Research For High Precision And High Stability Slot-structrue MEMS Gyroscopes

Micro-electro-mechanical systems(MEMS)gyroscope is a kind of inertial sensor that measures rate or angle of rotation.The silicon micromachined gyroscope has such advantages as small size,low power consumption,high reliability and batch fabrication when compared with traditional mechanical rotor gyroscope or optical gyroscope.Thus,it has a wide application spectrum in the consumer electronics,automotive,industrial and military markets.After more than 20 years of development,there has been a steady improvement in the performance of micro-gyroscopes,showing potential of applying to high-precision applications.This Ph.D.dissertation is aimed at developing high precision and high stability slot-structure gyroscopes.Various techniques such as system identification,capacitive sensing,system noise analysis and mode-matching algorithm are deeply studied in this work.The main content and contributions are given below:1)A systematic study on the measurement methods for resonant frequency and quality factor is carried out.By means of theoretical analysis and numerical simulation,three conventional methods are discussed to explore their advantages and disadvantages as well as applicable scenarios,i.e.frequency sweeping scheme,vibration decay scheme(VDS)and PLL-AGC control loop scheme.Notice that when used to test the high-Q gyros,the conventional VDS can be time-consuming and the measurement circuitry is prone to saturation.Then,an improved version of VDS is proposed to tackle these issues.During the start-up phase,the PLL control loop is used to enable fast measurement of the resonant frequency,and meanwhile the AGC control loop works to accelerate the start-up time and to control the vibration amplitude to a proper level.Afterwards,the quality factor can be accurately detected using VDS.Finally,experimental results show that the drive-mode resonant frequency is equal to 1515.9 Hz while the Q-factor is measured as 9177 in high vacuum.Notice that the measured Q-factor shows good repeatability with a relative error as low as 0.05%.2)For the first time,a novel variable-area capacitive sensing method with self-calibration is proposed.This approach constructively utilizes the inherent nonlinearity of the triangular-electrode based(TEB)sense capacitor to accurately and robustly measure the amplitude and phase information in sinusoidal motion.Theoretical analysis reveals that,in the case of TEB detection signal,two harmonics exist and each carries information about the motional amplitude and phase.The TEB method robustly extracts the motional amplitude from the ratio of two sideband amplitudes and extracts the motional phase from the subtraction of two sideband phases.As a result,the TEB measured amplitude and phase are robust to such system parameters as the probing carrier voltage,the nominal sense capacitance,and the gain and phase shift in signal conditioning electronics.Experimental results demonstrate that,compared with the conventional method,the sensitivity of the measured amplitude and phase to system parameter variations is highly suppressed up to 95%.This technique is especially valuable for capacitive detection of periodic motion in MEMS resonant devices,such as the resonant accelerometer and Coriolis vibratory gyroscope.Furthermore,an oscillation control system with TEB capacitive detection is introduced for micromachined vibratory gyroscopes.First measurement results show that the amplitude variance of the drive displacement is 34 ppm in an hour while the phase variance is 30 ppm.What is more,the long-term stability performance of the sensor is enhanced by 1.6 times,and Allan variance analysis indicates a bias instability of 1.6°/h at atmosphere.3)In order to achieve high-performance micromachined gyroscopes,a deep study of system noise is performed:a)In the drive loop,for the first time,a novel oscillation control for MEMS vibratory gyroscopes using a modified electromechanical amplitude modulation(MEAM)technique is introduced.Theoretical analysis reveals that the phase delay of the drive-mode processing circuitry will cause IQ coupling at the gyroscope output.In the MEAM method,the carrier voltage exerted on the proof mass is frequency-modulated by the drive resonant frequency.Accordingly,the pick-up signal from the interface circuit involves a constant-frequency component that contains the amplitude and phase information of the vibration displacement,which translates to a fixed electric phase delay.In other words,the dependence of the detection electronic on the drive resonant frequency is mitigated and this will enhance the robustness against structural and thermal parameter fluctuations.Further,a simulation model is set up to verify the correctness and feasibility of the proposed MEAM method.Finally,the MEAM method is validated using an FPGA-based digital platform on a micromachined vibratory gyroscope.Allan variance analysis demonstrates that,by virtue of the MEAM method,the long-term stability performance and noise performance are improved up to 2.4 times and 1.4 times compared with the CEAM method,respectively.The tested gyroscope with a 28 Hz mode mismatch achieves a bias instability of 0.9°/h and an angular random walk(ARW)of 0.068°/?h at atmosphere,respectively.b)In the sense loop,the transfer functions of the force-rebalanced control are obtained through analytical derivation,and they are decomposed into two unity negative feedback systems,which effectively reduces the complexity of loop analysis or loop design.Furthermore,three different kinds of microgyroscopes(mode-matched gyros,nearly mode-matched gyros and mode-split gyros)are studied by means of the theoretical analysis and numerical simulation,respectively.The attained conclusions can be helpful to optimize the loop parameters,so that the sense loop can meet the requirements of stability,transient response and system bandwidth.c)In the force-rebalanced sense loop,the dominant noise source that defines the angular rate resolution of micromachined gyroscopes is studied deeply.The effects of mechanical-thermal noise,interface circuit noise and front-end circuit noise on the gyro's total system noise are compared and analyzed under different conditions such as mode-split/mode-matched and high-Q/low-Q.In addition,the correctness of the theoretical analysis is verified by five control experiments.It is pointed out that reducing the frequency difference and increasing the drive displacement are the two most effective methods to enhance the resolution of the senor.The tested gyro#3 with a mode-split of 10 Hz achieves the best performances in a vacuum environment:[?]The amplitude stability of the drive displacement is 18 ppm,while the phase stability is about 0.00017°(1?).[?]The nonlinearity of the gyroscope is measured as 0.04%within the range of ±500°/s.[?]The standard deviation of bias offset is equal to 5.5°/h in an hour.[?]Allan deviation results demonstrate that the bias instability and ARW are 0.3°/h and 0.025°/?h,respectively.4)A novel mode-matching algorithm for MEMS gyroscopes is proposed for the first time.Compared to other methods in the literature,this approach offers such advantages as fast tuning response(<1s),high tuning accuracy(<0.01 Hz)and robustness against the Coriolis accelerations.Besides,it is compatible with the traditional force-rebalance loop,thus adding negligible hardware complexity.Based on the analysis of the mode-matched condition,one mode-tuning procedure is summarized,and then the steady-state solution of the control system is deduced by virtue of the averaging method,verifying that the algorithm will finally eliminate the initial frequency mismatch.Further,a simulation model is set up to evaluate the control system.Notice that if Iref varies between 0 and At in the step manner,the transient response of the Coriolis output can be so large to exceed the sensor's measurement range,which results into failure of closed-loop operation.Instead,the slope-Iref is preferred to reduce the aforementioned risk.Finally,the proposed mode-matching algorithm is validated using an FPGA-based digital platform on a capacitive vibratory gyroscope.Experimental results show that this scheme successfully realizes the mode-matched condition.Besides,the tests under various angular rates verify that the proposed algorithm is insensitive to input rotation,which is consistent with the theory.Allan variance analysis demonstrates that the mode-matched gyroscope achieves a bias instability of 0.4°/h and an ARW of 0.015°/?h.Notice that the corresponding noise equivalent angular rate can be calculated to be 0.9°/h/?Hz,and it is the best resolution performance among all tested gyroscopes.