光纤陀螺的动态性能研究
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摘要
光纤陀螺广泛应用于捷联惯性导航系统中,它的工作性能在很大程度上决定着整个惯性系统的精度。目前国内外对处于静止或匀速运动状态下的光纤陀螺性能即光纤陀螺的静态性能进行了大量的研究报道,而对处于角加速运动状态的光纤陀螺性能即光纤陀螺的动态性能则研究的较少。本文系统研究了光纤陀螺动态条件下的误差理论、测试方法、测试结果的分析方法和性能的改进方法。
捷联系统直接与运动载体固连,在实际运动中经常处于角加速运动状态。因此,角加速运动下光纤陀螺性能的优劣决定着捷联惯导系统的导航精度。在分析光纤陀螺系统模型和角加速运动响应特性的基础上,建立了光纤陀螺动态条件下的误差模型。详细剖析了光纤陀螺的稳定性条件,结构参数、信号处理周期以及外界环境对光纤陀螺动态性能的影响。从理论上阐述了光源平均波长和反馈通道增益的变化作用于结构参数的机理,台阶高度信号和输出信号的滤波作用于信号处理周期的机理。仿真结果证明所建立的光纤陀螺动态条件下的误差模型准确可靠。
为了对光纤陀螺的动态性能进行合理评价,采用三轴惯导测试转台来模拟光纤陀螺的角加速运动状态,给光纤陀螺施加瞬时变化的角速度输入,对其进行动态测试。对测试原理和测试步骤进行详细阐述。采用位置差商法、分周期离散理论曲线法和公式变换法确定动态测试中的基准值。分析结果表明分周期离散理论曲线法和公式变换法较适合。
三轴转台的精度是制约光纤陀螺测试结果精确性的瓶颈因素。根据转台在摇摆状态下输出信号的特点,采用皮萨伦科谱分解法对其进行辨识。由此得到转台信号的幅度失真、频率失真以及夹杂在其中的分量谐波的幅度和频率。并通过比较辨识前后转台误差的标准差,证明了辨识结果的可靠性。同时,分析了不同转台框在相同摇摆条件下的失真规律和同一转台框在不同摇摆条件下的失真规律。实验结果表明,皮萨伦科谱分解法应用于转台正弦信号的失真辨识中是非常适用的。
为了避免转台摇摆运动轨迹中夹杂的噪声传递到动态测试的基准信号中,结合小波多分辨分析和空间局部化的性质,选用db5小波对转台的运动轨迹进行降噪。结果表明,小波滤波法的噪声滤除效果理想,提高了对光纤陀螺动态测试结果评定的准确性。
采用时延估计理论分析和补偿动态测试中基准信号与实际信号之间的时间延迟。利用测试中信号与噪声、噪声与噪声互不相关的特点,对两个信号进行相关运算,估计出两信号之间的时间延迟,并进一步对其补偿。结果表明,时间延迟对测试结果有较大影响,经过补偿后的动态误差更符合实际情况。
为了更好的分析光纤陀螺的动态性能,采用动态Allan方差法对光纤陀螺的动态误差进行分析。根据动态Allan方差法中窗函数的原理,讨论了不同窗口长度对动态误差分析结果的影响。并且,提供了单一摇摆运动和两种复合摇摆运动的分析结果。从分析图中方差的起伏变化可以看出,动态Allan方差法可以准确地反映动态误差里的突变和周期性变化等非稳定性因素,能够清晰地辨识出隐藏在动态误差里的不同摇摆状态。由理论分析和实验结果可知,动态Allan方差法对光纤陀螺的动态性能分析是非常适用的。
动态Allan方差法是一种分析非平稳性信号的有效工具,但在辨识噪声时存在功率泄漏和定量表示单一的缺陷。为此,提出窗函数组合法和噪声量值的二维表示法对其改进,并将其用于分析和定量描述光纤陀螺动态误差中的各种噪声项。窗函数组合法在光纤陀螺动态误差分解的基础上采用矩形窗和汉宁窗对其中的低频噪声和高频噪声分别进行分析。噪声量值的二维表示法根据动态Allan方差法原理得到噪声量值随采样点数目增加的变化规律。实验结果表明窗函数组合法可以满足不同频段噪声的辨识要求,减小功率泄漏；噪声量值的二维表示法可以准确地反映出动态误差中噪声项的变化特征。
为了改善光纤陀螺的动态性能,将普通PID控制器的设计思想应用到光纤陀螺的动态误差控制器中,并进一步基于光纤陀螺动态条件下的误差特性设计出一种新型的动态误差控制器结构。前者主要通过普通PID控制器的设计思想与光纤陀螺的控制方式相结合,即基于光纤陀螺内部控制方式实现。而后者将微分环节设置在输出信号之前,使输出信号和反馈信号同时具有提前预测功能,并在微分环节后面加一个低通滤波器以抑制微分环节带来的高频干扰。这一新控制器结构既可以使控制量减小,各个时刻的控制误差不累积,还可以使输出跟踪输入,反映输入的变化。两种动态误差控制器均通过在光纤陀螺数字信号处理芯片FPGA的各模块中编写VHDL语言实现。实验结果表明两种动态误差控制器都可以明显地改善光纤陀螺的动态性能,且基于光纤陀螺动态条件下误差特性的动态误差控制器具有更优的控制效果。
Fiber optic gyroscope (FOG) is widely applied in strapdown inertial navigation system (SINS), and its performance largely determines the precision of SINS. At home and abroad, lots of researches on the performance of FOG are reported in the state of rest or uniform motion, i.e., the static properties of FOG, however, the study on the performance of FOG in the state of angular acceleration motion is less, i.e., the dynamic performance of FOG. In this paper, study the error theory of FOG under the dynamic conditions, test methods, analysis of test results and the improvement methods of performance systematically.
