Study On Automatic Mode-matching Technology Of Silicon Vibratory Microgyroscopes

Silicon vibratory micro-gyroscopes,which are designed based on the Coriolis effect of the moving mass subject to the rotation of carriers,are inertial sensors to measure the rotating rate or angle of objects.At present,silicon gyroscopes are mostly used in the field requiring low and middle precision for their low performance.To improve their precision and application,more deep research is required on their working principle and experimental verification.As the resonators'vibration amplitude is maximized when the driving frequency is equal to their natural frequency,the gyroscopes equipped with work modes of equal natural frequency are designd for larger sensitivity.But the fabrication error caused the practical frequency of the prototypes to deviate from the designed value.Thus,it is necessary to keep the natural frequencies of silicon gyroscopes equal for high precision after fabrication.The frequency tuning and automatic mode-matching technology is studied in this thesis,and the details are as follows:(1)Structure design of dual-mass silicon micro-gyroscopes with electrostatic tuning comb'sBased on the analysis of the dynamics of dual-mass gyroscopes,the influence of the asymmetry of the structure parameters and the applied force on the natural frequencies as well as the differential frequency response is firstly studied.The generated electrostatic force and electrostatic stiffness matrix are deduced for four tuning comb configurations,of which some are used in the gyroscope structure design for force loading,quadrature error nullling and frequency tuning.The dual-mass gyroscope equipped with electrostatic tuning combs is expected to be of high performance under sophisticated driving,sensing and tuning design.The nonlinear dynamic equation of the sense resonator is solved by numerical simulation and the nonlinear phenomena are illustrated with amplitude-frequency charateristic bending towards lower frequency,which can be avoided by compromising input angular rate,quality factor and frequency tuning voltage.(2)Experimental verification of the effect of tuning capacitors on the gyroscopesWith the aid of Labview FPGA,a graphical programming device,the basic parameters,such as the natural frequency,the quality factor,the electrostatic tuning rate of frequency difference,and their temperature characteristic are measured.The quadrature disturbance is quantified based on the coupled movement of the sense resonator,and corrected by both the quadrature stiffness correction and the force rebalance methods.The gyroscope performance is given under different frequency difference and quadrature correction' methods.It is found that the scale factor and bias stability improves with the decrement of frequency difference,and when the modes are matched the bias stability obtained using qudrature stifEness correction is better than that using the force rebalance.(3)Study on the automatic mode-matching and rotation detection algorithm based on the phase-frequency characteristicAccording to the phase-frequency characteristic of the mass-spring-damper second-order system,the automatic frequency tuning method to make the drive and sense resonators vibrate at their natural frequencies is illustrated based on the knowledge of phase-locked loop(PLL).The quadrature and Coriolis response are respectively used for mode matching,while the analysis and experiment results show that the frequency split controlled by the two methods are susceptible to varied input angular rate.Thus,a third algorithm based on the forced response of the applied external signal on the sense resonator is demonstrated and verified.It is proved that,controlled by the tuning method using the external applied force,the frequency difference is less influenced by the quadrature disturbance and the input rotation rate.Besides,this method doesn't affect the detection of input rate,whose range is improved when the matching algorithm works with the closed force rebalance detection method.(4)Study on the automatic mode-matching algorithm based on the amplitude-frequency characteristicThe vibration amplitude of a resonator is maximized when it works at its natural frequency.In other words,the amplitude-frequency characteristic is a single-peak curve.Thus,the extremum-seeking method,realized by seeking the amplitude of vibration and its gradient,is used to find the mode-matching frequency tuning voltage.The algorithm is verified analytically and numerically.Moreover,the experiment results using the Labview FPGA tell that it takes long time to reach the steady state.(5)Study on the automatic mode-matching and rotation detection algorithm based on the symmetry of the frequency characteristicAs for the linear second-order system,the amplitude-frequency curve is axisymmetric about the natural frequency,and the phase-frequency curve is centrosymmetric about the natural frequency and the 90° phase delay.Thus,two forces,whose frequencies are equally below and above the work frequency,are applied on the sense resonator and the response is used to tune the natural frequency towards the work frequency automatically.The algorithm is verified analytically,numerically and experimentally.The relationship between the frequency tuning and rate detection channels is studied.It turns out that the disturbance from the input rate is decreased by enhancing the filter performance or force rebalancing the Coriolis response.Besides,it is derived that the frequency difference is closer to 0Hz and less sensitive to work temperature when the phase delay of tuning loop is compensated.Based on the previous gyroscope research in our lab,several automatic mode-matching methods are demonstrated and compared analytically and experimentally on the dual-mass vibratory gyroscope with electrostatic correction,force rebalance and frequency tuning functions.It is proved that all the three matching methods works,among which the frequency split under the control of phase and symmetric characteristics is much smaller.Besides,when the algorithm based on the symmetric characteristics is used,the the gyroscope's frequency difference and bias is more stable.The research made in the thesis paves the way for further improving gyroscope's performance.