半球谐振陀螺误差建模补偿与力平衡控制方法研究
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摘要
半球谐振陀螺具有精度高，寿命长，可靠性高，抗冲击强，本征抗辐射等突出优点，特别适用于航天器的空间定姿，地质钻井系统的定位定向等领域。但是，国内半球谐振陀螺的研究水平与国外还存在较大差距，特别是在陀螺零偏稳定性，标度因数线性度以及温度漂移补偿方面。并且，美国政府要求世界上唯一高精度的半球谐振陀螺生产商诺斯罗普·格鲁曼(Northrop Grumman)公司对大陆地区施行严格的产品禁运政策。因此，自主研制高性能的半球谐振陀螺对我国的深空探测，地质钻探等国防、国民经济建设等领域具有重要的战略意义。
本论文从半球谐振陀螺数学建模，误差分析，控制方法以及温度漂移补偿等几个方面进行了深入细致的研究，为半球谐振陀螺的发展提供了一些有用的借鉴。论文的主要工作有：
1.为研究半球谐振陀螺的振动特性，依据薄壳理论，建立了半球谐振陀螺的动力学模型。采用变分法以及虚功原理，通过等效系统的方法，将复杂的固体波二阶振动模态简化为一质点在二维空间中的简谐振动，建立了二维空间中质点的振动微分方程，通过等效系统的分析方法揭示了复杂的固体波进动现象。
2.基于二维质点振动模型，对半球谐振陀螺的误差进行了分析。详细分析了半球谐振陀螺的主要误差来源，并依据分析结果建立了半球谐振陀螺的误差传播方程。依据各误差项对半球谐振陀螺振动模态的不同影响，分别地对其在半球谐振陀螺振动模态参数中的影响进行了仿真，并得出抑制与减小误差的一些有用结论。
3.首次全面详细地阐述了力平衡模式下半球谐振陀螺的控制方法。半球谐振陀螺可以工作于全角模式与力平衡模式。相比较而言，力平衡模式下的半球谐振陀螺具有更高的精度。论文详细介绍了力平衡模式下半球谐振陀螺正常工作所需要的四个控制回路：相位跟踪回路，幅度控制回路，正交控制回路以及速率控制回路的作用和具体实现。并对控制回路抑制误差的原理进行了理论分析和试验验证。通过转台试验标定的方法测试了半球谐振陀螺的主要性能参数，诸如零偏稳定性，标度因素等等。
4.依据半球谐振陀螺动力学模型和力平衡模式下半球谐振陀螺的控制方法，设计了基于FPGA的半球谐振陀螺全数字检测与驱动控制系统。研究了半球谐振陀螺电容驱动与检测的原理和方案，设计了ADC和DAC模块与FPGA的接口。依据控制方案，完成了FPGA中控制模块的功能划分与结构布局，详细介绍了信号解调单元，嵌入式控制单元和信号合成单元的设计与实现。设计并实现了半球谐振陀螺数字控制系统与上位机之间的通信接口模块，为监测陀螺的工作状态，系统参数的调试分析提供了简便易行的手段。
5.基于谐振频率对半球谐振陀螺温度漂移进行了补偿。推导了温度与半球谐振陀螺谐振频率之间的相关性及其数学表达式。依据此推导结论，提出采用谐振频率变化来敏感谐振子的温度变化的温度测量新方法，基于此温度测量方法实现半球谐振陀螺的温度漂移实时补偿方案。此方案不仅可以提高陀螺在全温区工作的精度，而且成本低廉，不用增加任何硬件部分，且补偿效果较好。
Hemispherical Resonator Gyro (HRG) is a solid state gyroscope with features ofhigh accuracy, long life span, inherent high reliability, anti-impact and natural radiationhardness. With its excellent performance, the HRG can be used for spacecraft andsatellite stabilization, precision pointing, as well as oil borehole exploration. However,there is still much room to improve the quality of dometic HRG, especially in the aspectof gyroscope bias stability, scale factor nonlinearity and so on. In addition, Americangovernment bans Northrop Grumman which is the world’s only high-performance HRGproducer from exporting HRG to China. Therefore, in the areas of aircraft navigation,strategic accuracy systems and oil borehole, it is of great necessity to make researcheson improving the performance of HRG.