SINS fix directly with the carrier, which are always under angular acceleration state in the actual movement. Therefore, the performance of FOG under angular acceleration state determines the accuracy of SINS.The error model of FOG under the dynamic condition is established, basing on the analysis of FOG system model and response characteristics under angular acceleration motion. The influence of FOG stability conditions, structural parameters, signal processing cycle as well as the external environment on the dynamic performance of FOG are discussed. In theory, the affect mechanism of light average wavelength and feedback channel gain on the structural parameters are analyzed; the influence mechanism of the step height signal and the output signal filtering on the signal processing cycle are discussed. Simulation results indicate that the error model of FOG under the dynamic conditions is accurate and reliable.
To evaluate the dynamic performance of FOG reasonably, the three-axis inertial test turntable is chosen to test the dynamic performance of FOG. The input angular velocity signal of FOG changes according to sine law. The test principle and procedures are presented. In this paper, three methods are presented to determine the reference value in dynamic test, which are location divided difference, separated period discretization theory curve and transform formula method. Separated period discretization theory curve and transform formula method are suitable among these.
The accuracy of three-axis turntable is one of the key factors that constrain the precision of FOG test results. Based on the characteristics of output signals under the sway states, use of the Pisarenko spectrum decomposition method is preferred for identifying the output signals of turntable, which include the amplitude distortion, frequency distortion and the component harmonics. In this paper, the standard deviations of turntable errors are compared and analyzed to identify the credibility. Moreover, the distortion laws are analyzed under two conditions:different turntable frames the same sway conditions and identical turntable frame the different sway conditions. The results indicate that the Pisarenko spectrum decomposition method is applicable to identify the sinusoidal signal distortion of turntable.
Based on the wavelet natures of multiresolution analysis and spatial localization, db5wavelet is choosed to fiter the noise of turntable trajectory for avoiding it to pass in the reference signal of dynamic test. The results indicate that the filtering effect of wavelet is satisfactory and it improves the accuracy of the dynamic test results of FOG.
The time delay between the reference signal and the actual signal in dynamic test is analyzed and compensated using time delay estimation theory. Related operation is done to estimate and further compensate the time delay between the two signals, based on signals and noises, noises and noises are irrelevant in the test. The results indicate that time delay has a greater impact on test results and the dynamic error after compensation is in accordance with the actual situation.
