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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張家歐(Chia-Ou Chang) | |
| dc.contributor.author | Yu-Han Wang | en |
| dc.contributor.author | 王郁涵 | zh_TW |
| dc.date.accessioned | 2021-07-11T14:36:00Z | - |
| dc.date.available | 2022-09-04 | |
| dc.date.copyright | 2017-09-04 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-08-18 | |
| dc.identifier.citation | [1] David M. Rozell, 2009, 'The Hemispherical Resonator Gyro: From Wineglass to the Planets,' Proc. 19th AAS/AIAA Space Flight Mechanics Meeting, pp.1157-1178.
[2] A.D. Meyer and D.M. Rozelle, 2012, “Milli-HRG inertial navigation system,” Position Location and Navigation Symposium (PLANS), IEEE/ION, 23-26 April 2012, pp.24-29. [3] 謝發華。2001。壓電驅動半圓球殼振動陀螺儀原理與誤差分析。博士論文。台北：台灣大學應用力學研究所。 [4] Rayleigh, L, 1881, “On the Infinitesimal Bending of Surfaces of Revolution,” Proc. Math. Soc., London, Vol.13, pp. 4-16. [5] Love, A. E. H., 1888, “On the Small Free Vibrations and Deformation on Thin Elastic Shells,” Phil. Transactions Roy. Soc., A179, pp. 491-546. [6] Washizu, K., 1980, Variational Methods in Elasticity and Plasticit, Pergamon Press Ltd., 3rd. [7] Niordson, F. I., 1985, Shell Theory, North Holland, Amsterdam.. [8] Bryan, G. H., 1890, “On the Beats in the Vibrations of a Revolving Cylinder or Bell,” Proc. Cambridge Philos. Soc., Vol. VII, Nov. 24, pp. 101-111. [9] Quick, W. H, 1964, “Theory of the Vibrating String as an Angular Motion Sensor,” Transactions ASME, J. Appl. Mech., pp. 523-534. [10] Friedland, Bernard and Maurice F. Hutton,1978, “Theory and Error Analysis of Vibrating-Member Gyroscope,” IEEE Transactions on Automatic Control, Vol. AC-2345, No. 4, pp. 545-556. [11] Lynch, D. D., 1995 ,“Vibratory gyro analysis by the method of averaging,” IN proceedings of the 2nd International Conference on Gyroscopic Technology and Navigation, Sant Petersburg, Russia, May. 24-25, pp. 26-34. [12] Chang, C. O., Hwang , J. J., and Chou, C. S., 1996, “Modal Procession of a Rotating Hemispherical Shell,” International Journal of Solids and Structures, Vol. 33, No. 19, pp. 2739-2757. [13] Chou, C. S., Chang, C. O., and Huang, J. J., 1996, “The Vibration of a Rotating Hemispherical Shell Excited by Electrostatic Field,” International Journal of Applied Electromagnetics in Materials, Vol. 7, No. 2, pp. 21-42. [14] Chou, C. S., and Chang, C. O., 1997, “Modal Precession of a Hemispherical Shell Gyro Excited by Electrostatic Field,” Japanese Journal of Applied Physics, Vol. 36, No. 11, pp. 7073- 7081. [15] Chou, C. S., Chang, C. O., and Huang, J. J., 1999, “Vibration of a Hemispherical Shell Gyro Excited by an Electrostatic Field,” International Journal of Applied Electromagnetics in Materials, Vol. 10, No. 4, pp. 425-49. [16] 黃正吉。1993。半圓球殼諧振陀螺儀的動力分析。博士論文。台北：台灣大學應用力學研究所。 [17] 謝發華。2001。壓電驅動半圓球殼振動陀螺儀原理與誤差分析。博士論文。台北：台灣大學應用力學研究所。 [18] P. W. Loveday and C. A. Rogers, 2002, “The Influence of Control System Design on the Performance of Vibratory Gyroscopes,” Journal of Sound and Vibration, 255(3), 417-432. [19] Gallacher, B. J., 2012, “Principles of a Micro-Rate Integrating Ring Gyroscope,” IEEE Transactions om Aerospace and Electronnic Systems, Vol. 48, No. 1. [20] 陳劭詮，2014，諧振半球殼缺陷分析與控制，碩士論文，台灣大學應用力學研究所。 [21] 王文呈，2014，諧振半球殼質量補償模擬與分析，碩士論文，台灣大學應用力學研究所。 [22] 林思嘉，2015，諧振半球殼之質量瑕疵分析與修正，碩士論文，台灣大學應用力學研究所。 [23] 翁銘宗，2015，諧振半球殼陀螺儀的設計與質量瑕疵的修正，碩士論文，台灣大學應用力學研究所。 [24] 簡孟俞，2016，石英諧振半球殼之電極分析與值量瑕疵修正，碩士論文，台灣大學應用力學研究所。 [25] 曾子恒，2016，瑕疵石英諧振半球殼之有限元素法分析與修正，碩士論文，台灣大學應用力學研究所。 [26] Kemin Zbou, J. C. Doyle, and K. Glover, 1996 , “Robust Optimal Control,” Prentice-Hall, pp. 22-23. [27] Jungshin Lee *, Sung Wook Yun and Jaewook Rhim, 2016, “Design and Verification of a Digital Controller for a 2-Piece Hemispherical Resonator Gyroscope,” Journal of Sensors. [28] Bernard Friedland, 1986, “Control System Design,” Chapter five, pp.190-218. [29] 盧中仁，2016，振動學講義，台大機械系。 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/77850 | - |
| dc.description.abstract | 半圓球殼諧振陀螺儀會因為石英毛胚的密度非均勻特性以及製造過程產生幾何的誤差而使陀螺儀呈現瑕疵狀態，而瑕疵會造成兩振動模態自然頻率分歧的問題，因此，本研究提出一控制方法來消除瑕疵對半圓球殼諧振陀螺儀的影響。
本研究將廣義座標下之含質量-勁度瑕疵和阻尼瑕疵的運動方程式轉換到橢圓座標中，並透過微擾法中的平均法來近似方程式，然後透過數值解來觀察瑕疵對橢圓變數的影響。了解瑕疵對橢圓變數的影響後，本研究隨即透過強迫振盪的技術找出質量-勁度主軸角度位置，並可使用雷射消融技術以及藉由對電極施加電壓進行補償來消除質量-勁度瑕疵的頻率分歧。 欲達到同時控制阻尼瑕疵和殘餘的質量-勁度瑕疵對角速率量測的效應之目的，本研究將透過設計與分析控制器來控制橢圓變數至期望值，最後將控制力從橢圓座標轉回至廣義座標中以控制兩廣義座標主軸上的振幅，而因為本研究是利用球殼上鍍的金屬電極和驅動座內側電極間因電位差所產生的靜電場來驅動，所以須將廣義座標中的控制力轉成電壓值，然後透過適當地配置電極對的方式，分配電壓來控制瑕疵對半圓球殼諧振陀螺儀造成的效應。 | zh_TW |
| dc.description.abstract | The non-uniformity in density of the quartz blanks and the geometrical error due to manufacturing cause the hemispherical resonator gyroscope (HRG) to be imperfect. This imperfection will result in the frequency-splitting problem. Therefore, the purpose of the study is to propose a control method to eliminate the influence of the imperfection on the performance of the HRG.
In this study, we transform the equations of motion concluding mass-stiffness and damping imperfections from general coordinates into elliptical coordinates, and then use the method of averaged perturbation theory to approximate these equations. After that, we observe the influence of imperfection on the elliptical variables through the numerical solution. Afterwards, we find the angles of mass-stiffness principal axes by the technique of forced vibration, so that we can use the technique of Laser-ablation as well as the compensation by applied voltage to the electrodes to eliminate the frequency-splitting of the mass-stiffness imperfection. For the purpose of simultaneously controlling the effect of both the damping and the residual mass-stiffness imperfections on the angular-rate measurement of HRG, this study will design and analyze the controller to control elliptical variables to those desired values. Finally, we transform the control force from elliptical coordinates backward to the generalized coordinates to control the amplitudes of the two principal axes in generalized coordinates. However, the shell is driven by the electrostatic field generated by the potential difference between the metal electrode on the hemispherical shell and the inner electrode of the driving seat, so the control force in the generalized coordinates must be converted into voltage. Therefore, we adjust the voltage to control the imperfection by proper layout of the electrode pairs. | en |
