基于半球谐振陀螺仪的姿态测量系统研究
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摘要
半球谐振陀螺以其精度高，稳定性强，可靠性高，抗冲击性良好，抗辐射能力卓越以及寿命长的特点，非常适合在空间飞行器等长时间工作场合使用。开展基于半球谐振陀螺的长寿命姿态测量系统的研制，将对我国空间技术的发展，特别是长寿命卫星的工程实施，有着极其深远的意义。本文以研制基于半球谐振陀螺的高性能姿态测量系统为目的，针对制约系统性能的关键技术进行了深入研究。其中关键技术包括：半球谐振陀螺漂移机理及补偿技术、惯性姿态测量系统初始对准技术、基于半球谐振陀螺与星敏感器的组合姿态测量系统技术等。具体研究安排如下：
在惯性器件级层面，由于半球谐振陀螺的漂移是系统的最大误差源，因此开展参数漂移的机理、建模和补偿研究是提高系统性能的最有效手段。针对陀螺漂移，开展了两种误差源的研究：其一，研究了陀螺表头结构误差对陀螺性能的影响。表头结构误差主要通过影响振动检测系统及激励系统而导致陀螺漂移，为此首先对拾振器结构及电容间隙变化等问题深入研究，结合谐振子二阶谐振状态下形变的动力学方程，建立了半球谐振陀螺振动检测系统仿真模型。同时，通过对多电极作用下谐振子的动力学特性研究，以及对振幅控制系统与振型角控制系统的耦合分析，建立了半球谐振陀螺激励系统仿真模型。然后将表头结构误差引入到振动检测系统及激励系统的仿真模型中。通过仿真研究，对表头结构误差中的可标定误差提出了标定补偿方法，对不可标定误差给出了定量评估的模型，为表头加工和装配精度指标的确定提供了理论依据。其二，研究了加速度作用下半球谐振陀螺的漂移机理。首先通过求解谐振子的动力学方程，给出了低频加速度作用下谐振子变形的解析形式。其次完成了谐振子变形对半球谐振陀螺振动检测系统及激励系统的影响分析，最终提出了一种能够极大减小加速度对陀螺影响的振动检测方案与谐振子激励方案。并建立了加速度导致陀螺漂移的静态误差模型，通过半球谐振陀螺在重力场中的翻滚试验给予了验证。通过对试验数据残差的进一步分析，给出了陀螺制造及装配的改进措施。
在惯性姿态测量系统级层面，为提高系统初始对准精度，缩短对准时间，研究了大方位失准角静基座初始对准问题。提出了基于高斯-厄米特滤波器的初始对准方法。针对高斯-厄米特滤波器中的均值和协方差阵的多元非线性高斯积分求解问题，利用初始对准误差方程的非线性是由大方位失准角导致的特点，将高维积分转化成一元数值积分，在不损失精度前提下，解决了高斯-厄米特滤波器在对准应用的“维数灾难”问题。将此算法用于实际系统，对比于扩展卡尔曼滤波、无迹卡尔曼滤波方法，结果表明在大方位失准角条件下，提高了对准精度，缩短了对准时间。
在组合系统级层面，研制了基于半球谐振陀螺与星敏感器的组合姿态测量系统。为解决当观测到的导航星数量小于3颗时松组合系统无法进行数据融合的问题，提出了基于惯性姿态测量系统的快速星图识别方法，给出了基于HRG与星敏感器紧组合姿态测量系统的构建形式和滤波方法。最后系统测试表明，紧组合系统使得上述问题得到了较好的解决，增加了组合系统的全天域适应性。
最终，将上述的一系列技术措施应用于课题所研制的基于半球谐振陀螺的姿态测量系统工程样机中，并通过以三轴转台为核心的半实物仿真平台的测试验证，所研制工程样机在精度、适应性及可靠性等方面都得到了较大提升，特别是精度性能达到了高精度卫星姿态控制系统的使用要求。
Hemispherical resonance gyroscope (HRG) is very suitable to be used in long-term working occasions such as space vehicles due to the high accuracy andreliability, good impact and radiation resistance properties, as well as long life.Hence, the design of long life attitude measurement systems is of great significanceto the development of space technology, especially to the engineer construction ofsatellites in China. In order to develop a high performance attitude measurementsystem, this thesis researches several key technologies of restricting theperformance improvement of attitude measurement systems, including the gyrodrift mechanism and the drift compensation technology of HRG, the initialalignment technology of inertial measurement systems, and the technology ofintegrated attitude measurement systems based on HRG and star sensors. The maincontents of this thesis are as follows:
The biggest error source of attitude measurement systems is the drift of HRGin the level of inertial instruments, so the most efficient way for improving thesystem performance is to explore the mechanism, modeling and compensation ofparameter drift. Two error sources of gyro drift are studied in the thesis and theresearch are focused on the following two parts: The influence of gyro’s structureerrors to its performance is studied. Since structure errors induce gyro drift byaffecting the vibration detecting system, the structure of pickoff and the capacitorgap is analyzed firstly, and a simulation model of the HRG’s vibration detectingsystem is built by incorporating the deformation dynamic equation of the resonatorin second-order free resonant condition. And a simulation model of the forcingsystem is also obtained by analyzing the dynamic characteristics of the resonator inthe action of multiple electrodes and the coupling between the amplitude controlsystem and the precession angle control system. Then, a compensation method forcalibratable errors and a quantitative evaluation model for uncalibratable errors areproposed, respectively, by simulation research, and this provides theoretical basisfor the determination of machining and assembly accuracy indexes. The driftmechanism of HRG under accumulation is studied. The analytical form of theresonator’s deformation under low frequency accumulation is obtained by solving its dynamic equation firstly. Then, the influence of the deformation to the vibrationdetecting system and the forcing system is analyzed. Finally, a vibration detectingscheme and a resonator exciting scheme are proposed, respectively, which canweaken the influence of accumulation greatly. Additionally, a static error model ofdrift caused by accumulation is founded, which is verified by rolling experiment ofHRG in gravitational field. And some improvement measures for gyro machiningand assembly are provided by analyzing the residual error of test data.