In this dissertation, the math model of HRG, error analysis, control technology andtemperature drift compensation are studied, which provide valuable suggestions for thefurther improvement of HRG. The main content of this dissertation is as follows:
1. On the basis of thin shell theory, a theoretical modeling is established in order tostudy the vibration feature of HRG. By applying methods of virtual work principle andcalsulus of variations, the complicated solid wave virabtion phenomenon is simplifiedinto a two dimensional mass vibration model through equivalent method. As a result,the differential equation of the point virabtion is established from which the peocessionphenomenon of the solid wave can be revealed.
2. The error analysis of HRG is carried out basing on two dimensional massvibration model. With a detailed analysis of the main error sources, the errorpropergation equations are established. Then, different influences on the vibrationmodel parametres of HRG by each error term are simulated, from which some usefulconclusions are drawn.
3. It is the first time that the control method of HRG under the force to rebalancemode is thoroughly described. HRG can work not only under whole angle mode butalso under force to rebalance mode, and the latter one has a higher accuration. Besides,four control loops, namely, reference-phase loop, amplitude-control loop,quadrature-control loop and rebalance control loop, which are employed for HRGworking under force to rebalance mode are introduced in details. Furthermore, the errorsuppress principle of control loop is theoretically analysed and validated throughexperiments. Finally, the main performance parameters such as bias stability and scalefactor of HRG are obtained through calibration on the turntable.
4. The digital detection and drive systems of HRG based on FPGA are designedaccording to the math mode and the control method metioned before. Capacitivereadout and exciation circuit principle are studied and the interfaces of DAC and ADC seperatedly with FPGA are designed in this chapter. The design framework and overallarrangement are introduced according to the control method. The modulation anddemodulation unit, the embedded control unit and signal synthesize unit are thoroughlydescribed. The communication interface module which is used to transfer data betweenFPGA board and upper computer is implemented, through which the working status ofthe HRG can be easily obtained and can also facilitate the realization of debuggingmode.
5. A temperature compensation model for HRG based on the natural frequency ofthe resonator is established. A math model of the relationship between the temperatureand the natural frequency of HRG is deduced. On the basis of these deductions, a newmethod decting the temperature changes through analysing frequcncy change of theresonater is proposed in this chapter. As a result, this new method can be used tocompensate the temperature drift of HRG. The compensation results show thattemperature-frequency method is valid and suitable for the gyroscope driftcompensation, which would ensure HRG’s application in a larger temperature range inthe future without any more hardware cost.
本论文从半球谐振陀螺数学建模，误差分析，控制方法以及温度漂移补偿等几个方面进行了深入细致的研究，为半球谐振陀螺的发展提供了一些有用的借鉴。论文的主要工作有：
1.为研究半球谐振陀螺的振动特性，依据薄壳理论，建立了半球谐振陀螺的动力学模型。采用变分法以及虚功原理，通过等效系统的方法，将复杂的固体波二阶振动模态简化为一质点在二维空间中的简谐振动，建立了二维空间中质点的振动微分方程，通过等效系统的分析方法揭示了复杂的固体波进动现象。
2.基于二维质点振动模型，对半球谐振陀螺的误差进行了分析。详细分析了半球谐振陀螺的主要误差来源，并依据分析结果建立了半球谐振陀螺的误差传播方程。依据各误差项对半球谐振陀螺振动模态的不同影响，分别地对其在半球谐振陀螺振动模态参数中的影响进行了仿真，并得出抑制与减小误差的一些有用结论。
3.首次全面详细地阐述了力平衡模式下半球谐振陀螺的控制方法。半球谐振陀螺可以工作于全角模式与力平衡模式。相比较而言，力平衡模式下的半球谐振陀螺具有更高的精度。论文详细介绍了力平衡模式下半球谐振陀螺正常工作所需要的四个控制回路：相位跟踪回路，幅度控制回路，正交控制回路以及速率控制回路的作用和具体实现。并对控制回路抑制误差的原理进行了理论分析和试验验证。通过转台试验标定的方法测试了半球谐振陀螺的主要性能参数，诸如零偏稳定性，标度因素等等。
4.依据半球谐振陀螺动力学模型和力平衡模式下半球谐振陀螺的控制方法，设计了基于FPGA的半球谐振陀螺全数字检测与驱动控制系统。研究了半球谐振陀螺电容驱动与检测的原理和方案，设计了ADC和DAC模块与FPGA的接口。依据控制方案，完成了FPGA中控制模块的功能划分与结构布局，详细介绍了信号解调单元，嵌入式控制单元和信号合成单元的设计与实现。设计并实现了半球谐振陀螺数字控制系统与上位机之间的通信接口模块，为监测陀螺的工作状态，系统参数的调试分析提供了简便易行的手段。
5.基于谐振频率对半球谐振陀螺温度漂移进行了补偿。推导了温度与半球谐振陀螺谐振频率之间的相关性及其数学表达式。依据此推导结论，提出采用谐振频率变化来敏感谐振子的温度变化的温度测量新方法，基于此温度测量方法实现半球谐振陀螺的温度漂移实时补偿方案。此方案不仅可以提高陀螺在全温区工作的精度，而且成本低廉，不用增加任何硬件部分，且补偿效果较好。
