臺灣博碩士論文加值系統

本篇論文，擬針對一類時間延遲控制系統提出一項新型性能指標。此外，吾人將針對時間延遲控制系統，利用時域分析法，設計一些簡單且容易硬體製作的回授型控制器，促使整個閉迴路控制系統之暫態響應、穩態響應、時域響應及頻域響應的性能指標均可分別達到某特定範圍內。最後，吾人將提出多個數值範例並輔以電腦模擬來說明本篇論文之主要定理。

In this thesis, we represent a new performance indexes for a class of time-lag control systems. According to the requirement of control system, we can utilize time-domain method to design a simple feedback compensation as follows:
(1)We propose simple compensation designs of under which the frequency-domain specifications and time-domain specifications of close-loop time-lag control system can be kept within prescribed limit.
(2)We propose a simple compensation designs of some specifications under which the transient response and steady-state response of close-loop time-lag control systems can be kept within prescribed limit.
Finally, several numerical examples and computer simulations are provided to illustrate the use of the main results.

目錄
致謝I
中文摘要II
英文摘要III
目IV
圖表目錄VII
第一章 前言1
1.1 簡介1
1.2 符號定義2
第二章 定義與定理3
2.1 控制系統及其基本架構3
2.2 時間響應分析5
2.2.1 時間響應的基本觀念5
2.2.2 一階系統的暫態響應6
2.2.3 二階系統的暫態響應8
2.2.4 二階系統的暫態響應的性能指標13
2.2.5 穩態響應：穩態誤差 17
2.3 頻率響應分析24
2.3.1 頻率響應的基本觀念24
2.3.2 二階系統的暫態響應的性能指標27
2.3.3 引數定理32
2.3.4 奈氏穩定準則33
2.4 Lyapunov 的穩定性35
2.4.1 定義Lyapunov穩定35
2.4.2 Lyapunov穩定性判斷36
2.4.3 證明Lyapunov穩定37
第三章 主要定理39
3.1 系統描述(I)39
3.1.1 主要定理(I)40
3.1.2 範例說明(I)43
3.2 系統描述(II)45
3.2.1 主要定理(II)46
3.2.2 範例說明(II)49
3.3 系統描述(Ⅲ)52
3.3.1 主要定理(Ⅲ)52
3.3.2 範例說明(Ⅲ)56
第四章 結論與未來研究方向59
4.1 結論59
4.2 未來研究方向59
參考文獻60
圖表目錄
圖2-1 開路控制系統的基本方塊示意圖3
圖2-2 閉路控制系統的基本方塊示意圖4
圖2-3 標準一階系統方塊圖6
圖2-4 標準一階系統的單位步階響應圖6
圖2-5 標準一階系統的單位脈衝響應圖7
圖2-6 一階系統的比例回授控制7
圖2-7 標準二階系統方塊圖8
圖2-8 標準二階系統的單位步階響應圖10
圖2-9 標準二階系統的單位脈衝響應圖11
圖2-10 標準二階低阻尼系統的暫態響應性能指標13
圖2-11 二階系統16
圖2-12 單位回授控制系統17
圖2-13(a) 控制系統23
圖2-13(b) 帶輸入濾波器的控制系統23
圖2-14 一階系統26
圖2-15(a) 標準二階系統的頻率響應大小圖28
圖2-15(b) 標準二階系統的頻率響應相位圖28
圖2-16 共振峰值與共振頻率關係圖29
圖2-17 頻帶寬度與頻率關係圖30
圖2-18 對 與 對 的曲線圖31
圖2-19 BW對 的曲線圖31
圖2-20 經由 映射至 平面的 32
圖2-21 奈氏曲線34
圖2-22 極座標圖34
圖2-23 Lyapunov 穩定圖36
圖2-24 Lyapunov 漸進穩定圖37
圖3-1 DREA物理波動示意圖39
圖3-2 系統(3.1)之回授控制器設計41
圖3-2.1 系統(3.16)之單位步階響應圖（原始響應圖）43
圖3-2.2 系統(3.16)之單位步階響應圖（加入補償器後的圖形）45
圖3-3 系統(3.20)之回授控制器設計47
圖3-3.1 系統(3.34)之單位步階響應圖（原始響應圖）49
圖3-3.2系統(3.34)之單位步階響應圖（加入補償器後的圖形）51
圖3-4 系統(3.38)之回授控制器設計53
圖3-4.1 系統(3.54)之單位步階響應圖（原始響應圖） 56
圖3-4.2 系統(3.54)之單位步階響應圖（加入補償器後的圖形）58
表2-1 標準測試訊號的數學描述5
表2-2 穩態誤差綜合摘要21

