臺灣博碩士論文加值系統

本論文探討多輸入多輸出控制系統來分析設計。在第一部份，首先運用增益相位裕度測試器，結合穩定方程式法和參數空間法，分析多輸入多輸出系統的增益裕度與相位裕度關係。並說明四種多輸入多輸出系統之增益裕度與相位裕度的物理意義；當僅知系統的狀態方程式，而不知系統方塊圖時，雖然可以用穩定方程式法來分析系統的穩定性，但在分析增益裕度與相位裕度時卻會發生不唯一的情形。因此對以狀態方程式表示的系統加上一些條件限制，使由狀態方程式轉換至系統方塊圖能夠吻合。如此便可順利設計分析增益裕度和相位裕度。在第二部份，利用序列迴路的設計方法，將混合H與參數空間法之互動式控制系統設計方法應用於多輸入多輸出系統的設計，此舉解除原文獻中所提方法僅能用於單輸入單輸出系統設計的限制。以本文所提方法設計之控制器其階數較應用H-最佳控制法所得控制器之階數為低。論文最後以兩個強健設計的範例驗證此設計方法。

In first part of this thesis, we use the gain-phase margin tester technique combine with the stability-equations method and the parameter plane technique to analyze gain-margins and phase-margins of MIMO system. Control systems expressed both by block diagrams and by state equations are considered. The physical meanings of gain-margins and phase-margins of MIMO systems are presented first, and then the effects due to time-delays are studied. In the second part, by applying the sequential loop closing approach, the mixed H-parameter space method is extended to MIMO systems. A diagonal stabilizing controller is designed by the proposed approach, with the order lower than those obtained by the H-optimal control method. The effectiveness of the proposed design methods are illustrated by examples.

書名頁
論文指導教授推薦函
論文口試委員審定書
授權書
中文摘要
Abstract
誌謝
List of Contents
List of Tables
List of Figures
Notations
Chapter 1 Introduction
I. Background and Motivation
II. Organization of this thesisChapter 2 The Concept of Gain-Phase Margin Tester
I. Introduction
II. Basic concept and approach
2.1 The gain margin and phase margin
2.2 The gain margin and phase margin of MIMO control system
Chapter 3 Gain Margin and Phase Margin of MIMO Systems with Time-delays
I. Introduction
II. GMs and PMs of MIMO Systems with Time-Delays
III. Conclusions
Chapter 4 Gain-Margins and Phase-Margins of MIMO Time-Delay Systems Expressed by Time Domain Models
I. Introduction
II. Construction of Proper Block Diagrams from Time Domain Models
III. Analysis of Gain-Margins and Phase-Margins of a Missile
Auto-Pilot System Expressed by Time-Domain Model
IV. Conclusions
Chapter 5 Robust Design of MIMO systems by the Mixed H- Parameter Space Method for Robust Performance: A Sequential Loop Closing Approach
I. Introduction
II. The Background of Decoupling Design
5.1 Sequential Loop Closing
5.2 Mixed H-infinity Parameter Space Method
III. Design Technique
IV. IMPLEMENTATION OF THE METHOD
Numerical Design Example
Large Space Structure Design Example
V. Conclusions
Chapter 6 Conclusions and Suggestions for Future Research
I. Conclusions
II. Suggestions for Future Research
Appendices
Appendix IManipulation of the AOLTF
Appendix IIMixed H-Parameter Space Design Method
II.1Expression of the sensitivity constrains
II.2Representation of the sensitivity constrains in the parameter space
II.3The stability condition
References

