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研究生:盧信豪
研究生(外文):Shin-Hao Lu
論文名稱:一類具有邊界輸入之分佈參數系統的強健穩定性分析及控制器設計
論文名稱(外文):Boundary Controller Design and Robust Stability Analysis of a Class of Distributed Parameter Systems
指導教授:馮蟻剛
指導教授(外文):I-Kong Fong
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:電機工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:90
中文關鍵詞:分布參數系統邊界控制強健穩定性分析邊界控制器
外文關鍵詞:Distributed Parameter SystemsBoundary ControlRobust Stability AnalysisBoundary Controller
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對於一類具有邊界條件的分佈參數系統,本論文討論其強健穩定性分析及邊界控制器設計問題。本論文說明如何處理分佈參數系統的邊界值問題,及如何應用此處理方法解決分佈參數系統的強健穩定性分析及控制器設計問題。
關於分佈參數系統之強健穩定性分析問題,本論文中考慮正規式分佈參數系統,其擾動模式為未知擾動參數乘以已知擾動算子。擾動算子可出現於系統方程式本體中,亦可出現於邊界條件之算式上。但擾動算子須屬一類相對於系統算子為相對有界之算子集。對此類問題,首先將出現於邊界算式中之擾動算子,透過邊界轉換之方式轉換至系統方程式中,再進行定理之推導,而可求得一簡單之上限。若系統在不受擾動時為穩定,則若未知參數之範數小於此一簡單上限時,可保證系統在受到擾動時仍為穩定。
在邊界控制器之設計上,首先考慮定義在一維及二維平面上,具有線性邊界條件之線性偏微分方程式系統,並討論此類偏微分方程式系統具有邊界轉換之特性,即其屬於一類稱為一般邊界輸入系統之分佈參數系統的條件。屬於一般邊界輸入系統之偏微分方程式系統可透過邊界轉換之方式,將邊界算子整合進入系統算式中。
對於這樣具邊界轉換特性的系統,本論文提出兩種邊界回饋控制器之設計方式,第一種為頻譜一致性位移之邊界控制器設計,即設計一邊界控制器將原系統之頻譜一致性的移往所需求之方向,而使系統成為穩定。另一控制器設計方式則希望尋求以觀測器為基礎之次佳式有限維邊界控制器。這種控制器之設計方式是利用近似於有限維最佳控制器設計之方式,設計出有限維之邊界控制器,但此邊界控制器在全系統上並非最佳控制器,故而稱之為次佳式有限維邊界控制器。此有限維邊界控制器仍能使系統為穩定,且其性能表現的差異亦是可估計的。
This dissertation presents the study of robust stability analysis and boundary feedback controller design problems for a class of distributed parameter systems. The basis of the study is a theory of how to integrate nonzero boundary conditions into the system equation of the distributed parameter systems in discussion.
For the robust stability analysis problems, we consider the nominally normal distributed parameter systems which contain known perturbation operators multiplied by uncertain parameters. The perturbation operators may appear in the system equation itself as well as in the boundary conditions, but are assumed to have the relative boundedness property. The boundary perturbations are first integrated into the system equation, and then by using the Lyapunov stability criterion, simple bounds on uncertain parameters are derived to ensure the stability of the perturbed systems.
For the boundary controller design problems, we first consider a class of distributed parameter systems defined on the one-dimensional domains. The systems are described by linear partial differential equations with mixed boundary conditions. Then we consider distributed parameter systems defined on two-dimensional domains with the Neumann boundary conditions. All systems are assumed to be the so-called general boundary input systems. For such systems, the boundary operators may be integrated into the system equation in certain interpolation spaces, and new state-space descriptions without boundary operators may be established.
Based on the state-space descriptions without boundary operators, we propose two methods for the boundary feedback controller design. The first method is called the spectrum shift boundary controller design, which produces controllers that shift part of the spectrum of the distributed parameter systems to the desired direction. The second method is called the sub-optimal finite-dimensional observer-based boundary controller design. This method produces finite-dimensional controllers based on the finite-dimensional linear quadratic optimal control theory. Although the finite-dimensional controllers are only sub-optimal for the distributed parameter systems, an estimation for the performance degradation from that of the ideal case is derived for the comparison purpose.
