回授裝置為運動控制中重要的元件之一，而市面上位置回授裝置種類繁多，各自的性能表現與適用性也不盡相同。尤近年來自動化與產業機械的蓬勃發展，對於運動控制的需求增加外，對定位精準度與極限速度的要求日漸嚴苛。
簡單來說回授裝置是由感測頭與資料記錄媒體所構成。在本論文中，資料記錄媒體根據編碼原則，並基於磁學理論，提出適用於線性裝置的絕對編碼。透過數學模型的建立，分析資料記錄媒體的磁場空間分布，以及磁阻感測器於變化磁場中的訊號響應特性，開發出一種具有絕對式位置回授的磁性裝置。透過實驗的方法測試本論文所開發的絕對式回授裝置，得到定位精度、重現度、最大速度等特性，此些特性可以勝任一般自動化產業的應用。磁紀錄媒體的磁場分布與定位精度之間的模型建立，有助於縮短品質檢驗所需要的時間。感測器於磁場分布中的姿態對於輸出訊號以及定位精度的影響，也在本文中進行分析探討。
本文透過絕對編碼的建立與分析磁阻感測器於不同磁場分布下的特性，提出具有高精度與高解析度並克服原點賦歸的位置回授裝置，且可安裝於嚴苛的環境下使用，未來有機會應用於加工機台上。

Feedback device is one of the most important components of motion control. There are various types of feedback devices available on the market. However, the properties of feedback devices are different with each other and adaptive to diverse applications.
Generally, feedback device consists of a read head and recording media. In this dissertation, the encoding method on recording media was proposed to apply on linear system based on magnetism. An analytical model was presented to calculate magnetic field distribution and corresponding response of MR sensor. An absolute position sensing system was carried out and tested for its accuracy, repeatability and maximum traveling speed, which are able to fulfill the requirement in automation industry application. In order to reduce the time costing in quality examination process, an analytical model was established to retrieve accuracy directly from magnetic field distribution. The assembled attitude of sensor in magnetic field was investigated into its corresponding output signal and accuracy.
An absolute position sensing system was proposed through presented encoding method and analysis of sensor characteristics under various magnetic field, which could achieve high accuracy and resolution.

摘要 vi
Abstract vii
Acknowledgement viii
Table of Contents ix
List of Tables xiii
List of Illustrations xiv
1 Introduction 1
1.1 Principles 1
1.2 Motivations 4
1.3 Objectives 8
2 Related State of Art in Absolute Type Position Sensing System 11
2.1 Existing Commercial Products 12
2.1.1 Categorized by Assembly Method 12
2.1.2 Categorized by Sensing Technology 13
2.2 Literature Review 22
3 Design of Absolute Type Magnetic Position Sensing System 29
3.1 Reasons for Absolute Position 29
3.2 Absolute Pattern with Mixed Incremental Pole Pitches 30
3.2.1 Absolute Coding and Decoding 30
3.2.2 Compatibility of Sensors Integration 31
3.2.3 Algorithm Design for Absolute Positioning 35
3.3 Pattern with Mixed Arbitrary Pole Pitches 39
3.3.1 Absolute Coding and Decoding 39
3.3.2 Compatibility of Sensors Integration 41
3.3.3 Algorithm Design for Absolute Positioning 45
3.4 Performance of Designed System 49
3.4.1 Accuracy and Repeatability 52
3.4.2 Maximum Velocity 55
3.4.3 Velocity Ripple 62
3.5 Chapter Summary 63
4 Modelling of Magnetic Strip 64
4.1 System Overall Structure 65
4.2 Mathematical Modeling 66
4.2.1 Magnetic Characterization 66
4.2.2 Governing Equation 67
4.3 Assumptions 69
4.4 General Solutions to Governing Equations 69
4.4.1 By Laplace Equation 71
4.4.2 By Poisson Equation 73
4.5 Boundary Conditions 74
4.6 Solutions to Flux Density Distribution 75
4.7 Verification of Flux Density Distribution 78
4.7.1 By Finite Element Method 78
4.7.2 By Experiment 81
4.8 Discussion 84
4.9 Chapter Summary 87
5 Analytical Model for Transforming Magnetoresistance and Hall Signal into Position 88
5.1 Approach to Position Accuracy from Magnetoresistance Signal 89
5.1.1 Characteristic of a Magnetoresistance Sensor 89
5.1.2 Signal Measured from Magnetoresistance Sensor 95
5.1.3 Signal Processing of Measured MR signal 98
5.1.4 Approach to Position Accuracy 104
5.2 Approach to Position Accuracy from Hall Signal 110
5.2.1 Characteristic of a Three-axis Hall Sensor 110
5.2.2 Signal Correction 112
5.2.3 Indirect Approach to Position Accuracy 113
5.2.4 Direct Approach to Position Accuracy 115
5.3 Approach to Position Accuracy from Simulated Signal 118
5.3.1 Approach to Position Accuracy 118
5.3.2 Analysis of Signal Quality 121
5.4 Experimental Accuracy Verification 123
5.5 Chapter Summary 125
6 Analysis of Assembly Errors 127
6.1 Types of Assembly Errors 128
6.2 Experimental Setup 128
6.3 Effects upon MR Signal 131
6.4 Effects upon Position 135
6.5 Chapter Summary 139
7 Summary 140
7.1 Contributions 141
7.2 Directions for Future Work 143
References 145

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