提高小型光电编码器分辨力和精度的方法研究
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摘要
随着机载、星载、便携式军用侦查、定位、指挥武器系统的飞速发展，对小型光电编码器的分辨力和精度提出了更高的要求。由于莫尔条纹光电信号质量制约了小型光电编码器的高分辨力细分，细分误差和长周期误差影响了光电编码器的精度，因此开展莫尔条纹信号误差校正、新的细分方法研究和长周期误差修正方法研究，对提高小型光电编码器的分辨力和精度、跟踪国际先进水平具有重要意义。
在参考国内外文献的基础上，首先从莫尔条纹光电信号产生的原理出发，深入分析了莫尔条纹信号质量对光电编码器高分辨力细分的影响、细分误差产生的原因、长周期误差对光电编码器精度产生的影响，研究了提高小型光电编码器分辨力和精度的方法。
提出了近似三角波莫尔条纹光电信号的误差校正方法。建立含有直流误差、幅值误差、波形畸变的莫尔条纹信号波形参数方程，通过傅里叶变换求解波形参数，利用多倍角公式将信号波形中的高次谐波分量转换为高阶分量，采用牛顿迭代法将莫尔条纹光电信号校正至标准正(余)弦信号；通过最小二乘法对信号间的相位误差进行校正处理，将两路信号校正至标准正交的正余弦信号，提高了小型光电编码器的细分精度。
提出了基于CORDIC算法的小型光电编码器高分辨力细分方法。利用简单的移位和加法操作对码盘精码莫尔条纹光电信号细分求相位，避免了信号波形偏离理想值时传统“计算法细分”引入的细分误差。针对CORDIC算法存在运算速度和计算精度的矛盾，提出了旋转角度近似和旋转方向预测两项改进措施，提高了小型光电编码器的分辨力。
建立了傅里叶神经网络长周期误差修正模型。以高精度基准编码器作为学习目标，以正交三角函数基作为神经网络中间隐层节点的激活函数，利用引入模拟退火策略的差分进化算法对网络进行训练，求解误差修正模型参数，实现对光电编码器长周期误差修正，有效提高了小型光电编码器的精度。
运用本文研究的方法对长春光机所生产的某型号小型光电编码器进行处理，经实际测试编码器分辨力由16位提高到18位，均方根误差由60″减小到20″。实验结果表明：本文研究的方法可有效地提高小型光电编码器的分辨力和精度，对于研制小型化、高精度、高分辨力光电编码器具有重要意义。
With the rapid development of airborne and spaceborne applications, portablemilitary investigation, positioning, command weapon system, higher demands wererequired for the angular accuracy and resolution of small photoelectric encoders.Since the quality of Moiré fringe photoelectric signals constrains high-resolutioninterpolation of small photoelectric encoder, and the interpolation error and thelong-period error are main factors that affect the accuracy of photoelectric encoders,it is very important to carry out research on the Moiréfringe signals calibration, newinterpolation methods, and long-period error correction to improve the resolutionand accuracy of small photoelectric encoders and thus follow the internationaladvanced level.
Based on large reference at home and abroad, starting from the principle ofMoiré fringe photoelectric signals generation, the factors which affected theaccuracy of photoelectric signals were analyzed thoroughly, including the Moiréfringe signal’s quality for high-resolution interpolation, reasons of interpolation errorgeneration, and long-period errors for the accuracy of photoelectric encoders. Mucheffort was paid on the methods of improving the resolution and accuracy of smallphotoelectric encoders.
The error calibration method was proposed for Moiré fringe photoelectric signals in the form of approximate triangular waves. The parameter equation ofMoiréfringe photoelectric signal waveform was built firstly, which contained directcurrent errors, amplitude errors and waveform distortions, and then Foruiertransform was applied to solve the waveform parameters. The high spatial harmonicsin the signal waveform were transformed into higher order components using themultiple angle formula, and photoelectric signals were calibrated to standard sineand cosine ones using the Newton iteration method. After that, the phase errorsbetween signals were calibrated by the least squares fitting method. The calibrationfrom two channels sample signals to the standard orthogonal sine and cosine signalswas realized, which improved the interpolation accuracy of small photoelectricencoders.
A novel high-resolution interpolation method based on CORDIC algorithm wasproposed. Simple shifting and addition operations were used to resolve theinterpolation phases of Moiré fringe photoelectric signals, which could get rid ofconventional computed interpolation error cased by the deviation of samplesignals from the ideal ones. For the contradiction of calculation speed and accuracyexisting in CORDIC algorithm, two sorts of improvement were proposed includingapproximation of rotation angles and prediction of rotation direction. The resolutionof small photoelectric encoder was thus improved.
The Fourier neural network model to correct long-period error of smallphotoelectric encoder was established. Output values of a high accuracy benchmarkencoder were set as the learning reference, and orthogonal trigonometric basisfunctions served as activation function of nodes in intermediate hidden layers. Thedifferential evaluation algorithm combined with simulated annealing strategy wasapplied for training to solve the error correction parameters. The correction of thelong-period error improved the accuracy of small photoelectric encoder effectively.
