied on its test mass. Two types of accelerometer biases are evaluated separately using in-orbit measurement data of a space electrostatic accelerometer. Based on the preliminary analysis, the bias of the accelerometer onboard of an experiment satellite is evaluated to be around 10-4 m/s2, about 4 orders of magnitude greater than the noise limit. Finally, considering the two asymmetries, a comprehensive bias model is analyzed. A modified method to directly calibrate the accelerometer comprehensive bias is proposed.

Improving the measurement sensitivity of angular deflection of a torsion pendulum by an electrostatic spring

The torsion pendulum is widely employed in gravitational experiments as a weak force sensitive instrument, and its resolution is limited by the thermal noise of the pendulum and detection noise of angular deflection. Different kinds of angular deflection transducers are proposed and realized to improve its resolution. A torsion pendulum combined with an electrostatic spring is proposed here in order to improve the measurement sensitivity of angular deflection. Noise analysis and demonstration experiments show that the electrostatic torsion pendulum can relax the requirement of angular deflection detection, which is useful for gravitational experiments with much higher precision requirements.

A low-frequency vibration insensitive pendulum bench based on translation-tilt compensation in measuring the performances of inertial sensors

The performance test of precision space inertial sensors on the ground is inevitably affected by seismic noise. A traditional vibration isolation platform, generally with a resonance frequency of several Hz, cannot satisfy the requirements for testing an inertial sensor at low frequencies. In this paper, we present a pendulum bench for inertial sensor testing based on translation-tilt compensation. A theoretical analysis indicates that the seismic noise effect on inertial sensors located on this bench can be attenuated by more than 40 dB below 0.1 Hz, which is very significant for investigating the performance of high-precision inertial sensors. We demonstrate this attenuation with a dedicated experiment.