動態次結構系統是一種混和測試技術，將一個複雜的受測工程系統拆解成物理原型和數值模擬兩種次結構，進行同步測試，可減少全尺試驗所需的空間與建模成本、適用於測試大型複雜的工程系統。測試中，兩個次結構的輸出需經由傳動系統(致動器)作為媒合界面，但因傳動系統存在著不理想的動態響應，常使得兩個次結構的連接面輸出無法同步、測試失真，因此次結構測試成功關鍵在於，需藉由設計高品質、強健控制器來消除傳動系統造成的不良影響。
本論文將目前次結構測試控制文獻，分類為「幾何基礎」與「動態基礎」控制系統兩種。幾何基礎控制方法最具代表性、具高引用度的就是「適應型順向預測控制器」，以曲線近似、最小平方多項式、及延遲微分方程為設計主要觀念。本論文先提出創新直接補償法以及奇異值分解法，來改善適應型順向預測控制器的控制表現和數值誤差，接著探討及分析適應型順向預測演算法中的最小平方理論，及其動態實踐議題。另一方面，動態基礎控制方法，則以近期提出之線性「數值次結構基礎控制器」為代表，進行控制文獻比較，其利用典型常微分方程式與狀態空間模型，作為控制器設計框架。
藉由一系列理論分析、控制推導、實驗驗證，並以非線性質量彈簧單擺次結構系統為例，本論文證明了適應型順向預測控制器存在著不可避免的預測誤差、實用性隨著訊號波型改變、適應型補償非即時、非連續，因此即使適應型順向預測控制器是高引用文獻，其可控性、穩定性、強健性、實用性，都不及新提出之線性數值次結構基礎控制器；更進一步推論，次結構測試文獻常使用時延致動器模型、延遲補償觀念來設計控制器，其理論根據與工程實用性，實有待更嚴謹的確認。

Dynamically substructured system (DSS) is a hybrid testing technique, which decompose a complex, entire engineering system into numerical and physical substructures. Components are tested via numerical simulation or full-size experiments, and thus the required testing space and costs are reduced. Additional actuator systems, which interface the numerical and physical parts, are required within the physical substructure. A high-quality controller, which is designed to cancel unwanted dynamics introduced by actuators, is important in order to synchronize the numerical and physical outputs and ensure successful tests.

The current DSS control literature is divided into geometry-based and dynamics-based strategies. The highly-citied adaptive forward prediction algorithm is defined as the geometry-based control method, which uses curve fitting, least-squares polynomial, and delay differential equations to tailor the control system. This thesis first improves the controller settling performance and numerical conditions by using new direct-compensation and singular value decomposition methods. Then, the least-squares technique is analyzed in order to discuss the control implementation issues. On the other hand, the numerical-substructure-based state-space linear substructuring controller (N-SSLSC) is selected as the example of dynamics-based method for DSS control comparison, which are designed based on typical ordinary differential equations and state-space model.

From theoretical analysis, controller development, experimental verification, and using a nonlinear mass-spring-pendulum system as an example, the thesis proves that adaptive forward prediction algorithm possesses inevitable prediction error, the feasibility changes with the wave form, and the adaptive compensation is non-real-time, non-continuous. Therefore, even if adaptive forward prediction is a high-citation compensation method, its controllability, stability, robustness, and feasibility are not comparable with the new N-SSLSC. Furthermore, this thesis also points out that, the theoretical background and feasibility of using time delays and delay differential equations to model the actuator dynamics and to design the DSS controller, requires more stringent validation.

