在實際控制系統中，為確保系統面對外部干擾或模型不確定性時仍具備穩定性，往往需設計具備抗外擾能力之強健控制器。然而，傳統強健控制設計方法常伴隨高度的數學複雜性，導致其設計流程缺乏直觀性與解析性。為提升控制器設計透明度與系統性能掌握度，本研究著重於探討控制器結構與閉迴路特性之間的對應關係，進一步釐清動態權重參數如何影響系統極點配置與控制性能。本文以特殊架構為分析基礎，並結合靈敏度函數與動態權重設計概念，探討誤差通道與控制輸出通道之加權方式對閉迴路系統的影響。相較於常見的狀態回授型架構，外擾前饋型架構能更明確地呈現權重設計對控制器極零點與閉迴路極點的影響，亦便於建構對應之解析解。

In practical control systems, the design robust controllers with disturbance rejection capabilities is essential to ensure system stability in the presence of external disturbances or model uncertainties. However, conventional robust control design methods are often characterized by substantial mathematical complexity, which renders the design process less intuitive and hinders interpretability. To address these challenges, this study seeks to improve the transparency of controller design and to provide a clearer understanding between system performance and controller structure. Specifically, it explores the correspondence between controller architectures and closed-loop characteristics, with a particular focus on clarifying the influence of dynamic weighting parameters on pole placement and control performance. This thesis is based on the analysis of specialized control architectures and incorporates the theoretical frameworks of sensitivity functions and dynamic weighting strategies. It systematically investigates how introduction of weighting in the error and control output channels shapes the behavior of the closed-loop system. In comparison with the widely used state feedback (SF) architecture, the disturbance feedforward (DF) structure can more explicitly reveal the relationship between controller’s poles and zeros and the effects of weight design. This property not only enhances interpretability but also facilitates the derivation of analytical solutions, thereby offering valuable insights into the underlying mechanisms of robust controller synthesis.

[1] K. Glover and J. C. Doyle, “State-space formulae for all stabilizing controllers that satisfy an H∞-norm bound,” Systems & Control Letters, vol. 11, no. 3, pp. 167–172, 1988.
[2] M.-C. Tsai, “A chain-scattering description for generalized control configuration,” Int. Journal of Control, 1992
[3] H. Kimura, “Chain-scattering representation, J-lossless factorization and H∞ control,” J. Math. Systems, Estimation & Control, vol. 5, no. 2, 1995
[4] M.-C. Tsai and F.-Y. Yang, "Chain-scattering description approach to characterize stabilizing controllers and optimal H2 solution", IET Control Theory Appl., vol. 5, pp. 1022-1032, 2011.
[5] M.-C. Tsai and D.-W. Gu, Robust and Optimal Control: A Two-port Framework Approach, Advances in Industrial Control, Springer, 2014.
[6] T. Iwasaki, “Robust H∞ control and spectral factorization,” Automatica, vol. 31, no. 10, 1995
[7]史忠科，鲁棒控制理論，國防工業出版社，中國北京， 2003。
[8]S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, Chichester, UK: Wiley, 2005.
[9] M. Green and D. J. N. Limebeer, Linear Robust Control, London, UK: Prentice Hall, 1995.
[10] H. Kimura, "Chain-Scattering Approach to H∞-Control", 1998
[11] M.-C. Tsai, Y.-Q. Zhou, B.-C. Tsai and C. U. Ubadigha, "Solution Analysis of H∞ /H2 Control Formulations Based on Chain-Scattering Description Approach," 26th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Cambridge, UK, 2024.
[12] 張易軒，「簡易之結構化H₂/H∞控制器求解法與實用設計工具箱」， 碩士論文，國立成功大學機械工程學系，2025。
[13] B.-C. Tsai, C. U. Ubadigha and M.-C. Tsai, "An Optimal H2 Observer Controller Design Formulation and Solution Based on Chain-Scattering Description Approach," 2023 International Automatic Control Conference (CACS), Penghu, Taiwan, 2023, pp. 1-6, doi: 10.1109/CACS60074.2023.10326204.
[14] 周妍綺，「基於雙端網路架構之馬達強健控制器設計工具包開發」， 碩士論文，國立成功大學機械工程學系，2024。
[15] 蔡博丞，「基於雙端網路架構之馬達強健觀測器設計工具包開發」， 碩士論文，國立成功大學機械工程學系，2024。
[16] F. L. Lewis, Optimal Control, Wiley, 1986.
[17] B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods, Prentice-Hall, 1990.
[18] K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, 1996.
[19] JP Hespanha, Lecture Notes on LQR/LQG Controller Design, University of Zielona Góra, 2005.
[20] J. B. Burl, Linear Optimal Control: H₂ and H∞ Methods, Reading, MA: Addison-Wesley, 1998.
[21] E.J. Adam, J.L. Marchetti, “Designing and tuning robust feedforward controllers,” Computers & Chemical Engineering, Volume 28, Issue 9, Pages 1899-1911, 2004, ISSN 0098-1354,
[22] J. van Ekeren, Robust Control of High-Precision Motion Systems, Ph.D. dissertation, Dept. Mech. Eng., Eindhoven Univ. of Tech., Eindhoven, The Netherlands, 2015.
[23] 簡伸漢，「應用於電動滑板車之輪轂式游標永磁馬達設計與實現」，碩士論文，國立成功大學電機工程學系研究所，2021。