The methods proposed above were applied to a small photoelectric encoderwhich was made by CIOMP (Changchun Institute of Optics, Fine Mechanics andPhysics, Chinese Academy of Sciences). After actual measurement, the resolution ofthe photoelectric encoder was improved from16-bit to18-bit and the root mean square error was reduced from60″to20″. The experiment result shows that, themethods could effectively improve the resolution and accuracy of smallphotoelectric encoders, and it is beneficial for development of miniaturized,high-resolution and high-accuracy small photoelectric encoders.
在参考国内外文献的基础上，首先从莫尔条纹光电信号产生的原理出发，深入分析了莫尔条纹信号质量对光电编码器高分辨力细分的影响、细分误差产生的原因、长周期误差对光电编码器精度产生的影响，研究了提高小型光电编码器分辨力和精度的方法。
提出了近似三角波莫尔条纹光电信号的误差校正方法。建立含有直流误差、幅值误差、波形畸变的莫尔条纹信号波形参数方程，通过傅里叶变换求解波形参数，利用多倍角公式将信号波形中的高次谐波分量转换为高阶分量，采用牛顿迭代法将莫尔条纹光电信号校正至标准正(余)弦信号；通过最小二乘法对信号间的相位误差进行校正处理，将两路信号校正至标准正交的正余弦信号，提高了小型光电编码器的细分精度。
提出了基于CORDIC算法的小型光电编码器高分辨力细分方法。利用简单的移位和加法操作对码盘精码莫尔条纹光电信号细分求相位，避免了信号波形偏离理想值时传统“计算法细分”引入的细分误差。针对CORDIC算法存在运算速度和计算精度的矛盾，提出了旋转角度近似和旋转方向预测两项改进措施，提高了小型光电编码器的分辨力。
建立了傅里叶神经网络长周期误差修正模型。以高精度基准编码器作为学习目标，以正交三角函数基作为神经网络中间隐层节点的激活函数，利用引入模拟退火策略的差分进化算法对网络进行训练，求解误差修正模型参数，实现对光电编码器长周期误差修正，有效提高了小型光电编码器的精度。
运用本文研究的方法对长春光机所生产的某型号小型光电编码器进行处理，经实际测试编码器分辨力由16位提高到18位，均方根误差由60″减小到20″。实验结果表明：本文研究的方法可有效地提高小型光电编码器的分辨力和精度，对于研制小型化、高精度、高分辨力光电编码器具有重要意义。
With the rapid development of airborne and spaceborne applications, portablemilitary investigation, positioning, command weapon system, higher demands wererequired for the angular accuracy and resolution of small photoelectric encoders.Since the quality of Moiré fringe photoelectric signals constrains high-resolutioninterpolation of small photoelectric encoder, and the interpolation error and thelong-period error are main factors that affect the accuracy of photoelectric encoders,it is very important to carry out research on the Moiréfringe signals calibration, newinterpolation methods, and long-period error correction to improve the resolutionand accuracy of small photoelectric encoders and thus follow the internationaladvanced level.
Based on large reference at home and abroad, starting from the principle ofMoiré fringe photoelectric signals generation, the factors which affected theaccuracy of photoelectric signals were analyzed thoroughly, including the Moiréfringe signal’s quality for high-resolution interpolation, reasons of interpolation errorgeneration, and long-period errors for the accuracy of photoelectric encoders. Mucheffort was paid on the methods of improving the resolution and accuracy of smallphotoelectric encoders.
The error calibration method was proposed for Moiré fringe photoelectric signals in the form of approximate triangular waves. The parameter equation ofMoiréfringe photoelectric signal waveform was built firstly, which contained directcurrent errors, amplitude errors and waveform distortions, and then Foruiertransform was applied to solve the waveform parameters. The high spatial harmonicsin the signal waveform were transformed into higher order components using themultiple angle formula, and photoelectric signals were calibrated to standard sineand cosine ones using the Newton iteration method. After that, the phase errorsbetween signals were calibrated by the least squares fitting method. The calibrationfrom two channels sample signals to the standard orthogonal sine and cosine signalswas realized, which improved the interpolation accuracy of small photoelectricencoders.
A novel high-resolution interpolation method based on CORDIC algorithm wasproposed. Simple shifting and addition operations were used to resolve theinterpolation phases of Moiré fringe photoelectric signals, which could get rid ofconventional computed interpolation error cased by the deviation of samplesignals from the ideal ones. For the contradiction of calculation speed and accuracyexisting in CORDIC algorithm, two sorts of improvement were proposed includingapproximation of rotation angles and prediction of rotation direction. The resolutionof small photoelectric encoder was thus improved.
The Fourier neural network model to correct long-period error of smallphotoelectric encoder was established. Output values of a high accuracy benchmarkencoder were set as the learning reference, and orthogonal trigonometric basisfunctions served as activation function of nodes in intermediate hidden layers. Thedifferential evaluation algorithm combined with simulated annealing strategy wasapplied for training to solve the error correction parameters. The correction of thelong-period error improved the accuracy of small photoelectric encoder effectively.
The methods proposed above were applied to a small photoelectric encoderwhich was made by CIOMP (Changchun Institute of Optics, Fine Mechanics andPhysics, Chinese Academy of Sciences). After actual measurement, the resolution ofthe photoelectric encoder was improved from16-bit to18-bit and the root mean square error was reduced from60″to20″. The experiment result shows that, themethods could effectively improve the resolution and accuracy of smallphotoelectric encoders, and it is beneficial for development of miniaturized,high-resolution and high-accuracy small photoelectric encoders.
引文
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