1. Introduction
1.1 Motivation and Background
1.2 Analysis and Design Methodology
1.3 Organication of this Dissertation
2. Robust Stability Analysis
2.1 Introduction
2.2 System Description
2.3 Stability Robustness with Zero Boundary Conditions
2.4 Stability Robustness with Boundary Perturbation
2.5 Examples
3. General Boundary Input Systems
3.1 Introduction
3.2 Systems Defined on One-Dimensional Domain
3.2.1 Plant Formulation
3.2.2 Boundary Input Transformation
3.3 System Defined on Two-Dimensional Domain
3.3.1 Plant Formulation and Normalization
3.3.2 Boundary Input Transformation
4. Spectrum Shift Boundary Controller Design
4.1 Introduction
4.2 Spectrum Shift Controller Design for Boundary Control- The One-Dimensional Case
4.2.1 Spectrum Shift
4.2.2 Example
4.3 Spectrum Shift Controller Design for Boundary Control- The Two- Dimensional Case
4.3.1 Spectrum Shift
4.3.2 Example
5. Sub-Optimal Finite-Dimensional Oberver-Based Boundary Controller Design
5.1 Introduction
5.2 Observer-Based Finite-Dimensional Controler
5.3 Sub-Optimal Controller Design
5.4 Example
6 Conclusions and Future Work
6.1 Conclusions
6.2 Future Work
Appendix
A. Semigroup Theory for Partial Differential Equations
A.1 Introduction
A.2 Strongly Continuous Semigroup and Infinitesimal Generator
A.3 The Abstract Cauchy Problem
\bibitem{Ahmed} Ahmed, N. U., and P. Li, ''Invariance of Asymptotic Stability of Perturbed Linear Systems on Hilbert Space,'''' {\it J. Optim. Theory App.}, vol. 68, no. 1, pp. 75-93, 1991.
\bibitem{Amann} Amann, H., ''Parabolic Evolution Equations and Nonlinear Boundary Conditions,'''' {\it J. Differ. Equations}, vol. 72, pp. 201-269, 1988.
\bibitem{Anderson} Anderson, B. D. O., and J. B. Moore, {\it Optimal Control: Linear Quadratic Methods}, Prentice-Hall, Englewood Cliffs, NJ, 1990.
\bibitem{Barmish} Barmish, B. R., {\it New Tools for Robustness of Linear Systems}, Macmillan Publishing Company, New York, NY, 1994.
\bibitem{Bensoussan} Bensoussan, A., G. D. Prato, M. C. Delfour, and S. K. Mitter, {\it Representation and Control of Infinite Dimensional Systems}, Volume I, Birkh\"{a}user, Boston, MA, 1992.
\bibitem{Bernstein} Bernstein, D. S., and D. C. Hyland, ''The Optimal Projection Equation for Finite Dimensional Fixed-order Dynamic Compensation of Infinite Dimensional Systems,'''' {\it SIAM J. Contr. and Optim.}, vol. 24, no. 1, pp. 122-151, 1986.
\bibitem{Birkhoff} Birkhoff, G. and G.-C. Rota, {\it Ordinary Differential Equations}, John Wiley {\&} Sons, Inc., New York, NY, 1989.
\bibitem{Brudnyi} Brudnyi, Y. A., and N. Y. Krugljak, {\it Interpolation Functions and Interpolation Spaces}, Elsevier Science Publishers, Amsterdam, Holland, 1991.
\bibitem{Conway} Conway, J. B., {\it A Course in Functional Analysis}, Springer-Verlag, New York, NY,1990.
\bibitem{Curtain84} Curtain, R. F., ''Finite Dimensional Compensators for Parabolic Distributed Systems with Unbounded Control and Observation,'''' {\it SIAM J. Contr. and Optim.}, vol. 22, no. 2, pp. 255-276, 1984.
\bibitem{Curtain86} Curtain, R. F. and D. Salamon, ''Finite Dimensional Compensators for Infinite Dimensional Systems with Unbounded Input Operators,'''' {\it SIAM J. Contr. and Optim.}, vol. 24, no. 4, pp. 797-816, 1986.
\bibitem{Curtain93} Curtain, R. F., ''A Comparison of Finite-Dimensional Controller Design for Distributed Parameter Systems,'''' {\it Control --- Theory and Advanced Technology}, vol. 9, no. 3, pp. 609-628, 1993.
