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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 劉進賢(Chein-Shan Liu) | |
| dc.contributor.author | Po-Ying Chen | en |
| dc.contributor.author | 陳柏穎 | zh_TW |
| dc.date.accessioned | 2021-06-16T05:32:38Z | - |
| dc.date.available | 2016-08-21 | |
| dc.date.copyright | 2014-08-21 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-08-13 | |
| dc.identifier.citation | [1] Dabroom, A. M.; Khalil, H. K. (1997): Discrete-time implementation of high-gain observers for numerical differentiation. Int. J. Contr., vol. 72, pp. 1523-1537.
[2] Golembo, B. Z.; Emelyanov, S. V.; Utkin, V. I.; Shubladze, A. M. (1976): Application of piecewise-continuous dynamic systems to filtering problems. Auto. Re-mote Contr., vol. 37, pp. 369-377. [3] Guo, B. Z.; Han, J. Q.; Xi, F. B. (2002): Linear tracking-differentiator and application to online estimation of the frequency of a sinusoidal signal with random noise perturbation. Int. J. Sys. Sci., vol. 33, pp. 351-358. [4] Guo, B. Z.; Zhao, Z. L. (2011a): On convergence of tracking differentiator and application to frequency estimation of sinusoidal signals. Int. J. Contr., vol. 84, pp. 693-701. [5] Guo, B. Z.; Zhao, Z. L. (2011b): On finite-time stable tracking differentiator without Lipschitz continuity of Lyapunov function. Proc. Chinese Control Conference, 2010, pp. 354-358. [6] Han, J. Q.; Wang, W. (1994): Nonlinear tracking-differentiator. J. Sys. Sci. Math. Sci., vol. 14, pp. 177-183 (in Chinese). [7] Ibrir, S. (2004): Linear time-derivative trackers. Automatica, vol. 40, pp. 397-405. [8] Levant, A. (1993): Sliding order and sliding accuracy in sliding mode control. Int. J. Contr., vol. 58, pp. 1247-1263. [9] Levant, A. (1998): Robust exact differentiation via sliding mode technique. Auto-matica, vol. 34, pp. 379-384. [10] Levant, A. (2003): Higher-order sliding modes, differentiation and output-feedback control. Int. J. Contr., vol. 76, pp. 924-941. [11] Levant, A.; Livne, M. (2012): Exact differentiation of signals with unbounded higher derivatives. IEEE Trans. Auto. Contr., vol. 57, pp. 1076-1080. [12] Liu, C.-S. (2013a): A method of Lie-symmetry for solving non-linear dynamical systems. Int. J. Non-Linear Mech., vol. 52, pp. 85-95. [13] Liu, C.-S. (2013b): A state feedback controller used to solve an ill-posed linear system by a iterative algorithm. Commu. Numer. Anal., vol. 2013, Article ID cna00181, 22 pages. [14] Liu, C.-S.; Atluri, S. N. (2009): A fictitious time integration method for the numerical solution of the Fredholm integral equation and for numerical differentiation of noisy data, and its relation to the filter theory. CMES: Computer Modeling in Engineering & Sciences, vol. 41, pp. 243-261. [15] Su, Y. X.; Sun, D.; Duan, B. Y. (2005): Design of an enhanced nonlinear PID controller. Mechatronics, vol. 15, pp. 1005-1024. [16] Su, Y. X.; Zheng, C. H.; Mueller, P. C.; Duan, B. Y. (2006): A simple improved velocity estimation for low-speed regions based on position measurements only. IEEE Trans. Contr. Sys. Tech., vol. 14, pp. 937-942. [17] Tang, Y.; Wu, Y.; Wu, M.; Hu, X.; Shen, L. (2009): Nonlinear tracking-differentiator for velocity determination using carrier phase measurements. IEEE J. Selec. Top. Signal Proce., vol. 3, pp. 716-725. [18] Wang, J.; Zhang, J.; Yan, J. (2010): A new second-order nonlinear tracking differentiator and application, 2010 International Conference on Computer Design and Applications (ICCDA), pp. 1318-1322 [19] Wang, X.; Chen, Z.; Yang, G. (2007): Finite-time-convergent