| dc.description.provenance | Made available in DSpace on 2021-07-11T14:36:00Z (GMT). No. of bitstreams: 1 ntu-106-R04543003-1.pdf: 6210269 bytes, checksum: 43579fe56b51b59f80b8f0f47519c677 (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 誌謝 i
中文摘要 ii Abstract iii 目錄 v 圖目錄 viii 表目錄 xvii 第1章 緒論 1 1.1 前言 1 1.2 文獻回顧 3 1.3 論文架構 5 第2章 無瑕疵半圓球殼陀螺儀感測原理 7 2.1 半圓球殼諧振陀螺儀結構模型 7 2.2 雷利近似解 9 2.3 無瑕疵半圓球殼諧振陀螺儀感測方程式 14 2.4 橢圓軌跡 15 2.4.1 能量與角動量 16 2.4.2 橢圓傾角 19 2.4.3 軌道角度 20 2.5 角速度感測 21 2.5.1 橢圓軌跡變化率 22 2.5.2 平均法 26 第3章 含瑕疵半圓球殼陀螺儀運動方程式與誤差分析 29 3.1 含瑕疵半圓球殼陀螺儀運動方程式 29 3.1.1 質量-勁度瑕疵 29 3.1.2 阻尼瑕疵 34 3.1.3 質量-勁度、阻尼瑕疵 37 3.2 含瑕疵半圓球殼陀螺儀的誤差分析 38 3.2.1 無質量-勁度、阻尼瑕疵 40 3.2.2 只有質量-勁度瑕疵 41 3.2.3 只有阻尼瑕疵 52 3.2.4 有質量-勁度、阻尼瑕疵 53 第4章 強迫振盪找質量-勁度主軸角度位置 57 4.1 橢圓軌跡變化率 57 4.2 平均法 61 4.3 質量-勁度主軸角度位置分析 63 4.3.1 自由振盪 63 4.3.2 強迫振盪 73 第5章 控制器的設計與分析 85 5.1 橢圓座標中含控制力運動方程式 85 5.1.1 無瑕疵半圓球殼諧振陀螺儀 85 5.1.2 含瑕疵半圓球殼諧振陀螺儀 90 5.2 控制器設計與分析 96 5.2.1 控制定律設計 96 5.2.2 無瑕疵和含瑕疵半圓球殼陀螺儀的控制比較 98 5.2.3 增益值對控制時間的影響 101 5.2.4 角速度對增益值的影響 102 5.2.5 瑕疵量大小對增益值的影響 105 5.2.6 Whole-angle 111 5.2.7 輸出信號處理 120 第6章 電場驅動力 123 6.1 電場驅動力 123 6.2 瑕疵修正之控制力與電壓轉換 126 6.2.1 角速度 126 6.2.2 角速度 142 6.3 找質量-勁度主軸角度位置之外力與電壓轉換 153 6.3.1 外力角度位置 153 6.3.2 外力角度位置 156 6.3.3 外力角度位置 159 第7章 結論與未來展望 163 7.1 研究結論 163 7.2 未來展望 165 參考文獻 166 附錄A 橢圓軌跡一般解 169 附錄B 橢圓長軸a與橢圓短軸b和能量E與角動量H之間的關係 170 附錄C 雅可比(Jacobian)計算過程 172 附錄D 雅可比(Jacobian)的反矩陣 174 附錄E 彈簧阻尼系統的一般解[29] 178 作者簡歷 179 | |
| dc.language.iso | zh-TW | |
| dc.subject | 控制器 | zh_TW |
| dc.subject | 半圓球殼 | zh_TW |
| dc.subject | 頻率分歧 | zh_TW |
| dc.subject | 橢圓座標 | zh_TW |
| dc.subject | 平均法 | zh_TW |
| dc.subject | Hemispherical shell | en |
| dc.subject | controller | en |
| dc.subject | the method of average | en |
| dc.subject | elliptical coordinates | en |
| dc.subject | frequency-splitting | en |
| dc.title | 在廣義橢圓座標下分析石英半球殼振子的瑕疵與控制器 | zh_TW |
| dc.title | Analysis on the Imperfection and Controller of a Fused Quartz Hemispherical Shell Resonator in terms of Generalized Elliptical Coordinates | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 謝發華(Fa-Hua Hsieh) | |
| dc.contributor.oralexamcommittee | 周傳心,張簡文添,陳柏志 | |
| dc.subject.keyword | 半圓球殼,頻率分歧,橢圓座標,平均法,控制器, | zh_TW |
| dc.subject.keyword | Hemispherical shell,frequency-splitting,elliptical coordinates,the method of average,controller, | en |
| dc.relation.page | 179 | |
| dc.identifier.doi | 10.6342/NTU201703956 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2017-08-19 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| 顯示於系所單位： | 應用力學研究所 | |
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