\bibitem{Curtain} Curtain, R. F., and H. Zwart, {\it An Introduction to Infinite-Dimensional Linear System Theory}, Springer-Verlag, New York, NY, 1995.
\bibitem{Datko} Datko, R., ''Extending a Theorem of A. M. Liapunov to Hilbert space,'''' {\it J. Math. Anal. Appl.}, vol. 32, pp. 610-616, 1970.
\bibitem{Doyle} Doyle, J. C., ''Analysis of Feedback Systems with Structured Uncertainties,'''' {\it Proc. IEE}, vol. 129, Part D, pp. 242-250, 1982.
\bibitem{Fattorini} Fattorini, H. O. ''Boundary Control Systems,'''' {\it SIAM J. Contr.}, vol. 6, pp. 349-385, 1968.
\bibitem{Glashoff} Galshoff, K., and N. Wech, ''Boundary Control of Parabolic Differential Equations in Arbitrary Dimensions: Supremum-Norm,'''' {\it SIAM J. Contr. and Optim.}, vol. 14, no. 4, pp. 662-681, 1976.
\bibitem{Gahinet} Gahinet, P., M. Sorine, A. J. Laub, and G. Kenney, ''Stability Margins and Lyapunov Equations for Linear Operators in Hilbert Space,'''' {\it Proc. 29th IEEE Conference on Decision and Control}, Honolulu, Hawaii, pp. 2638-2639, 1990.
\bibitem{Gohberg} Gohberg, I., S. Goldberg, and M. A. Kaashoek, {\it Classes of Linear Operators Vol. I}, Birkh\"{a}user, Boston, MA, 1990.
\bibitem{Hille} Hille, E., and R. S. Philips, {\it Functional Analysis and Semi-groups}, American Mathematical Society Colloquium Publications, vol. 31, 1957.
\bibitem{Hinrichsen} Hinrichsen, D., and A. J. Pritchard, ''Robust Stability of Linear Evolution Operators on Banach Spaces,'''' {\it SIAM J. Contr. and Optim.}, vol. 32, no. 6, pp. 1503-1541, 1994.
\bibitem{Ho} Ho, L. F., and D. L. Russell, ''Admissible Input Elements for Systems in Hilbert Space and a Carleson Measure Criterion,'''' {\it SIAM J. Contr. and Optim.} vol. 21, no. 4, pp. 614-640, 1983.
\bibitem{Hinata} Hinata, H., ''Distributed Input Systems Equivalent to General Boundary Input Systems with Bounded Outputs,'''' {\it Proc. of American Contr. Conf.}, San Diego, California, pp. 2227-2231, 1999.
\bibitem{Inaba} Inaba, H., and H. Hinata, ''A Mathematical Model for Boundary Input Systems,'''' {\it Proc. of the 32nd IEEE Conference on Decision and Control}, San Antonio, Texas, pp. 1854-1859, 1993.
\bibitem{Kato} Kato, T., {\it Perturbation Theory of Linear Operators}, Springer-Verlag, New York, NY, 1966.
\bibitem{Kobayashi} Kobayashi, T. ''Spectrum Assignability of Parabolic Distributed Parameter Systems,'''' {\it Int. J. System Sci.}, vol. 20, pp. 1779-1785, 1989.
\bibitem{Kozlov} Kozlov, D. R., ''Existence of Quadratic Lyapunov Functionals for Equations with Unbounded Operator in Hilbert Space,'''' {\it Siberian Mathematical Journal}, vol. 37, no. 2, pp. 268-275, 1996.
\bibitem{Lasiecka} Lasiecka, I., ''Unified Theory for Abstract Parabolic Boundary Problems --- A Semigroup Approach,'''' {\it Appl. Math. Optim.}, vol. 6, pp. 287-333, 1980.
\bibitem{Lion} Lion, J. L., and E. Magenes, {\it Non-Homogeneous Boundary Value Problems and Applications, Volume I}, Springer-Verlag, New York, NY, 1972.
\bibitem{Lu98} Lu, S.-H., and I-K. Fong, ''Stability Radius of Linear Distributed Parameter Systems with Directional Perturbation via Lyapunov Approach,'''' {\it Proceedings of the 1998 R.O.C. Automatic Control Conference}, R.O.C., pp. 239-244, 1998.