In order to study the dynamic performance of FOG better, it is proposed that the dynamic error which is obtained by test of FOG is analyzed by dynamic Allan variance. According to the principle of window function of dynamic Allan variance method, the analysis results of dynamic error are discussed under the different window length conditions. Furthermore, a kind of single sway movement and two kinds of composite sway movement are analyzed by dynamic Allan variance method and their results are provided. There is fluctuating variation of variance in analysis figures, by which the various non-stationary factors in the dynamic error such as mutation and periodic variation are accurately reflected and the different sway states hidded in the dynamic errors are clearly identified. Both the theoretical analysis and experimental results indicate that the dynamic Allan variance method is very applicable to analyze the dynamic performance of FOG.
The dynamic Allan variance is an effective method for analyzing non-stationary signal. However, it has defects in noise identification:power leakage and single quantification. Therefore, window function combination method is introduced for their improvements as well as two-dimensional expression of noise value. They are used for analysis and quantitative measurement of various noise terms in the FOG dynamic error. Based on the dynamic error resolution of FOG, rectangular window is applied to analyze low&intermediate frequency noise, while hanning window does high-frequency noise. According to the principle of DAVAR, the noise variation laws with the numbers of sampling point are obtained, namely, two-dimensional expression of noise value. The experimental results indicate that window function combination method satisfies the identification requirements of noise in different frequency ranges and reduces power leakage; moreover, the change characteristics of every noise item in the dynamic error are accurately reflected by the two-dimensional expression of noise value.
The design idea of normal PID controller is applied in the dynamic error controller of FOG to improve its dynamic performance; moreover, a novel dynamic controller structure is designed basing on the error characteristics of FOG under dynamic state. The former is implemented by the combination of design idea of normal PID with the control idea of FOG, i.e. implemented by the inner control model of FOG. For the later (the novel one), the differential link is set before the output signal, which make the output signal and feedback signal to predict in advance; meanwhile, a low-pass filter is set after the differential link to suppress the high frequency interference brought by the differential link. The novel control structure can not only decrease the control amount and avoid the calculation of control error, but also allows the output to track the input and reflects the input change. Both the controllers are realized through writing VHDL language in the digital signal processing chip FPGA of FOG. The test results indicate that both the dynamic error controllers can significantly improve the FOG dynamic performance, furthermore, the novel dynamic error controller, i.e. the dynamic error controller basing on the error characteristic of FOG under dynamic condition, has better error control performance.