differentiator based on singular perturbation technique. IEEE Trans. Auto. Contr., vol. 52, pp. 1731-1737. [20] Wang, X.; Lin, H. (2011): Design and analysis of a continuous hybrid differentiator. IET Contr. Theo. Appl., vol. 5, pp. 1321-1334. [21] Wang, X.; Lin, H. (2012): Design and frequency analysis of continuous finite-time-convergent differentiator. Aerospa. Tech., vol. 18, pp. 69-78. [22] Wang, X.; Shirinzadeh, B. (2012): Rapid-convergent nonlinear differentiator. Mech. Sys. Sign. Proces., vol. 28, pp. 414-431. [23] Xue, W.; Huang, Y.; Yang, X. (2010): What kinds of system can be used as tracking-differentiator. Proc. Chinese Control Conference, 2010, pp. 6113-6120. [24] 謝馥亘 (2012): 應用特徵時間展開法鑑別非線性工程問題之恢復力，國立台灣海洋大學碩士論文。 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/56518 | - |
| dc.description.abstract | 在土木領域裡，對結構的保護及控制來說，能夠即時地重建施於系統的外力向來是個不可忽視的研究議題。
過去雖有許多重建外力的方案提出，但因運算求解費時，故欲達到「即時」重建的方法仍舊有限。本論文中，將過去已廣泛應用的強健微分器及追蹤微分器，自常微分方程轉換為一微分代數方程組，透過控制力加以調配控制，並利用結合隱格式李群法和牛頓迭代法的新數值方法——李群微分代數方程法進行運算求解，內外迴圈雙重迭代增加穩定性。此方法可利用於設計線上偵測器，意為可在僅有已受噪音干擾的位移訊號資料下，即時重建施於系統的未知外力。隨著線性結構、杜芬方程式、范德波爾方程式及地震力作用下的線性結構等四個數值算例顯示，此方法呈現的效果有相當不錯的精度與效率，且簡單易於使用，未來發展應用的機會極大。 | zh_TW |
| dc.description.abstract | For structure protection and control, it is utmost to immediately detect the external force being imposed on the structure currently in civil engineering. In this thesis, we remodel the famous robust exact differentiator and tracking differentiator into a type of differential algebraic equations (DAEs), and then we solve the resultant DAEs by a Lie-group method, which can be used as an on-line estimator to detect unknown external force by using only a real-time measurement of the structural displacement under random noise in time. The estimated results obtained by the novel methods are quite promising. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T05:32:38Z (GMT). No. of bitstreams: 1 ntu-103-R01521227-1.pdf: 6335657 bytes, checksum: e5831279312fe931c91151b3c290884b (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 口試委員會審定書 i
誌謝 ii 摘要 iii ABSTRACT iv 目錄 v 圖目錄 vii 1第一章 緒論 1 1.1 前言 1 1.2 文獻回顧 2 1.3 論文架構 3 2第二章 數值分析方法 5 2.1 群 5 2.1.1 群的歷史 5 2.1.2 群的定義 6 2.1.3 李群與李代數 6 2.2 數值分析方法 8 2.2.1 微分方程中的 結構 9 2.2.2 隱格式李群 法 11 2.2.3 牛頓法求解非線性代數方程 14 2.2.4 數值計算流程圖 15 3第三章 現有偵測器之改良 16 3.1 方法一 16 3.1.1 強健微分器（Robust Exact Differentiator, RED）之改良 16 3.1.2 LGDAE於強健微分器的解析與應用 18 3.1.3 方法一數值計算流程圖 21 3.2 方法二 22 3.2.1 追蹤微分器（Tracking Differentiator, TD）之改良 22 3.2.2 LGDAE於追蹤微分器的解析與應用 23 3.2.3 方法二數值計算流程圖 26 4第四章 數值算例 27 4.1 算例一 線性結構 27 4.1.1 計算量測位移無噪音影響下之外力 27 4.1.2 計算當量測位移具有噪音影響下之外力 35 4.2 算例二 Duffing Oscillator 47 4.2.1 計算量測位移無噪音影響下之外力 47 4.2.2 計算當量測位移具有噪音影響下之外力 55 4.3 算例三 Van der Pol Oscillator 67 4.3.1 計算量測位移無噪音影響下之外力 67 4.3.2 計算當量測位移具有噪音影響下之外力 75 4.4 算例四 線性結構下地震力重建 87 5第五章 結論與未來展望 98 參考文獻 99 | |
| dc.language.iso | zh-TW | |
| dc.title | 利用李群微分代數方程法即時重建作用於非線性結構之外力 | zh_TW |
| dc.title | A Real-Time Estimation of External Force Exerted on Nonlinear Structure by Using a GL(n,R) Lie-group method | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 張建仁(Jiang-Ren Chang),陳永為(Yung-Wei Chen) | |
| dc.subject.keyword | 李群,反算問題,微分代數方程,偵測器,微分器,重建外力, | zh_TW |
| dc.subject.keyword | Lie-group,differential algebra equation,estimator,differentiator,Inverse problem,Recovery of external force, | en |
| dc.relation.page | 100 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-08-13 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
| 顯示於系所單位： | 土木工程學系 | |
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