REFERENCES
[1] C. H. Chang and K. W. Han, “Gain-margin and phase-margin analysis of a nuclear reactor control system with multiple transport lags,” IEEE Trans. Nuclear Science, Vol.36, No.4, pp.1418-1424, 1989.
[2] C. S. Tao, C. H. Chang and K. W. Han, “Gain-margins and phase-margins for multivariable controls systems with adjustable parameters,” Int. J. Contr., Vol.54, No.2, pp.435-452, 1991.
[3] G. H. Lii, C. H. Chang and K. W. Han, “Analysis of robust control systems using stability-equations,” J. Control Systems and Technology, R.O.C., Vol.1, No.1, pp.83-89, 1993.
[4] C. H. Chang, “The physical meanings of gain margins and phase margins of mimo systems,” research report, E.E. Dept. Chung-Cheng Institute of Technology, 1989.
[5] D. D. Šiljak, Nonlinear Systems: The Parameter Analysis and Design. New York: Wiley, 1969.
[6] C. H. Chang and K. W. Han, “Gain-margins and phase-margins for control systems with adjustable parameters,” AIAA J. Guidance, Vol. 13, No.3, pp.404-408, 1990.
[7] A. T. Shenton and Z. Shafiei, “Relative stability for control systems with adjustable parameters,” AIAA J. Guidance Control and Dynamics, Vol. 17, No. 2, pp.304-310, 1994.
[8] G. L. Chao, J. W. Perng and K. W. Han, “Robust stability analysis of time-delay systems using parameter-plane and parameter-space methods,” J. Franklin Institute, Vol. 335B, No.7, pp. 1249-1262, 1998.
[9] I. Postlethwaite, J. M. Edmunds and G. J. MacFarlane, “Principal gains and principal phases in the analysis of linear multivariable feedback systems,” IEEE Trans. Automat. Contr., Vol. AC-26, No. 1, pp.32-46, 1981.
[10] G. M. Schoen and H. P. Geering, “Stability condition for a delay differential system,” Int. J. Contr., Vol. 58, No. 1, pp.247-252, 1993.
[11] J. H. Su, “The asymptotic stability of linear autonomous systems with commensurate time delays,” IEEE Trans. Automat. Contr., Vol. 40, No. 6, pp.1114-1117, 1995.
[12] T. N. Lee and S. Dianat, “Stability of time-delay systems,” IEEE Trans. Automat. Contr., Vol. AC-26, No. 4, pp.951-953, 1981.
[13] N. A. Lehtomaki, N. R. Sandell, and Jr. M. Athans, “Robustness results in linear-quadratic gaussian based multivariable control designs,” IEEE Trans. Automat. Contr., Vol. AC-26, No. 1, pp.75-92, 1981.
[14] C. Zhang and M. Fu, “A revisit to the gain and phase-margins of linear quadratic regulators,” IEEE Trans. Automat. Contr., Vol. 41, No. 10, pp.1527-1530, 1996.
[15] 羅基福，含時滯之多輸入多輸出系統的增益邊際和相位邊際分析，元智大學電研所，民國87年。
[16] 楊忠山，強健設計的一些實用方法研究，元智大學電研所，民國87年。
[17] 李錫棋，鋼板滾壓控制系統之控制器設計，元智大學電研所，民國87年。
[18] V. Besson and A. T. Shenton, “Interactive control systems design by a mixed H-parameter space method,” IEEE Trans. Automat. Contr., Vol. 42, No. 7, pp.946-955, 1997.
[19] V. Besson and A. T. Shenton, “An interactive parameter space method for robust performance in mixed sensitivity problems,” IEEE Trans. Automat. Contr., Vol. 44, No. 6, pp.1272-1276, 1999.
[20] I. Egaña and M. García-Sanz, “Quantitative non-diagonal MIMO controller design for uncertain systems,” International Symposium on Quantitative Feedback Theory and Robust Frequency Domain Methods, pp. 187-198, 1999.
[21] J. Kocijan, J. O’Reilly and W. E. Leithead, “An integrated undergraduate teaching laboratory approach to multivariable control,” IEEE Trans. Education, Vol. 40, No.4, pp.266-272, 1997.
[22] J. M. Maciejowski, Multivariable Feedback Design. Great Britain: T. J. Press, Cornwall, 1993.
[23] B. A. Francis, A Course in H Theory. New York: Springer-Verlag, 1987.
[24] J. C. Doyle, B. A. Francis, and A. Tannenbaum, Feedback Control Theory. New York: Macmillan, 1992.
[25] G. Zames and B. A. Francis, “Feedback, minimax sensitivity, and optimal robustness,” IEEE Trans. Automat. Contr., Vol. AC-28, pp.585-600, 1983.
[26] P. A. Iglesias and K. Glover, “State-space approach to discrete-time H control,” Int. J. Contr., Vol. 54, No. 5, pp. 1031-1073, 1991.
[27] T. Chai, K. Mao and X. Qin, “Decoupling design of multivariable generalised predictive control,” IEE Proc.-Control Theory Appl., Vol. 141, No. 3, pp.197-201, 1994.
[28] R. Ortega and A. Herrera, “A Solution to the continuous-time adaptive decoupling problem,” IEEE Trans. Automat. Contr., Vol. 39, No. 8, 1994.
[29] 葉芳柏、楊憲東，後現代控制理論與設計，修訂版。台北狀元出版社，民國81年。
[30] 葉芳柏、楊憲東，線性與非線性H控制理論，初版一刷。台北全華圖書，民國86年。
[31] G. J. Balas, J. C. Doyle, K. Glover, A. Packard, and R. Smith, µ-Analysis and Synthesis Toolbox. Natick, MA: The MathWorks, 1991.
[32] Y. R. Chiang and M. G. Safonov, Robust Control Toolbox. Natick, MA: The MathWorks, 1992.
[33] M. G. Safonov and R. Y. Chiang, “ CACSD using the state-space L theory A design example,” Proc. IEEE Conf. CACSD, Contr., AC-33, No. 5, pp. 477-479, 1988.
[34] Y. S. Hung and B. Pokrud, “An H approach to feedback design with two objective functions,” IEEE Trans. Automat. Contr., Vol. 37, No. 6, pp. 820-824, 1992.
[35] J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H control problems,” IEEE Trans. Automat. Contr., Vol. 34, No. 8, pp. 831-847, 1989.
[36] A. T. Shenton, “Parameter partition of these term control systems,” Dept. Mechanical Eng., Univ. Liverpool, MES/ATS/INT/013/95, Nov. 1995.
[37] W. J. Johnston, Analytical Geometry. London: Clarendon, 1893.