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研究生:吳昭儀
研究生(外文):Chao-YiWu
論文名稱:類比式編碼器之細分割與解析度提升
論文名稱(外文):A Subdivision Method for Improving Resolution of Analog Encoders
指導教授:何明字
指導教授(外文):Ming-Tzu Ho
學位類別:碩士
校院名稱:國立成功大學
系所名稱:工程科學系
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:中文
論文頁數:119
中文關鍵詞:類比編碼器正交弦波校正細分割
外文關鍵詞:analog encodercalibration of quadrature encoder signalssubdivision algorithm
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本論文旨在提高增量型類比編碼器之解析度。由於實際上類比編碼器之輸出訊號並非完全等振幅、正交弦波訊號,且平均準位也有偏差,故本論文為了得到高解析度之細分割結果,必須先對失真的弦波訊號做校正,吾人利用線性迴歸之形式以其最小平方法解求得校正係數,代入設定之失真正交弦波訊號即可得到更加準確之等振幅正交弦波訊號,並以MATLAB/Simulink軟體進行模擬,確認訊號校正與細分割之演算法流程。而在實作上,本系統使用德州儀器公司(Texas Instruments, TI)所生產的數位訊號處理器TMS320F28335做為核心以實現類比編碼器之細分割演算法,最後可將類比編碼器之解析度提升至原本的千倍,同時以細分割後之位置回授控制馬達也能夠正確地工作。
SUMMARY
The aim of this thesis is to improve the resolution of incremental analog encoders. In practice, the outputs of analog encoders are not the quadrature sinusoidal waves, in which there always are the mean offsets, phase offsets, and amplitude difference. To solve these problems, the correction coefficients are introduced. These coefficients can be obtained by the least-squares method to remove distortion of encoder outputs. Furthermore, MATLAB / Simulink are used to simulate the algorithm of signal calibration and subdivision algorithm to improve the resolution of analog encoders. In experiments, the algorithms are implemented on a digital signals processor (TMS320F28335) from Texas Instruments. Finally, through a motor driver, the motor can be controlled by using the improvement of analog encoder’s resolution.
Keywords: analog encoder; calibration of quadrature encoder signals; subdivision algorithm

INTRODUCTION
For better control, the motor needs a high resolution encoder when performing position control. However, the higher the resolution of an encoder, the higher the price it will cost. How to improve the resolution of an encoder with lower cost is the goal of this research. Encoders have different types and different output signals. There are digital encoders and analog encoders. Instead of using a high resolution encoder, the analog encoder with low resolution can be improved by some methods, for examples using the additional external circuit or algorithms. The aim of this thesis is to improve the resolution of any incremental analog encoders using the subdivision algorithm. Through MATLAB, the subdivision algorithm is tested to verify the improvement of resolution of analog encoders. In experiment, the subdivision codes are implemented and tested on a motor driver to obtain and process the actual encoder signals.

MATERIALS AND METHODS
In experiments, the algorithm is implemented on a digital signal processor (TMS320F28335) in the motor driver in which an incremental analog encoder is used as the input feedback. The motor driver can acquire the incremental analog encoder output signals and digital encoder output signals at the same time. The resolution of incremental analog encoder is 0.05 mm/count, while the resolution of incremental digital encoder is 0.5 . Both of them are put on a linear motor, so that the motor driver can obtain these signals simultaneously. The output signals from analog encoder always have some distortions. Thus, the first priority is to perform calibration of the analog encoder outputs. By collecting the encoder outputs data, the calibration coefficients can be obtained by the least-squares method, and then, the quadrature sinusoidal wave can be calculated by using the encoder output signals and the coefficients. After calibration, the subdivided angles can be obtained by performing arctangent processing. By combining these angles and the original position data (QEP), the position of the motor can be acquired accurately. In other words, the resolution of analog encoder becomes higher.

RESULTS AND DISCUSSION
Before calibration, phase A and phase B of analog encoders output signals are put together on the x-axis and y-axis as shown in Figure 1.
Then, after performing the algorithm of calibration, the encoder’s output signals are put together on the x-axis and y-axis as shown in Figure 2. It is shown in Figure 2 that the phase A and phase B data become more accurate as a perfect circle as it is compared to the results shown in Figure 1.
In these results, the original resolution of the analog encoder is 0.05 mm, and then, after subdivision, the resolution of analog encoder can be raised to 100 times. In other words, the resolution of analog encoder becomes 0.5 /count. Considering one period of a sinusoidal wave is 0.2 mm, the linear motor is controlled such that the movement of the analog encoder reaches 0.2 mm. Then, the output from analog encoder and digital encoder are recorded every 0.01 mm. The errors are obtained by comparing the analog encoder’s outputs and digital encoder’s outputs as shown in Figure 3.
In Figure 3, it is shown that the accuracy is about 4.5 with 2 repeatability. Let the resolution of the analog encoder raise to 1000 times. In other words, the resolution of the analog encoder becomes to 0.05 /count. Then, the outputs from the analog encoder and laser interferometer are recorded every 0.01 mm. The errors are obtained by comparing the analog encoder’s outputs and laser interferometer’s outputs as shown in Figure 4.
Finally, in Figure 4, the accuracy of position is 3.7 with repeatability 1.9 .
CONCLUSION
In this thesis, the output signals of an analog encoder is calibrated by using the least-squares method. By controlling the motor, the outputs of an analog encoder and calibration coefficients can be obtained. After calibration, there are two quadrature sinusoids, namely, phase A and phase B. By performing arctangent calculation from phase A and B, we can get the subdivided angle of the encoder. By combining the subdivided angle and original position (QEP) of the analog encoder, the position of motor can be obtained with high resolution. Thus, the resolution of the analog encoder can be improved higher than before.