捷联系统直接与运动载体固连,在实际运动中经常处于角加速运动状态。因此,角加速运动下光纤陀螺性能的优劣决定着捷联惯导系统的导航精度。在分析光纤陀螺系统模型和角加速运动响应特性的基础上,建立了光纤陀螺动态条件下的误差模型。详细剖析了光纤陀螺的稳定性条件,结构参数、信号处理周期以及外界环境对光纤陀螺动态性能的影响。从理论上阐述了光源平均波长和反馈通道增益的变化作用于结构参数的机理,台阶高度信号和输出信号的滤波作用于信号处理周期的机理。仿真结果证明所建立的光纤陀螺动态条件下的误差模型准确可靠。
为了对光纤陀螺的动态性能进行合理评价,采用三轴惯导测试转台来模拟光纤陀螺的角加速运动状态,给光纤陀螺施加瞬时变化的角速度输入,对其进行动态测试。对测试原理和测试步骤进行详细阐述。采用位置差商法、分周期离散理论曲线法和公式变换法确定动态测试中的基准值。分析结果表明分周期离散理论曲线法和公式变换法较适合。
三轴转台的精度是制约光纤陀螺测试结果精确性的瓶颈因素。根据转台在摇摆状态下输出信号的特点,采用皮萨伦科谱分解法对其进行辨识。由此得到转台信号的幅度失真、频率失真以及夹杂在其中的分量谐波的幅度和频率。并通过比较辨识前后转台误差的标准差,证明了辨识结果的可靠性。同时,分析了不同转台框在相同摇摆条件下的失真规律和同一转台框在不同摇摆条件下的失真规律。实验结果表明,皮萨伦科谱分解法应用于转台正弦信号的失真辨识中是非常适用的。
为了避免转台摇摆运动轨迹中夹杂的噪声传递到动态测试的基准信号中,结合小波多分辨分析和空间局部化的性质,选用db5小波对转台的运动轨迹进行降噪。结果表明,小波滤波法的噪声滤除效果理想,提高了对光纤陀螺动态测试结果评定的准确性。
采用时延估计理论分析和补偿动态测试中基准信号与实际信号之间的时间延迟。利用测试中信号与噪声、噪声与噪声互不相关的特点,对两个信号进行相关运算,估计出两信号之间的时间延迟,并进一步对其补偿。结果表明,时间延迟对测试结果有较大影响,经过补偿后的动态误差更符合实际情况。
为了更好的分析光纤陀螺的动态性能,采用动态Allan方差法对光纤陀螺的动态误差进行分析。根据动态Allan方差法中窗函数的原理,讨论了不同窗口长度对动态误差分析结果的影响。并且,提供了单一摇摆运动和两种复合摇摆运动的分析结果。从分析图中方差的起伏变化可以看出,动态Allan方差法可以准确地反映动态误差里的突变和周期性变化等非稳定性因素,能够清晰地辨识出隐藏在动态误差里的不同摇摆状态。由理论分析和实验结果可知,动态Allan方差法对光纤陀螺的动态性能分析是非常适用的。
动态Allan方差法是一种分析非平稳性信号的有效工具,但在辨识噪声时存在功率泄漏和定量表示单一的缺陷。为此,提出窗函数组合法和噪声量值的二维表示法对其改进,并将其用于分析和定量描述光纤陀螺动态误差中的各种噪声项。窗函数组合法在光纤陀螺动态误差分解的基础上采用矩形窗和汉宁窗对其中的低频噪声和高频噪声分别进行分析。噪声量值的二维表示法根据动态Allan方差法原理得到噪声量值随采样点数目增加的变化规律。实验结果表明窗函数组合法可以满足不同频段噪声的辨识要求,减小功率泄漏；噪声量值的二维表示法可以准确地反映出动态误差中噪声项的变化特征。
为了改善光纤陀螺的动态性能,将普通PID控制器的设计思想应用到光纤陀螺的动态误差控制器中,并进一步基于光纤陀螺动态条件下的误差特性设计出一种新型的动态误差控制器结构。前者主要通过普通PID控制器的设计思想与光纤陀螺的控制方式相结合,即基于光纤陀螺内部控制方式实现。而后者将微分环节设置在输出信号之前,使输出信号和反馈信号同时具有提前预测功能,并在微分环节后面加一个低通滤波器以抑制微分环节带来的高频干扰。这一新控制器结构既可以使控制量减小,各个时刻的控制误差不累积,还可以使输出跟踪输入,反映输入的变化。两种动态误差控制器均通过在光纤陀螺数字信号处理芯片FPGA的各模块中编写VHDL语言实现。实验结果表明两种动态误差控制器都可以明显地改善光纤陀螺的动态性能,且基于光纤陀螺动态条件下误差特性的动态误差控制器具有更优的控制效果。
Fiber optic gyroscope (FOG) is widely applied in strapdown inertial navigation system (SINS), and its performance largely determines the precision of SINS. At home and abroad, lots of researches on the performance of FOG are reported in the state of rest or uniform motion, i.e., the static properties of FOG, however, the study on the performance of FOG in the state of angular acceleration motion is less, i.e., the dynamic performance of FOG. In this paper, study the error theory of FOG under the dynamic conditions, test methods, analysis of test results and the improvement methods of performance systematically.
SINS fix directly with the carrier, which are always under angular acceleration state in the actual movement. Therefore, the performance of FOG under angular acceleration state determines the accuracy of SINS.The error model of FOG under the dynamic condition is established, basing on the analysis of FOG system model and response characteristics under angular acceleration motion. The influence of FOG stability conditions, structural parameters, signal processing cycle as well as the external environment on the dynamic performance of FOG are discussed. In theory, the affect mechanism of light average wavelength and feedback channel gain on the structural parameters are analyzed; the influence mechanism of the step height signal and the output signal filtering on the signal processing cycle are discussed. Simulation results indicate that the error model of FOG under the dynamic conditions is accurate and reliable.
