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研究生:蕭侑晟
研究生(外文):You-ChengHsiao
論文名稱:光學編碼器訊號誤差補償設計
論文名稱(外文):Error Compensation Design for Optical Encoders
指導教授:陳永裕陳永裕引用關係
指導教授(外文):Yung-Yu Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:系統及船舶機電工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:英文
論文頁數:98
中文關鍵詞:光學編碼器相位誤差修正凸包Peter HeydemannFFTButterworth filterPascal’s theorem
外文關鍵詞:Optical encodersPhase correctConvex hullPeter HeydemannFFTButterworth filterPascal’s theorem
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本篇論文主要開發微型光學編碼器訊號誤差補償系統,在光學編碼器尺度縮小與提高定位解析度的情況下,提高微型光學編碼器對環境油污、震動及組裝誤差的耐受度,使機器人、CNC工具機、精密設備在節能與輕量化的改善下,仍維持高定位精度與環境耐受能力。本篇論文使用三種方法修正光學編碼器的含誤差訊號: 1. 1981年,Peter Heydemann開發了一種方法來識別和修正正交訊號的干涉誤差。該方法可修正平均偏移誤差、波形失真和相位誤差。此方法的目的是利用含誤差的訊號建立一個理想訊號的模型,並利用理想訊號模型的反轉換,將含誤差的訊號作為輸入,輸出就為理想無相位誤差的訊號。2. 利用FFT 可以解析訊號大小及相位的特性去計算出訊號的相位差,再將相位誤差代入誤差模型內,修正訊號的相位誤差。3. 利用Pascal’s theorem 的幾何關係計算,因為相位差而形成的Lissajous 圖形參數,再將參數代回誤差模型內。
接著使用MATLAB軟體模擬、驗證上述三種方法,並且分別評估各別的計算量,最後選擇Pascal’s theorem 的算法寫入TI的DSP晶片內,以達成接近實際系統的驗證,並且利用Butterworth filter抑制高頻雜訊對系統造成的影響,此外還使用凸包的概念對訊號的取樣做優化,綜合上述形成一套即時的光學編碼器訊號相位誤差補償系統。
For improving the tolerance of grating miniature optical encoders and meeting the requirement of robots, CNC machines and various equipment needs ultra-high accuracy to the environmental noises in real-time, this study uses three methods to reduce the measurement error caused by dirt, vibration and component assemble misalignment for grating miniature optical encoders. The main ideas behind these methods are using the measured signals which contain phase errors to remove the noises and recover original signals based on the parameters’ solution of a nonlinear system error model formulated by the relationship between input signals and output signals. Based on system model, three methods can be briefly expressed as: 1. Correcting phase errors via inversion method with the collecting input raw data, 2. Using FFT method to calculate spectrum of the input signals, a phase difference can be obtained for correcting the phase error, and 3. Calculating the geometric relationship of Lissajous figure of two input signals based on Pascal’s theorem to search the optimal parameters for the nonlinear system error model to reduce the phase error effective.
For verifying the compensation performances, these three methods are simulated in the well-known software platform: Matlab first. The method based on Pascal’s theorem is selected for the realistic implementation due to its simple computational ability. From the simulation results, these three methods reveal almost the same compensation performances. However, the inversion method and FFT method suffer the consequence of computational burden due to their complicated process in practical. Finally, the Pascal’s theorem based method is realized practically.
中文摘要 I
ABSTRACT II
誌謝 III
CONTENTS IV
LIST OF TABLES VI
LIST OF FIGURES VII
NOMENCLATURES XX
CHAPTER 1 INTRODUCTION 1
1.1 RESEARCH MOTIVATION 1
1.2 LITERATURES REVIEW 2
1.3 RESEARCH METHODS 3
1.4 CONTRIBUTIONS OF THIS THESIS 4
CHAPTER 2 THE COMPENSATION METHODS FOR SIGNAL ERRORS OF OPTICAL ENCODER 5
2.1 THE LISSAJOUS FIGURE 5
2.2 THE COMPENSATION METHODS FOR RANDOM PHASE SHIFT 6
2.3 PSEUDO INVERSE 9
2.4 FFT METHOD 11
2.5 PASCAL’S THEOREM 12
CHAPTER 3 SIMULATION RESULTS 17
3.1 FIXED FREQUENCY AND PHASE SHIFT ERROR 19
3.1.1 Case 1: The Signals of 5k Hz Frequency 19
3.1.2 Case 2: The Signals of 19k Hz Frequency 26
3.2 RANDOM INPUT FREQUENCY AND PHASE SHIFT 33
3.2.1 Case 3: The Signals of 1Hz-10k Hz Frequency 34
3.2.2 Case 4: The Signals of 1Hz~40k Hz Frequency 42
3.3 COMPARISONS OF SIMULATION RESULTS 50
3.3.1 Static Situation Results 50
3.3.2 Dynamic Situation Results 50
3.3.3 Summary 51
CHAPTER 4 PRACTICAL RESULTS 52
4.1 SYSTEM ARCHITECTURE 52
4.1.1 Hardware Equipment 53
4.1.2 Low-Pass Butterworth Filter 54
4.2 THE PEOPOSED COMPENSATION ALGORITHM 57
4.3 THE PRACTICAL RESULTS FROM DSP 58
4.3.1 Case 1 noise: 10% 60
4.3.2 Case 2 noise: 20% 71
4.3.3 Case 3 noise: 50% 82
CHAPTER 5 CONCLUSIONS AND FUTURE WORKS 93
REFERENCES 95
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