二階向量微分系統的穩定性分析與控制

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：81

、訪客IP：3.138.125.197

姓名

黃文彥(Wen-Yan Huang) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

二階向量微分系統的穩定性分析與控制
(Analysis of Stability and Stabilization for Second-Order Vector Differential Systems)

相關論文

★ 小型化 GSM/GPRS 行動通訊模組之研究	★ 語者辨識之研究
★ 應用投影法作受擾動奇異系統之強健性分析	★ 利用支撐向量機模型改善對立假設特徵函數之語者確認研究
★ 結合高斯混合超級向量與微分核函數之語者確認研究	★ 敏捷移動粒子群最佳化方法
★ 改良式粒子群方法之無失真影像預測編碼應用	★ 粒子群演算法應用於語者模型訓練與調適之研究
★ 粒子群演算法之語者確認系統	★ 改良式梅爾倒頻譜係數混合多種語音特徵之研究
★ 利用語者特定背景模型之語者確認系統	★ 智慧型遠端監控系統
★ 正向系統輸出回授之穩定度分析與控制器設計	★ 混合式區間搜索粒子群演算法
★ 基於深度神經網路的手勢辨識研究	★ 人體姿勢矯正項鍊配載影像辨識自動校準及手機接收警告系統

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

本論文中，主要是研究有奇異矩陣領導的二階向量線性微分系統的指數穩定分析與控制，本論文用歸納範數(induced norm)、矩陣測度(matrix measure)和一些不等式的觀念，推導出了一個新的充份指數穩定條件，並且舉例說明來證實提出的定理比一些文獻的結果更不具保守性。我們以定理一的穩定條件和最佳化方法對此系統設計控制器，使系統從不穩定變穩定。
系統有適當的相位邊限(phase margin)以及增益邊限(gain margin)的話，將會使系統有良好的強健性，但對於多輸入多輸出(MIMO) 系統要使得整個系統達到所要求的規格將會是非常複雜而困難的，於是本論文就以相位邊限的規格要求（增益邊限規格可以類推適用），利用Gershgorin定理設計比例-微分控制器(Proportional-Derivative Controller)、比例-積分控制器(Proportional-Integral Controller)、以及相位領先或落後補償器(Phase Lead or Lag Compensator)。

摘要(英)

This thesis is concerned with exponential stability analysis and design of linear systems represented by the second-order vector differential equations with singular leading coefficient matrices. A new sufficient condition for exponential stability is derived. By illustrative examples, it is shown that the proposed criterion is less conservative as compared with some results in the literature. Then, we use the developed criterion and an optimization method to design controllers to make the considered systems stable.
In control theorems, the gain margin and the phase margin are important robustness specifications for the design of practical control systems. This thesis also considers the design of time-invariant systems with the specified phase margin. The Gershgorin theorem is used to design a proportional-derivative (PD) controller, or a proportional-integral (PI) controller, or a phase lead compensator, or a lag compensator to achieve the required phase margin. Examples are also given.

關鍵字(中)

★ 二階向量微分方程式
★ 指數穩定

關鍵字(英)

★ second-order vector differential equation
★ exponential stability

論文目次

List of Figures...........................................................................................................................III
List of Tables..............................................................................................................................V
Chapter 1 Introduction.............................................................................................................1
1-1 Background and the Motivation....................................................................................1
1-2 Organization of this Thesis............................................................................................3
Chapter 2 Fundamental Concept..............................................................................................4
2-1 Induced Norms...............................................................................................................4
2-2 Matrix Measures............................................................................................................6
2-3 Gain Margin and Phase Margin.....................................................................................8
2-3-1 Gain Margin.............................................................................................................8
2-3-2 Phase Margin..........................................................................................................11
2-4 Gershgorin Theorem....................................................................................................13
Chapter 3 Stability Analysis and Illustrative Examples.........................................................16
3-1 Stability Analysis.........................................................................................................16
3-2 Illustrative Examples...................................................................................................22
Chapter 4 Design of Controllers............................................................................................31
4-1 Time-domain Design...................................................................................................31
4-2 Frequency-domain Design...........................................................................................37
4-2-1 PD Controller.........................................................................................................38
4-2-2 PI Controller...........................................................................................................48
4-2-3 Phase Lead or Lag Compensator............................................................................55
Chapter 5 Conclusions...........................................................................................................63
References.................................................................................................................................64