中文部分：
[1]李宜達，“控制系統設計與模擬，”全華科技圖書，台北市，2004。
英文部分：
[1]Chen, J. D., Lien, C. H., Fan, K.K., and Cheng, J. S.,“Delay-dependent stability criterion for neutral time-delay systems.”Electron. Lett 2000; 36, pp.1897-1898.
[2]Chen, W. D., Yang, S. H., Wan, Z. L., Lin, Y.S., Sun, Y. J.,“Generalized error criterion and specifications improvement of time-delay systems.”The first Symposium Applications of Information, Management and Communication Technology, Jhongli, Taiwan 2006; pp. E-4-39-E-4-46.
[3] Chen, W. D., Wan, Z. L., Tsai, C. H., and Sun, Y. J.,“A novel oscillator design for a class of time-lag systems.”2007 The Third National Workshop on Internet and Communication Technology, Taipei, Taiwan 2007; pp. 165-168.
[4]Chuang, C. F., Yang, S. H., and Sun, Y. J.,“Guaranteed performance improvements for a class of retarded control systems.”Symposium on Applications of Information, Management and Communication Technology, Kaohsiung, Taiwan 2006; pp. 11-17.
[5]Chuang, C. F., Yang, S. H., and Sun, Y. J.,“Specifications improvement and easily-implemented compensation design for a class of time-lag control systems.” Proceedings of the 2006 Cross-Strait Manufacturing Technology Conference, RC-237, Kaohsiung, Taiwan 2006; pp. 1-5.
[6]Elmali, H., Renzulli, M., and Olgac, N., “Experimental comparison of delayed resonator and PD controlled vibration absorbers using electromagnetic actuators.” ASME Journal of Dynamic Systems,Measurement and Control 2000; 122, pp. 514-520.
[7]Fite, K. B., Speich, J. E., and Goldfarb, M.,“Transparency and stability robustness in two-channel bilateral telemanipulation.”ASME Journal of Dynamic Systems, Measurement, and Control 2001; 123, pp. 400-407.
[8]Fridman, E., Fridman, L., and Shustin, E.,“Steady modes in relay control systems with time delay and periodic disturbances.”ASME Journal of Dynamic Systems, Measurement, and Control 2000; 122, pp. 732-737.
[9]Franklin, G.. F., Powell, J. D. and Emani-Naeini, A., “Feedback Control of Dynamic System,” Addison-Wesley, Massachusetts, 1994.
[10]Hsiao, F. H., Pan, S. T., and Teng, C. C.,“Robust controller design for discrete uncertain multiple time-delay systems.”ASME Journal of Dynamic Systems, Measurement and Control 1997; 119, pp. 223-225.
[11]Insperger, T., and Stepan, G.,“Semi-discretization method for delayed systems.” International Journal for numerical methods in engineering 2002; 55, pp.503-518.
[12]Jalili, N., and Esmailzadeh, E.,“Optimum active vehicle suspensions with actuator time delay.”ASME Journal of Dynamic Systems, Measurement and Control 2001; 123, pp. 54-61.
[13]Kapila, V., Tzes, A. and Yan, Q.,“Closed-loop input shaping for flexible structures using time-delay control.”ASME Journal of Dynamic systems, Measurement and Control 2000; 122, pp. 454-460.
[14]Kuo, B. C., “Automatic control systems,” Seventh Edition, Prentice-Hall, Englewood Cliffs, Englewood Cliffs, New Jersey, 1995.
[15]Lien C. H.,“Further results on delay-dependent robust stability of uncertain fuzzy systems with time-varying delay.”Chaos, Solitons & Fractals 2006; 28, pp. 422-427.
[16]Liu J.,“Global exponential stability of Cohen–Grossberg neural networks with time-varying delays.”Chaos, Solitons & Fractals 2005; 26, pp. 935-945.
[17]Liu Y, Wang Z, and Liu X.,“Global asymptotic stability of generalized bi-directional associative memory networks with discrete and distributed delays.”Chaos, Solitons & Fractals 2006; 28, pp. 793-803.
[18]Olgac, N., and Sipahi, R.,“An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems.”IEEE Trans. Automat. Contr. 2002; 47, No. 5, pp. 793-797.