\bibitem{Lu} Lu, S.-H., and I-K. Fong, ''Stability Radius of Linear Normal Distributed Parameter Systems with Multiple Directional Perturbations,'''' {\it Proc. 37th IEEE Conference on Decision and Control}, Tampa, Florida, pp.819-820, 1998.
\bibitem{Lu00} Lu, S.-H., and I-K. Fong, ''Stability Robustness of Linear Normal Distributed Parameter Systems,'''' {\it Systems \& Control Letters}, vol. 41, pp. 317-323, 2000.
\bibitem{Lu01} Lu, S.-H., and I-K. Fong, ''Spectrum Assignment for Linear Parabolic Distributed Parameter Systems via Boundary Feedback Control,'''' {\it Preprints of the 1st IFAC Symposium on System Structure and Control}, Prague, Czech Republic, 2001.
\bibitem{Lu02} Lu, S.-H., and I-K. Fong, ''Boundary Feedback Spectrum Shift for Distributed Parameter Systems on a Planar Domain,'''' submitted for publication in the {\it J. Systems and Control Engineering}, {\it Proc. of the Institution of Mechanical Engineers}, Part I, 2001.
\bibitem{Lu03} Lu, S.-H., and I-K. Fong, ''Sub-Optimal Finite Dimensional Observer-Based Boundary Controller Design for Distributed Parameter Systems on Planar Domain,'''' submitted for publication in the {\it J. Chinese Inst. Eng.}, 2002.
\bibitem{Pazy} Pazy, A., ''On the Applicability of Lyapunov''s Theorem in Hilbert Space,'''' {\it SIAM J. Math. Anal.}, vol. 3, no. 2, pp. 291-294, 1972.
\bibitem{Pazy83} Pazy, A., {\it Semigroups of Linear Operators and Applications to Partial Differential Equations}, Springer-Verlag, New York, NY, 1983.
\bibitem{Pritchard} Pritchard, A. J., and S. Townley, ''Robustness of Linear Systems,'''' {\it J. Differ. Equations}, vol. 77, pp. 254-286, 1989.
\bibitem{Renardy} Renardy, M., and R. C. Rogers, {\it An Introduction to Partial Differential Equations}, Springer-Verlag, New York, NY, 1993.
\bibitem{Sakawa} Sakawa, Y., ''Feedback Stabilization of Linear Diffusion Systems,'''' {\it SIAM J. Contr. and Optim.}, vol. 21, no. 5, pp. 667-676, 1983.
\bibitem{Sakawa84} Sakawa, Y., ''Feedback Control of Second Order Evolution Equations with Damping,'''' {\it SIAM J. Contr. and Optim.}, vol. 22, no. 3, pp. 343-361, 1984.
\bibitem{Schmid} Schmid, E. J. P. G., and N. Wech, ''On the Boundary Behavior of Solutions to Elliptic and Parabolic Equations- with Applications to Boundary Control for Parabolic Equations,'''' {\it SIAM J. Contr. and Optim.}, vol. 16, no. 4, pp. 593-598, 1978.
\bibitem{Schumacher} Schumacher, J. M., ''A Direct Approach to Compensator Design for Distributed Parameter Systems,'''' {\it SIAM J. Contr. and Optim.}, vol. 21, no. 6, pp. 823-836, 1983.
\bibitem{Sun} Sun, S.-H., ''On Spectrum Distribution of Completely Controllable Linear Systems,'''' translated by L.-F. Ho, {\it SIAM J. Contr. and Optim.}, vol. 19, pp. 730-743, 1981.
\bibitem{Triebel} Triebel, H., {\it Interpolation Theory, Function Spaces, Differential Operators}, North-Holland Publishing Company, Amsterdam, Holland, 1978.
\bibitem{Tseng} Tseng, C.-L., I-K. Fong, and J.-H. Su, ''Analysis and Applications of Robust Nonsingularity Problem Using the Structured Singular Value,'''' {\it IEEE Trans. Automat. Contr.}, vol. 39, no. 10, pp. 2118-2122, 1994.
\bibitem{Walker} Walker, J. A., {\it Dynamic Systems and Evolution Equations Theory and Applications}, Plenum Press, New York, NY, 1980.
\bibitem{Yosida} Yosida, K., {\it Functional Analysis}, Springer-Verlag, New York, NY, 1966.
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