Hemispherical Resonator Gyro (HRG) is a solid state gyroscope with features ofhigh accuracy, long life span, inherent high reliability, anti-impact and natural radiationhardness. With its excellent performance, the HRG can be used for spacecraft andsatellite stabilization, precision pointing, as well as oil borehole exploration. However,there is still much room to improve the quality of dometic HRG, especially in the aspectof gyroscope bias stability, scale factor nonlinearity and so on. In addition, Americangovernment bans Northrop Grumman which is the world’s only high-performance HRGproducer from exporting HRG to China. Therefore, in the areas of aircraft navigation,strategic accuracy systems and oil borehole, it is of great necessity to make researcheson improving the performance of HRG.
In this dissertation, the math model of HRG, error analysis, control technology andtemperature drift compensation are studied, which provide valuable suggestions for thefurther improvement of HRG. The main content of this dissertation is as follows:
1. On the basis of thin shell theory, a theoretical modeling is established in order tostudy the vibration feature of HRG. By applying methods of virtual work principle andcalsulus of variations, the complicated solid wave virabtion phenomenon is simplifiedinto a two dimensional mass vibration model through equivalent method. As a result,the differential equation of the point virabtion is established from which the peocessionphenomenon of the solid wave can be revealed.
2. The error analysis of HRG is carried out basing on two dimensional massvibration model. With a detailed analysis of the main error sources, the errorpropergation equations are established. Then, different influences on the vibrationmodel parametres of HRG by each error term are simulated, from which some usefulconclusions are drawn.
3. It is the first time that the control method of HRG under the force to rebalancemode is thoroughly described. HRG can work not only under whole angle mode butalso under force to rebalance mode, and the latter one has a higher accuration. Besides,four control loops, namely, reference-phase loop, amplitude-control loop,quadrature-control loop and rebalance control loop, which are employed for HRGworking under force to rebalance mode are introduced in details. Furthermore, the errorsuppress principle of control loop is theoretically analysed and validated throughexperiments. Finally, the main performance parameters such as bias stability and scalefactor of HRG are obtained through calibration on the turntable.
4. The digital detection and drive systems of HRG based on FPGA are designedaccording to the math mode and the control method metioned before. Capacitivereadout and exciation circuit principle are studied and the interfaces of DAC and ADC seperatedly with FPGA are designed in this chapter. The design framework and overallarrangement are introduced according to the control method. The modulation anddemodulation unit, the embedded control unit and signal synthesize unit are thoroughlydescribed. The communication interface module which is used to transfer data betweenFPGA board and upper computer is implemented, through which the working status ofthe HRG can be easily obtained and can also facilitate the realization of debuggingmode.
5. A temperature compensation model for HRG based on the natural frequency ofthe resonator is established. A math model of the relationship between the temperatureand the natural frequency of HRG is deduced. On the basis of these deductions, a newmethod decting the temperature changes through analysing frequcncy change of theresonater is proposed in this chapter. As a result, this new method can be used tocompensate the temperature drift of HRG. The compensation results show thattemperature-frequency method is valid and suitable for the gyroscope driftcompensation, which would ensure HRG’s application in a larger temperature range inthe future without any more hardware cost.
引文
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