Research On Sliding Mode Control Of Rate Integral Vibrating Gyroscope

As a new generation of vibrating gyroscope,hemispherical resonator gyroscope has excellent characteristics such as easy miniaturization,high precision,strong stability,and no wear parts.It is especially suitable for long-term missions such as deep space exploration and ocean navigation.At present,the hemispheric resonator gyroscope in the force rebalance mode has begun to be applied in engineering,but the hemispheric resonator gyroscope in the rate integration mode is still at the stage of key technology research and development.Among them,the control problem of the rate-integrating hemispherical resonator gyroscope is an urgent problem to be solved.The control accuracy is related to whether the vibratory gyroscope can exert its best performance level.Sliding mode control has gradually been popularized and used in actual engineering due to its strong robustness,rapid response and high control accuracy.This paper introduces discrete sliding mode control into the control system of the elliptic parameters of the rate-integrating hemispherical resonator gyroscope,which provides some useful references for the application of sliding-mode control in the rate-integrating hemispherical resonator gyroscope.First,the working principle of the rate-integrating hemispherical resonator gyroscope and the conversion process of the elliptic parameter equation are briefly introduced.And a detailed derivation and proof of the calculation method of the ellipse parameter is given,which clearly point out the correspondence between the calculated ellipse parameters and the actual hemispherical resonator gyroscope’s main wave amplitude and quadrature wave amplitude.Secondly,the concepts of approaching motion,sliding mode motion,and reachability in sliding mode control are introduced,and the robustness of the sliding mode is proved.By summarizing the research progress of discrete sliding mode control based on the reaching law,the improvement direction of the discrete exponential reaching law is obtained.In order to better overcome the disturbance and reduce chattering,the approaching law suitable for the discrete sliding mode control of the hemispheric resonator gyroscope is selected.Thirdly,based on the signal processing and control flow of the rate-integrating hemispheric resonator gyroscope,a hemispherical resonator gyroscope Simulink simulation platform was built;the System-Function module was introduced to describe the non-ideal motion equation of the hemispherical resonator gyroscope,and the module frequency reduction,limiting output and other improvements were completed.Fourthly,three elliptic parameters such as main wave amplitude,quadrature wave amplitude,and phase difference,which can directly characterize the working state of the hemispherical resonator gyroscope,were selected as the objects of discrete sliding mode control,and the mathematical modeling,controllability analysis,observability analysis and stability analysis of the controlled object were completed,and recursive least squares was used to estimate the unknown parameters in the system matrix.Then,by selecting the reaching law and designing the sliding mode surface function,the discrete sliding mode control considering the matched disturbance(MD-DSMC)and the discrete sliding mode control considering the mismatched disturbance(UD-DSMC)are deduced respectively;the two kinds of discrete sliding mode control are tested on the simulation platform,and good simulation results have been achieved.Under the condition of variable speed rotation input,compared with PID control,MD-DSMC reduces the main wave amplitude error from 3 LSB to 0 LSB,the quadrature wave amplitude control error is reduced from 42 LSB to 0 LSB,the phase difference control error is reduced from 3×10-3 deg to 3×10-4 deg,and the root mean square error of angular rate tracking is reduced by 7.2°/h.From the estimation results of the disturbance observer,it can be seen that the mismatched disturbance in the simulation platform is very small,so the control effects of UD-DSMC and MD-DSMC are basically the same.Finally,MD-DSMC and UD-DSMC were tested on the rate-integrating hemispherical resonator gyro experimental platform respectively,and the problems in the actual use of discrete sliding mode control were analyzed,which pointed out the direction for further research.