本篇論文主要是針對藍寶石長晶爐的直徑控制做研究，以MATLAB做程式模擬、SIMULINK來做動態模擬，以實驗機台所能調整的參數而建構出模擬程式並於過程中得到主電腦控制器（ADC）之PID值與功率控制器之PID值的調整方法、功率輸出極限值(Slew Rate)以及LOADCELL取樣數(Smoothing Filter)對整個系統的影響。結果得到越接近輸出端者其反映時間需要越快，這樣整各系統的整體效應才會趨向穩定。

By using the Matlab and Simulink software, this work numerically simulates the dynamic situation of Sapphire crystal growth. The results of the simulation are then compared to the real diameter of grown record and refer to fine-tune the parameters of crystal growth, internationally.
The parameters of sapphire crystal growth include the slew rate, the PID of automatic diameter controller, the OID of power controller, smoothing filter, etc. As the slew rate increases, the diameters of the growing crystal become stable. The diameter variation, with respect to the crystal length, even turns into better after the fine-turn of the PID and the smoothing filter parameters.

中文摘要 ………………………………………………… I
Abstract …………………………………………………… II
誌謝 ……………………………………………………… III
目錄 ……………………………………………………… IV
表目錄 …………………………………………………… VII
圖目錄 …………………………………………………… VIII

第一章 緒論 ………………………………………… 01
1.1 研究動機與目的 ……………………………… 01
1.2 藍寶石晶體的性質與應用 …………………… 03
1.3 文獻回顧 ……………………………………… 04

第二章 長晶爐的系統與架構
2.1 長晶爐的簡介 ……………………………… 10
2.2 長晶爐體內部的熱場配置 ………………… 12
2.3 整個控制系統的架構 ……………………… 14
2.4 晶體成長的邏輯概念圖 …………………… 18
2.5 爐體內部之PID演算 ………………………… 21
2.6 開路特性測試 …………………………………… 22

第三章 功率控制的理論與模擬 …………………… 23
3.1 功率控制的理論 …………………………… 23
3.1.1 熱傳率與直徑的關係 …………………… 24
3.1.2 拉速對功率的影響 ……………………… 25
3.2 直徑的自動控制與模擬 ……………………… 26
3.2.1 模擬的建構 ……………………………… 28
3.2.2 模擬的結果 …………………………………….. 32

第四章 實驗結果 ……………………………………… 41
4.1 長晶初成長的測試 ………………………………41
4.2 用相同條件測試機台的重現性 ………………… 44
4.3 拉速變動測試 ………………………………… 47
4.4 ADC控制器PID變動測試 …………………… 50
4.5 機台PID參數修正 …………………………… 54
4.6 參數修正測試（二） ………………………… 57
4.7 參數修正測試（三）…………………………… 60
4.8 參數修正測試（四）…………………………… 63
4.9 參數修正測試（五）…………………………… 66
4.10 參數修正測試（六）……………………………… 69

第五章 分析與探討 ……………………………………… 72
5.1 整體參數控制的狀況 …………………………… 72
5.2 模擬與現狀的分析 ………………………………. 73

第六章 結論 …………………………………………… 83

參考文獻 ……………………………………………… 85

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