To evaluate the dynamic performance of FOG reasonably, the three-axis inertial test turntable is chosen to test the dynamic performance of FOG. The input angular velocity signal of FOG changes according to sine law. The test principle and procedures are presented. In this paper, three methods are presented to determine the reference value in dynamic test, which are location divided difference, separated period discretization theory curve and transform formula method. Separated period discretization theory curve and transform formula method are suitable among these.
The accuracy of three-axis turntable is one of the key factors that constrain the precision of FOG test results. Based on the characteristics of output signals under the sway states, use of the Pisarenko spectrum decomposition method is preferred for identifying the output signals of turntable, which include the amplitude distortion, frequency distortion and the component harmonics. In this paper, the standard deviations of turntable errors are compared and analyzed to identify the credibility. Moreover, the distortion laws are analyzed under two conditions:different turntable frames the same sway conditions and identical turntable frame the different sway conditions. The results indicate that the Pisarenko spectrum decomposition method is applicable to identify the sinusoidal signal distortion of turntable.
Based on the wavelet natures of multiresolution analysis and spatial localization, db5wavelet is choosed to fiter the noise of turntable trajectory for avoiding it to pass in the reference signal of dynamic test. The results indicate that the filtering effect of wavelet is satisfactory and it improves the accuracy of the dynamic test results of FOG.
The time delay between the reference signal and the actual signal in dynamic test is analyzed and compensated using time delay estimation theory. Related operation is done to estimate and further compensate the time delay between the two signals, based on signals and noises, noises and noises are irrelevant in the test. The results indicate that time delay has a greater impact on test results and the dynamic error after compensation is in accordance with the actual situation.
In order to study the dynamic performance of FOG better, it is proposed that the dynamic error which is obtained by test of FOG is analyzed by dynamic Allan variance. According to the principle of window function of dynamic Allan variance method, the analysis results of dynamic error are discussed under the different window length conditions. Furthermore, a kind of single sway movement and two kinds of composite sway movement are analyzed by dynamic Allan variance method and their results are provided. There is fluctuating variation of variance in analysis figures, by which the various non-stationary factors in the dynamic error such as mutation and periodic variation are accurately reflected and the different sway states hidded in the dynamic errors are clearly identified. Both the theoretical analysis and experimental results indicate that the dynamic Allan variance method is very applicable to analyze the dynamic performance of FOG.
The dynamic Allan variance is an effective method for analyzing non-stationary signal. However, it has defects in noise identification:power leakage and single quantification. Therefore, window function combination method is introduced for their improvements as well as two-dimensional expression of noise value. They are used for analysis and quantitative measurement of various noise terms in the FOG dynamic error. Based on the dynamic error resolution of FOG, rectangular window is applied to analyze low&intermediate frequency noise, while hanning window does high-frequency noise. According to the principle of DAVAR, the noise variation laws with the numbers of sampling point are obtained, namely, two-dimensional expression of noise value. The experimental results indicate that window function combination method satisfies the identification requirements of noise in different frequency ranges and reduces power leakage; moreover, the change characteristics of every noise item in the dynamic error are accurately reflected by the two-dimensional expression of noise value.
The design idea of normal PID controller is applied in the dynamic error controller of FOG to improve its dynamic performance; moreover, a novel dynamic controller structure is designed basing on the error characteristics of FOG under dynamic state. The former is implemented by the combination of design idea of normal PID with the control idea of FOG, i.e. implemented by the inner control model of FOG. For the later (the novel one), the differential link is set before the output signal, which make the output signal and feedback signal to predict in advance; meanwhile, a low-pass filter is set after the differential link to suppress the high frequency interference brought by the differential link. The novel control structure can not only decrease the control amount and avoid the calculation of control error, but also allows the output to track the input and reflects the input change. Both the controllers are realized through writing VHDL language in the digital signal processing chip FPGA of FOG. The test results indicate that both the dynamic error controllers can significantly improve the FOG dynamic performance, furthermore, the novel dynamic error controller, i.e. the dynamic error controller basing on the error characteristic of FOG under dynamic condition, has better error control performance.
引文
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