增量式磁性編碼器類比訊號為正弦與餘弦訊號，其誤差包含直流偏移、振幅不等、相位偏移、諧波誤差。現今對於前三種誤差已有許多處理方式，但大多數方法僅針對固定量值進行修正。在訊號誤差隨使用情況而改變的情境下，需要一套能夠即時修正訊號的方法。除這三種誤差之外，磁性編碼器訊號中常有諧波的成份出現，此特徵主要來自於磁性尺提供的磁場與異向性磁阻感測器的形狀異向性。
本研究提出新的自適應演算法對前三項誤差進行即時的量值估計與消除。此方法在演算法中加入虛擬的量測數據，以避免系統在停止運動時出現估計錯誤的現象。對於訊號中諧波成份，選用訊號交錯時的量值以估計誤差，在特定範圍內使用同樣的數值進行修正。藉本文所提之訊號修正方案，編碼器位置諧波誤差平均振幅可降低至0.5 μm以下。

The incremental magnetic encoder outputs quadrature signals with error components, these errors include DC offset, unequal gain, phase shift, and harmonic error. Nowadays, there are many ways to correct the first three types of errors by assuming that each error is constant. However, the signal errors vary with the environmental change. Hence, an algorithm that can track the signal errors in real-time is required. Besides the first three errors, the signals contain the harmonic error, which results from the harmonic magnetic field and the shape anisotropic of the anisotropic magnetoresistance (AMR) sensor.
This study proposes a new adaptive algorithm to estimate and then eliminate the magnitude of the first three errors. Virtual points are added to measurement data to prevent estimation errors when the motion of the system stops. The harmonic error is estimated with the magnitudes of the signals at crossingpoints, and is corrected with the same value at a certain range. With the proposed correction method, the average magnitude of harmonic component of position error reduces to below 0.5 μm.

摘要 I
ABSTRACT II
致謝 III
目錄 IV
圖表目錄 VII
第一章 緒論 1
1-1. 前言 1
1-2. 技術背景 2
1-3. 文獻回顧 7
1-3-1. 訊號修正 7
1-3-2. 細分割 10
1-4. 研究動機與目的 14
1-5. 本文架構 15
第二章 研究理論 16
2-1. 靜磁學 16
2-2. 磁性感測器 18
2-2-1. 霍爾效應 18
2-2-2. 磁阻效應 19
2-3. 編碼器訊號 22
2-3-1. 類比訊號 22
2-3-2. 數位訊號 25
2-4. 訊號修正方法 31
2-5. 自適應演算法 34
第三章 磁性尺磁場 42
3-1. 垂直交替磁化 42
3-1-1. 垂直磁化磁場模型 42
3-1-2. 磁場模型疊加方法 47
3-2. 水平交替磁化與海爾貝克陣列 53
第四章 訊號誤差分析 61
4-1. 訊號誤差與位置精度 61
4-1-1. 常見訊號誤差 64
4-1-2. 諧波誤差 69
4-1-3. 週期非理想誤差 72
4-2. 實驗架設與精度檢測 74
4-2-1. 實驗設備 74
4-2-1. 數據分析 76
第五章 訊號修正方法 87
5-1. 常見訊號誤差 87
5-2. 訊號諧波誤差 117
第六章 結論與未來工作 125
6-1. 結論 125
6-2. 未來工作 126
參考文獻 128

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