In order to improve the alignment accuracy of the system and shorten thealigning time, the initial alignment problem of stationary base with large azimuthmisalignment angles is researched and an initial alignment approach based onGauss-Hermite Filter (GHF) is proposed in the level of inertial attitudemeasurement system. Then, the multi-variable nonlinear Gauss integration of themean and the covariance is addressed. Since the nonlinearity of the alignment errorequation is induced by a large azimuth misalignment angle, the so called“dimension problem” in the application of GHF to alignment is solved without lossof accuracy, by converting multi-variable integration to single variable integration.The proposed alignment approach is applied to a practical system lastly, and thealignment accuracy under a large azimuth misalignment angle condition isimproved and the aligning time is decreased, compared with Extended KalmanFilter (EKF) and Unscented Kalman Filter (UKF).
An integrated attitude measurement system based on HRG and a star sensor isdeveloped in the level of integrated systems. A method of fast star patternrecognition is proposed firstly, and both a construction form and a filteringapproach of tightly-coupled integrated systems are given, in order to solve the datefusion problem in the case where the number of navigation stars is smaller thanthree in loosely-coupled integrated systems. Then, the integrated system is tested,and the result implies that the tightly-coupled integrated systems can solve thisproblem well, and hence enhances the adaptability for celestial sphere field.
At last, all the above technologies are applied to an engineering prototype ofthe attitude measurement system based on HRG. The prototype is tested by a semi-physical simulation platform whose primary component is a three-axis turntable,and the test result shows that the accuracy, adaptability and reliability of theprototype are improved greatly. Especially, its accuracy attains the usage standard of high precision satellite attitude control systems.
在惯性器件级层面，由于半球谐振陀螺的漂移是系统的最大误差源，因此开展参数漂移的机理、建模和补偿研究是提高系统性能的最有效手段。针对陀螺漂移，开展了两种误差源的研究：其一，研究了陀螺表头结构误差对陀螺性能的影响。表头结构误差主要通过影响振动检测系统及激励系统而导致陀螺漂移，为此首先对拾振器结构及电容间隙变化等问题深入研究，结合谐振子二阶谐振状态下形变的动力学方程，建立了半球谐振陀螺振动检测系统仿真模型。同时，通过对多电极作用下谐振子的动力学特性研究，以及对振幅控制系统与振型角控制系统的耦合分析，建立了半球谐振陀螺激励系统仿真模型。然后将表头结构误差引入到振动检测系统及激励系统的仿真模型中。通过仿真研究，对表头结构误差中的可标定误差提出了标定补偿方法，对不可标定误差给出了定量评估的模型，为表头加工和装配精度指标的确定提供了理论依据。其二，研究了加速度作用下半球谐振陀螺的漂移机理。首先通过求解谐振子的动力学方程，给出了低频加速度作用下谐振子变形的解析形式。其次完成了谐振子变形对半球谐振陀螺振动检测系统及激励系统的影响分析，最终提出了一种能够极大减小加速度对陀螺影响的振动检测方案与谐振子激励方案。并建立了加速度导致陀螺漂移的静态误差模型，通过半球谐振陀螺在重力场中的翻滚试验给予了验证。通过对试验数据残差的进一步分析，给出了陀螺制造及装配的改进措施。
在惯性姿态测量系统级层面，为提高系统初始对准精度，缩短对准时间，研究了大方位失准角静基座初始对准问题。提出了基于高斯-厄米特滤波器的初始对准方法。针对高斯-厄米特滤波器中的均值和协方差阵的多元非线性高斯积分求解问题，利用初始对准误差方程的非线性是由大方位失准角导致的特点，将高维积分转化成一元数值积分，在不损失精度前提下，解决了高斯-厄米特滤波器在对准应用的“维数灾难”问题。将此算法用于实际系统，对比于扩展卡尔曼滤波、无迹卡尔曼滤波方法，结果表明在大方位失准角条件下，提高了对准精度，缩短了对准时间。
在组合系统级层面，研制了基于半球谐振陀螺与星敏感器的组合姿态测量系统。为解决当观测到的导航星数量小于3颗时松组合系统无法进行数据融合的问题，提出了基于惯性姿态测量系统的快速星图识别方法，给出了基于HRG与星敏感器紧组合姿态测量系统的构建形式和滤波方法。最后系统测试表明，紧组合系统使得上述问题得到了较好的解决，增加了组合系统的全天域适应性。
最终，将上述的一系列技术措施应用于课题所研制的基于半球谐振陀螺的姿态测量系统工程样机中，并通过以三轴转台为核心的半实物仿真平台的测试验证，所研制工程样机在精度、适应性及可靠性等方面都得到了较大提升，特别是精度性能达到了高精度卫星姿态控制系统的使用要求。
Hemispherical resonance gyroscope (HRG) is very suitable to be used in long-term working occasions such as space vehicles due to the high accuracy andreliability, good impact and radiation resistance properties, as well as long life.Hence, the design of long life attitude measurement systems is of great significanceto the development of space technology, especially to the engineer construction ofsatellites in China. In order to develop a high performance attitude measurementsystem, this thesis researches several key technologies of restricting theperformance improvement of attitude measurement systems, including the gyrodrift mechanism and the drift compensation technology of HRG, the initialalignment technology of inertial measurement systems, and the technology ofintegrated attitude measurement systems based on HRG and star sensors. The maincontents of this thesis are as follows:
The biggest error source of attitude measurement systems is the drift of HRGin the level of inertial instruments, so the most efficient way for improving thesystem performance is to explore the mechanism, modeling and compensation ofparameter drift. Two error sources of gyro drift are studied in the thesis and theresearch are focused on the following two parts: The influence of gyro’s structureerrors to its performance is studied. Since structure errors induce gyro drift byaffecting the vibration detecting system, the structure of pickoff and the capacitorgap is analyzed firstly, and a simulation model of the HRG’s vibration detectingsystem is built by incorporating the deformation dynamic equation of the resonatorin second-order free resonant condition. And a simulation model of the forcingsystem is also obtained by analyzing the dynamic characteristics of the resonator inthe action of multiple electrodes and the coupling between the amplitude controlsystem and the precession angle control system. Then, a compensation method forcalibratable errors and a quantitative evaluation model for uncalibratable errors areproposed, respectively, by simulation research, and this provides theoretical basisfor the determination of machining and assembly accuracy indexes. The driftmechanism of HRG under accumulation is studied. The analytical form of theresonator’s deformation under low frequency accumulation is obtained by solving its dynamic equation firstly. Then, the influence of the deformation to the vibrationdetecting system and the forcing system is analyzed. Finally, a vibration detectingscheme and a resonator exciting scheme are proposed, respectively, which canweaken the influence of accumulation greatly. Additionally, a static error model ofdrift caused by accumulation is founded, which is verified by rolling experiment ofHRG in gravitational field. And some improvement measures for gyro machiningand assembly are provided by analyzing the residual error of test data.
In order to improve the alignment accuracy of the system and shorten thealigning time, the initial alignment problem of stationary base with large azimuthmisalignment angles is researched and an initial alignment approach based onGauss-Hermite Filter (GHF) is proposed in the level of inertial attitudemeasurement system. Then, the multi-variable nonlinear Gauss integration of themean and the covariance is addressed. Since the nonlinearity of the alignment errorequation is induced by a large azimuth misalignment angle, the so called“dimension problem” in the application of GHF to alignment is solved without lossof accuracy, by converting multi-variable integration to single variable integration.The proposed alignment approach is applied to a practical system lastly, and thealignment accuracy under a large azimuth misalignment angle condition isimproved and the aligning time is decreased, compared with Extended KalmanFilter (EKF) and Unscented Kalman Filter (UKF).
An integrated attitude measurement system based on HRG and a star sensor isdeveloped in the level of integrated systems. A method of fast star patternrecognition is proposed firstly, and both a construction form and a filteringapproach of tightly-coupled integrated systems are given, in order to solve the datefusion problem in the case where the number of navigation stars is smaller thanthree in loosely-coupled integrated systems. Then, the integrated system is tested,and the result implies that the tightly-coupled integrated systems can solve thisproblem well, and hence enhances the adaptability for celestial sphere field.
At last, all the above technologies are applied to an engineering prototype ofthe attitude measurement system based on HRG. The prototype is tested by a semi-physical simulation platform whose primary component is a three-axis turntable,and the test result shows that the accuracy, adaptability and reliability of theprototype are improved greatly. Especially, its accuracy attains the usage standard of high precision satellite attitude control systems.
引文
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