目錄
頁次
摘要 Ⅰ
Extended Abstract Ⅱ
致謝 VII
目錄 VIII
圖表目錄 ⅩI
第一章 緒論
1-1 研究背景 1-1
1-2 研究動機及目的 1-1
1-3 研究步驟 1-2
1-4 相關文獻探討 1-4
1-5 論文結構 1-5
第二章 增量型類比編碼器之細分割方法介紹
2-1 前言 2-1
2-2 增量型編碼器之編碼原理 2-2
2-3 細分割方法介紹與比較 2-3
2-3-1 比較器法 2-3
2-3-2 PLL鎖相迴路法 2-8
2-3-3 相位編碼法 2-8
2-3-4 三角波倍頻法 2-10
2-4 細分割技術之實現分析 2-13
第三章 類比編碼器之正弦訊號細分割設計與模擬
3-1 前言 3-1
3-2 正交弦波之失真校正 3-1
3-3 弦波正交訊號之取樣建表 3-6
3-4 細分割演算法流程 3-10
3-5 細分割演算法模擬結果 3-12
第四章 系統控制核心晶片與周邊電路介紹
4-1 前言 4-1
4-2 控制核心晶片與模組 4-2
4-2-1 數位訊號處理器TMS320F28335 4-2
4-2-2 正交編碼脈衝介面 4-3
4-2-3 類比數位轉換器介面 4-4
4-2-4 脈衝寬度調變介面 4-5
4-2-5 通用型輸入輸出介面 4-5
4-2-6 PWM電壓位準提升與隔離電路 4-5
4-3 馬達變頻驅動模組 4-6
4-4 回授感測電路模組 4-7
4-4-1 電流感測電路 4-7
4-4-2 電壓感測電路 4-8
第五章 編碼器細分割韌體實現與線性馬達平台測試驗證
5-1 前言 5-1
5-2 旋轉馬達實驗平台之器材介紹與資料讀取 5-1
5-2-1 校正編碼器訊號流程及實作結果 5-3
5-2-2 細分割對照表之建立與查表方法 5-9
5-2-3 細分割程式化與TW4細分割晶片輸出比較 5-13
5-2-4 位置歸零 5-17
5-3 線性馬達平台架設及測試 5-21
5-3-1 細分割對於索引(index)之計算 5-23
5-3-2 細分割非線性補償 5-27
5-3-3 以雷射干涉儀驗證細分割結果 5-30
5-3-4 細分割演算法優化 5-32
5-4 細分割最高倍數之測試 5-40
第六章 類比編碼器校正係數計算程式自動化
6-1 前言 6-1
6-2 正交弦波失真之校正係數計算自動化流程 6-1
6-3 類比編碼器自動校正結果 6-8
第七章 結論與未來展望
7-1 結論 7-1
7-2 未來展望 7-1
參考文獻 Ref-1

參考文獻
[1]K. K. Tan, T. H. Lee, and H. X. Zhou, “New Interpolation Method for Quadrature Encoder Signals, IEEE Transactions on Instrumentation and Measurement, Vol. 51, No. 5, pp.1073-1079, Oct. 2002.
[2]Schmitt trigger, Wikipedia, https://en.wikipedia.org/wiki/Schmitt_trigger
[3]iC-TW4 8-Bit Sin/Cos Interpolator with Automatic Offset Correction Datasheet, iC-Haus, 2008
[4]林勇全,「高倍頻編碼器之設計」,南台科技大學電機工程研究所碩士論文碩士論文,民國九十五年七月。
[5]H. Rieder, M. Schwaiger, RSF. Elektronik, and GmbH. Tarsdorf, Austria, “Method of Electronically Correcting Position Errors in an Incremental Measuring System and Measuting System for Carrying out the Method, United States Patent: 5021650, June, 1991.
[6]T. Emura, L. Wang, and A. Arakawa, “A High-Resolution Interpolator for Incremental Encoders By Two-Phase Type PLL Method Proceedings of the International Conference on Industrial Electronics, Control, and Instrumentation, Vol. 3, pp. 1540-1545, 1993.
[7]N. Hagiwara, Y. Suzuki, and H. Murase, “A Method of Improving the Resolution and Accuracy of Rotary Encoders using a Code compensation Technique, IEEE Transactions on Instrumentation and Measurement, Vol. 41, No. 1, pp. 98–101, Feb. 1992.
[8]藍啟峰,「以FPGA 發展電子細分割及其於光柵干涉儀之應用」,國立台灣大學-機械工程研究所碩士論文,民國九十年六月。
[9]Linear regression, wolfram mathworld, http://mathworld.wolfram.com/LinearRegression.html
[10]Least squares fitting-polynomial , wolfram mathworld, http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html
[11]Multiple-angle formulas, wolfram mathworld, http://mathworld.wolfram.com/Multiple-AngleFormulas.html
[12]蕭景隆,「線性馬達驅動控制系統之設計與實現」,國立成功大學工程科學系碩士論文,民國一百零三年一月。
[13]iC-TW8 16-Bit Sin/Cos Interpolator with Automatic Calibration Datasheet, iC-Haus, 2012.
[14]RENISHAW, XL-80 laser measurement system, http://www.renishaw.com.tw/tw/xl-80-laser-measurement-system--8267
[15]Gauss-Jordan elimination, wolfram mathworld, http://mathworld.wolfram.com/Gauss-JordanElimination.html
[16]Moving average filter, Wikipedia, https://en.wikipedia.org/wiki/Moving_average
[17]S.W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing, California Technical Publishing, San Diego, CA, 1997.
[18]Median filter, Wikipedia, https://en.wikipedia.org/wiki/Median_filter
[19]Texas Instruments TMS320F2812 Digital Signal Processor Datasheet.
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