參考文獻

[1] Y. Fujisaki, M. Ikeda and K. Miki, “Robust stabilization of large space structures via displacement feedback,” IEEE Trans. Auto. Contr., vol. 46, pp. 1993-1996, 2001.
[2] M. Meisami-Azad, J. Mohammadpour and K. M. Grigoriadis, “An upper bound approach for control of collocated structural systems,” American Control Conference, July 11–13, New York City, USA, pp. 4631-4636, 2007.
[3] H. Tasso and G. N. Throumoulopoulos, “On Lyapunov stability of nonautonomous mechanical systems,” Phys. Lett. A, vol. 271, pp. 413–418, 2000.
[4] H. Tasso, “On Lyapunov stability of dissipative mechanical systems,” Phys. Lett. A, vol. 257, pp.309-311, 1999.
[5] S. G. Nersesov and W. M. Haddad, “On the stability and control of nonlinear dynamical systems via vector Lyapunov functions,” IEEE Trans. Auto. Contr., vol. 51, pp. 203–215, 2006.
[6] J. Sun, Q. G. Wang and Q. C. Zhong, “A less conservative stability test for second-order linear time-varying vector differential equations,” Int. J. Contr., vol. 80, pp. 523-526, 2007.
[7] K. Inoue and T. Kato, “A stability condition for a time-varying system represented by a couple of a second- and a first-order differential equations”, 43rd IEEE Conference on Decision and Control, Dec. 14–17, Atlantis, Paradise Island, Bahamas, pp. 2934-2935, 2004.
[8] K. Inoue, S. Yamamoto, T. Ushio, and T. Hikihara, “Torque-based control of whirling motion in a rotating electric machine under mechanical resonance,” IEEE Trans. Automat. Contr., vol. 11, pp. 335-344, 2003.
[9] E. E. Zajac, “The Kelvin-Tait-Chetaev theorem and extensions,” Journal of Astronautical Sciences, vol. 11, pp. 46-49, 1964.
[10] M. I. Gil’, “Stability of linear systems governed by second order vector differential equations,” Int. J. Contr., vol. 78, pp. 534–536, 2005.
[11] K. Inoue, S. Yamamoto, T. Ushio, and T. Hikihara, “Elimination of jump phenomena in a flexible rotor system via torque control,” Control of Oscillations and Chaos, 2000. Proceedings. 2000 2nd International Conference, vol. 1, pp. 58-61, 2000.
[12] K. Nonami and T. Ito, “ synthesis of flexible rotor-magnetic bearing systems,” IEEE Trans. Contr. Systems Technology, vol. 4, pp. 503-512, 1996.
[13] Y. L. Yu, L. Daletskii and M. G. Krein, “Stability of solutions of differential equations in Banah space,” Translations of Mathematical Monographs. Providence, RI: Amer. Math. Soc., vol. 43, 1974.
[14] E. A. Barbashin, Introduction to the Theory of Stability. Groningen, The Netherlands: Wolters-Noordhoff, 1970.
[15] A. Zevin and M. Pinsky, “Exponential stability and solution bounds for systems with bounded nonlinearities,” IEEE Trans. Automat. Contr., vol. 48, pp. 1779-1804, 2003.
[16] B. C. Kuo, Automatic Control Systems. Addison-Wesley, 8th ed., 2002.
[17] G. F. Franklin, J. D. Powell, and A. E. Naeini, “Feedback control of dynamic systems”, Addison-Wesley, 3rd ed., 1994.
[18] H. W. Fung, Q. G. Wang, and T. H. Lee, “PI tuning in Terms of Gain and Phase Margins,” Automatica, vol. 34, No. 9, pp. 1145-1149, 1998.
[19] Y. J. Huang and Y. J. Wang, “Robust PID controller design for non-minimum phase time delay systems”, ISA Transactions., vol. 40, no. 1, pp. 31-39, 2001.
[20] Yang Hong and Oliver W. W. Yang, “Self-Tuning Multiloop PI Rate Controller for an MIMO AQM Router With Interval Gain Margin Assignment”, IEEE, pp. 401-405, 2005.
[21] Yang Hong and Oliver W. W. Yang, “Adaptive Multiloop PI Rate-Based Controller Design for a MIMO IP Router Based on Phase Margin”, Proceedings of IEEE Globecom, pp. 1070-1074, 2005.
[22] Robert W. Newcomb, Nonlinear System Analysis. 新月書局,台北市,民國七十六年
[23] Y. Fang and T. G. Kincaid, “Stability analysis of dynamical neural networks,” IEEE Trans. Neural Networks, vol. 7, pp. 996–1006, 1996.
[24] Ljiljana Cvetkovic, Vladimir Kostic and Richard S. Varga, “A new Gersgorin-type eigenvalue inclusion set”, Electronic Transactions on Numerical Analysis, vol.18, pp. 73-80, 2004.
[25] 林俊良，控制系統數學，修訂版，全華書局，台北市，民國九十一年。
[26] P. Lancaster, Theory of Matrices. New York: Academic Press, 1969.
[27] L. Guilbeau, “The History of the Solution of the Cubic Equation”, Mathematics News Letter, vol. 5, pp. 8-12, 1930.
[28] Pradeep B. Deshpande, Multivariable Process Control. Instrument Society of America, Research Triangle Park, NC, 1989.
[29] W.K. Ho, Y. Hong, A. Hansson, H. Hjalmarsson and J.W. Deng, “Relay Auto-Tuning of PID Controllers using Iterative Feedback Tuning” Automatica, 39, (1), January 2003, pp.149-157.
[30] J. Bao, J. F. Forbes, and P. J. McLellan, “Robust Multiloop PID Controller Design: A Successive Semidefinite Programming Approach,” Ind. Eng. Chem. Res., vol. 38, pp. 3407–3413, 1999.

指導教授

莊堯棠(Yau-Tarng Juang)

審核日期

2008-6-23

推文