[19]Ogata, K., “Modern control engineering,” Second Edition, Prentice-Hall, Englewood Cliffs, Englewood Cliffs, New Jersey, 1990.
[20]Pan, S. T., Hsiao, F. H., and Teng, C. C.,“Stability bound of multiple time delay singularly perturbed systems.”Electron. Lett. 1996; 32, pp. 1327-1328.
[21]Park, J. H.,“Robust nonfragile decentralized controller design for uncertain large-scale interconnected systems with time-delays.”ASME Journal of Dynamic Systems, Measurement, and Control 2002; 124, pp. 332-336.
[22]Sun, Y. J.,“Exponential stability for continuous-time singular systems with multiple time delays.”ASME Journal of Dynamic Systems, Measurement, and Control 2003; 125, pp. 262-264.
[23]Sun, Y. J., and Hsieh, J. G.,“Exponential tracking control for a class of uncertain systems with time-varying arguments and deadzone nonlinearities.”ASME Journal of Dynamic Systems, Measurement, and Control 1997; 119, pp. 825-830.
[24]Sun, Y. J., Hsieh, J. G., and Yang, H. C.,“On the stability of uncertain systems with multiple time-varying delays.”IEEE Trans. Automat. Contr. 1997; 42, No. 1, pp. 101-105.
[25]Sun, Y. J., and Hsieh, J. G.,“On α-stability criteria of nonlinear systems with multiple time-delays.”Journal of the Franklin Institute, Engineering and Applied Mathematics 1998; 335B, No. 4, pp. 695-705.
[26]Sun, Y. J.,“Control design of exact specifications for time-delay control systems.” Proceeding of 28st National Conference on Theoretical and Applied Mechanics, Taipei, Taiwan 2004; pp. 2471-2476.
[27]Sun, Y. J., 2004,“Simple oscillator design for time-delay control systems.”Proceeding of 21st National Conference on Mechanical Engineering, Vol. B2, Kaohsiung, Taiwan, pp. 1973-1976.
[28]Sun Y. J., Lien C. H., and Hsieh J. G.., Comments on “D-stability of continuous time-delay systems subjected to a class of highly structured perturbations.” IEEE Transactions on Automatic Control 1998; 43, pp. 689-689.
[29]Sun Y. J.,“Global stabilizability of uncertain systems with time-varying delays via dynamic observer-based output feedback.”Linear Algebra and its Applications 2002; 353, pp. 91-105.
[30]Sun, Y. J.,“Simple identification of delay argument for a class of time-delay control systems.”Proceeding of 21st National Conference on Mechanical Engineering, Vol. B1, Kaohsiung, Taiwan 2004; pp. 1389-1392.
[31]Slotine, J. J. E., and Li, W., “Applied nonlinear control,” Prentice-Hall, New York, 1991.
[32]Tsai, C. H., Chen, W. D., Wan, Z. L. and Sun, Y. J., “Research on the Efficiency Improvement of Time-delay Systems.” NCDC2007 The 3rd National Conference on Digital Contents, pp. 18-23, 2007.
[33]Yan, J. J., “Robust stability analysis of uncertain time delay systems with delay-dependence.” Electronic Letters, 37, No. 2, pp.125-137, 2001.
[34]Yang, S. H., Ke, T. C., Chuang, C. F., and Sun, Y. J.,“Specifications improvement of time-lag control systems.”IEEE ICSS2005 International Conference on Systems & Signals, Kaohsiung, Taiwan 2004; pp. 962-967.
[35]Yang, S. H., Chuang, C. F., Ke, T. C., Chin-Jun Chen, and Sun, Y. J.,“Control design of exact specifications for a class of retarded control systems.”The 12th Military Academy Symposium on Fundamental Science, Kaohsiung, Taiwan 2005; pp. C156-C160.
[36]Yan, J. J., Tsai, J. S. H., and Sheen, I. E.,“Stability analysis of large-scale time-delay systems via evolutionary programming algorithm.”ASME Journal of Dynamic Systems, Measurement, and Control 2001; 123, pp. 293-296.

[37]Vidyasagar, M.,“Nonlinear systems analysis,”Prentice-Hall, Englewood Cliffs, 1993.