臺灣博碩士論文加值系統

本論文探討當線性非時變的連續廣義系統模型包含範數有界的結構化不確定量時，如何設計控制器使得閉迴路系統為可容許的或 D-可容許的，而且其轉移矩陣的 H-infinite 範數小於規範值 r 的問題。論文中將使用常數狀態迴授控制以及動態輸出迴授控制的設計方法。對於所提出的設計規格，如強韌 H-infinite 範數與根叢集限制等，均求得以線性矩陣不等式所表示的充分條件。最後，也將舉兩個數值模擬的實例來加以說明。

The paper investigates problems of designing controllers to linear time-invariant continuous descriptor systems subject to norm-bounded structured uncertainty so that the closed-loop systems are admissible or D-admissible with their transfer matrices having H-infinite norm bounded by a prescribed value. The constant state feedback and the dynamic output feedback designs are addressed. In both design methods, sufficient LMI conditions are derived to guarantee achievement of the desired specifications, such as robust H-infinite norm and pole-clustering constraints. Finally, two numerical examples are shown for the illustration.

目錄
摘要 i
符號表 iii
第一章緒論
1-1 節 文獻回顧與研究動機 1
1-2 節 論文綱要 2
第二章不確定連續廣義系統之強韌 H-infinite 與根叢集限制分析
2-1 節 基本性質 3
2-2 節 強韌 H-infinite 分析 5
2-3 節 根叢集限制分析 9
第三章狀態迴授控制器設計
3-1 節 問題描述 14
3-2 節 不確定廣義系統之強韌 H-infinite 設計 15
3-3 節 不確定廣義系統根叢集限制之強韌 H-infinite 設計 16
第四章動態輸出迴授控制器設計
4-1 節 問題描述 18
4-2 節 不確定廣義系統之強韌 H-infinite 設計 19
4-3 節 不確定廣義系統根叢集限制之強韌 H-infinite 設計 24
第五章數值模擬
5-1 節 狀態迴授控制器設計 29
5-2 節 動態輸出迴授控制器設計 34
第六章結論 42參考文獻 43
索引 46

參考文獻[1]N. H. McClamroch, “Singular systems of differential equations as dynamic models for constrained robot systems,” Proc. IEEE Conf. on Robotics and Automation, 1986.[2]L. Dai, Singular Control Systems- Lecture notes in control and information sciences, vol. 118, Springer-Verlag, Berlin, 1989.[3]J. D. Aplevich, Implicit Linear Systems- Lecture notes in control and information sciences, vol. 152, Springer-Verlag, Berlin, 1991.[4]F. L. Lewis, “A tutorial on the geometric analysis of linear time-invariant implicit systems”, Automatica, vol. 28, no. 1, pp. 119-137, 1992.[5]C.J. Wang, “Controllability and observability of linear time-varying singular systems”, Automat. Control, vol. 44, pp. 1901-1905, 1999.[6]K. Takaba, “Linear quadratic optimal control for linear implicit system”, Proc. of the 38th CDC, pp. 4074-4079, 1999.[7]V. L. Syrmos, P. Misra, and R. Aripirala, “On the discrete generalized Lyapunov equation”, Automatica, vol. 31, pp. 297-301, 1995.[8]L. Zhang, J. Lam, and Q. Zhang, “New Lyapunov and Riccati equations for discrete-time descriptor systems”, Proc. of the 14th IFAC, vol. D, pp. 7-11, 1999.[9]K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice- Hall, 1996.[10]C. H. Fang, L. Lee, and F. R. Chang, “Robust control analysis and design for discrete-time singular systems”, Automatica, vol. 30, p.p. 1741-1750, 1994.[11]C. H. Fang and L. Lee, “Robustness of regional pole placement for uncertain continuous-time implicit systems,” IEEE Trans. Automat. Control, vol. 39, pp. 2303-2307, 1994.[12]C. Lin, J. Wang, D. Wang, and C.B. Soh, “Robustness of uncertain descriptor systems”, Syst. Control Letters, vol. 31, pp. 129-138, 1997.[13]C. H. Fang, Robust Stability of Generalized State-Space Systems, Ph.D. dissertation, National Sun Yat-Sen University, Taiwan, Republic of China, 1997.[14]I., Masubuchi, U. Kamitane, A. Ohara, and N. Suda, “The H-infinite control for descriptor systems: a matrix inequalities approach”, Automatica, vol. 33, no. 4, pp. 669-673, 1997.[15]H. S. Wang, C. F. Yung and F. R. Chang, “Bounded real lemma and H-infinite Control for descriptor systems”, IEE Proc.-Control Theory Appl., vol. 145, no. 3, pp. 316-322, 1998.[16]G. Zames, “Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses,” IEEE Trans. Automat. Control, vol. 26, pp. 301-320, 1981.[17]J. C. Huang, H. S. Wang and F. R. Chang, “Robust H-infinite control for uncertain linear time—invariant descriptor systems”, IEE Proc.-Control Theory Appl., vol. 33, no. 6, pp. 648-654, 2000.[18]Y. Nesterov and A. Nemirovsky, Interior-Point Polynomial Algorithms in Convex Programming, SIAM studies in applied mathematics, Philadelphia, 1994.[19]P. Gahinet, A. Nemirovsky, A. J. Laub, and M. Chilali, LMI Control Toolbox User’s Guide, The MathWorks Inc., Mass., 1995.[20]L. El Ghaoui, R. Nikoukhah, and F. Delebecque, “LMITOOL: a package for LMI optimization,” Proc. of 34th CDC, pp. 3096-3101, 1994.[21]F. L. Lewis, “A survey of linear singular systems”, J. Circuit, Syst., Signal Processing, vol. 5, pp. 3-36, 1986.[22]M. Chilali and P. Gahinet, “H-infinite design with pole placement constraints: an LMI approach,” IEEE Trans. Automat. Control, vol. 41, no. 3, pp. 358-367.[23]K. M. Zhou and J. C. Doyle, Essentials of Robust Control, Prentice-Hall Inc., New Jersey, 1998.[24]R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.[25]K. L. Hsiung and L. Lee, “Lyapunov inequality and bounded real lemma for discrete-time descriptor systems,” IEE Proc.-Control Theory Appl., vol. 146, no. 4, pp. 327-331, 1999.[26]K. L. Hsiung and L. Lee, “Pole-clustering characterization via LMI for descriptor systems,” Proc. of the 36th CDC, pp. 1313-1314, 1997.