本文中的機械結構瑕疵包含：因製造過程造成的機械結構尺寸的誤差（不確定性）、因結構設計造成的陀螺儀動態的非理想性。本文中的感測介面與感測電路瑕疵包含：因光罩擺放所造成的誤差、運算放大器的電壓偏移量、因導線產生的寄生電容。本文的做法是將機械結構、感測介面的瑕疵與感測電路非理想效應所造成的影響整理成為未知的系統參數包括:系統質量、剛性係數、阻尼係數、訊號比例常
數(scale factor)、訊號偏壓飄移量(signal drifts)。
本文主要分為兩部分，一是沒有考慮感測電路的情況下，設計一狀態觀察器，並於單軸（驅動軸）輸入兩頻率的訊號或是兩頻率以上的訊號，以訊號處理的方式（軟體）來估測出陀螺儀動態與系統未知參數及待量測的角速度。因此，不需要兩軸控制輸入，不需要事先知道陀螺儀質量塊的重量。預計可大幅降低微機電陀螺儀的製造成本與技術
門檻，進而使得微機電陀螺儀可廣泛應用於各式電子產品。二是考慮感測電路且具有電路瑕疵的情況下，設計一狀態觀察器，於兩軸給予控制輸入，以訊號處理的方式來估測出陀螺儀動態與系統未知參數（包含訊號比例常數、訊號偏壓飄移量）及待量測的角速度，並補償其為理想陀螺儀動態系統，進而無須透過積分運算，直接估測待測物的角度。

The mechanical structure imperfections and circuit imperfections greatly affect the performance of a gyroscope system. Normally this problem is lessened by physically tooling the hardware structures, for example, expensive fabrication facilities, post-fabrication processes, and complicated circuit designs. The disadvantages of doing so are costly. Recently, more and more research proposed using control methods (software approaches) to compensate the effect resulting from those imperfections and obtain correct angular rates because they can be very cost effective. However, those approaches often require a gyroscope system equipped with dual-axis control inputs and
the mass of the proof mass must be known beforehand. The existing commercial gyroscopes only equips with single axis control input. Thus, those existing compensation methods can not apply.

摘要............................................... i
ABSTRACT ......................................... ii
誌謝 ............................................ iii
目錄 ............................................. iv
圖目錄 ........................................... vi
表目錄 .......................................... vii
第一章 緒論 ....................................... 1
1.1 研究動機 ...................................... 3
1.2 文獻回顧 ...................................... 4
1.3 預期貢獻 ...................................... 5
1.4 論文架構 ...................................... 6
第二章 微機電陀螺儀系統簡介 ....................... 7
2.1 微機電陀螺儀系統簡介 .......................... 7
2.2 微機電陀螺儀系統模型 .......................... 9
2.3 感測電路模型 ................................. 11
2.3.1 理想感測介面搭配感測電路 ................... 14
2.3.2 具瑕疵感測介面搭配感測電路 ................. 17
2.4 模型建構 ..................................... 19
第三章 單軸控制輸入微機電振動式陀螺儀系統 ........ 22
3.1 觀察器設計 ................................... 22
3.2 控制輸入 ..................................... 27
3.3 數值模擬結果 ................................. 28
3.3.1 角速度為定值 ............................... 28
3.3.2 角速度隨時間變動 ........................... 29
3.3.3 觀察性矩陣奇異值 ........................... 30
3.4 討論 ......................................... 31
第四章 雙軸控制輸入微機電振動式陀螺儀系統 ........ 33
4.1 代數變換 ..................................... 34
4.2 觀察器設計 ................................... 36
4.3 控制輸入 ..................................... 40
4.4 數值模擬結果 ................................. 42
4.4.1 比例常數與飄移量皆為固定值 ................. 42
4.4.2 比例常數為固定值、飄移量隨時間變化(0.1Hz) .. 43
4.4.3 比例常數與飄移量皆隨時間變化(0.1Hz) ........ 44
4.4.4 比例常數與飄移量皆為定值，初始值為零 ....... 45
4.4.5 比例常數與飄移量皆為定值，初始值為零，兩軸輸入頻率不同 .. 46
4.4.6 觀察性矩陣奇異值 ........................... 47
4.5 討論 ......................................... 48
第五章 結論與未來計畫 ............................ 51
5.1 結論 ......................................... 51
5.2 未來計畫 ..................................... 52
參考文獻 ......................................... 53
附錄一 數值模擬用參數 ............................ 55

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