[1] F. Aghili, "A Mechatronic Testbed for Revolute-Joint Prototypes of a Manipulator," Robotics, IEEE Transactions on, vol. 22, pp. 1265-1273, 2006.
[2] K. Dressler, Speckert, M., and Bitsch, G., "Virtual durability test rigs for automotive engineering," Vehicle System Dynamics, vol. 47, pp. 387-401, 2009.
[3] A. M. Reinhorn, M. Bruneau, S. Chu, X. Shao, and M. Pitman, "Large scale real time dynamic hybrid testing technique–Shake tables substructure testing," in Proceedings of ASCE Structures Congress, 2003, pp. 457-464.
[4] P. J. Gawthrop, Wallace, M. I., and Wagg, D. J., "Bond-graph based substructuring of dynamical systems," Earthquake Engineering & Structural Dynamics, vol. 34, pp. 687-703, 2005.
[5] D. P. Stoten, and R.A. Hyde, "Adaptive control of dynamically substructured systems: the single-input single-output case," in Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2006, pp. 63-79.
[6] A. Gonzalez-Buelga, Wagg, D. J., and Neild, S. A., "Parametric variation of a coupled pendulum-oscillator system using real-time dynamic substructuring," Structural Control and Health Monitoring, vol. 14, pp. 991-1012, 2007.
[7] A. P. Darby, Williams, M. S., Blakeborough, A., "Stability and Delay Compensation for Real-Time Substructure Testing," Journal of Engineering Mechnics, vol. 128, pp. 1276-1284, 2002.
[8] T. Horiuchi, Inoue, M., Konno, T., and Namita, Y., "Real-time hybrid experimental system with actuator delay compensation and its application to a piping system with energy absorber," Earthquake Engineering & Structural Dynamics, vol. 28, pp. 1121-1141, 1999.
[9] M. I. Wallace, Wagg, D. J., and Neild, S. A., "An adaptive polynomial based forward prediction algorithm for multi-actuator real-time dynamic substructuring," in Proceedings of the Royal Society Series A, 2005.
[10] P. A. Bonnet, Williams, M. S., Blakeborough, A, "Compensation of actuator dynamics in real-time hybrid tests," Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 221, pp. 251-264, 2007.
[11] A. K. Agrawal, and Yang, J. N., "Compensation of time-delay for control of civil engineering structures," Earthquake Engineering & Structural Dynamics, vol. 29, pp. 37-62, 2000.
[12] J. Y. Tu, "Development of numerical-substructure-based and output-based substructuring controllers," Structural Control and Health Monitoring, vol. 20, pp. 918-936, 2013.
[13] R. A. Ibrahim and J. W. Roberts, "Broad band random excitation of a two-degree-of-freedom system with autoparametric coupling," Journal of Sound and Vibration, vol. 44, pp. 335-348, 1976.
[14] M. I. Wallace, J. Sieber, S. A. Neild, D. J. Wagg, and B. Krauskopf, "Stability analysis of real-time dynamic substructuring using delay differential equation models," Earthquake Engineering & Structural Dynamics, vol. 34, pp. 1817-1832, 2005.
[15] T. Horiuchi, Nakagawa, M., Sugano, M., and Konno, T., "Development of a real-time hybrid experimental system with actuator delay compensation," 11th World Conference on Earthquake Engineering, 1996.
[16] I. Horowitz, "Some properties of delay controls(Smith regulator)," International Journal of Control, vol. 38, pp. 977-990, 1983.
[17] T. Shifrin and M. R. Adams, "Linear algebra a geometric approach," 2002.
[18] T. L. K. Engelborghs, and D. Roose, "Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL," ACM Transactions on Mathematical Software, vol. 28, pp. 1-21, 2002.
[19] S. Skogestad and I. Postlethwaite, Multivariable feedback control: analysis and design, 2nd ed. Chichester: John Wiley & Sons Ltd, 2005.
[20] J. Kautsky and N. K. Nichols, "Robust pole assignment in linear state feedback," International Journal of Control, vol. 41, pp. 1129-1155, 1985.
[21] 楊浩廷, "基底隔震建築動態次結構測試之同步控制系統發展," 國立清華大學動機系碩士論文, 2012.
[22] D. P. Stoten and R. A. Hyde, "Adaptive control of dynamically substructured systems: the single-input single-output case," Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 220, pp. 63-79, 2006.
[23] Y. Shaohong and Y. Aimin, "Explicit algorithm to the inverse of Vandermonde Matrix," International Conference on Test and Measurement, pp. 176-179, 2009 .
[24] I. Kaufman, "The inversion of the Vandermonde matrix and transformation to the Jordan canonical form," Automatic Control, IEEE Transactions on, vol. 14, pp. 774-777, 1969.
[25] T. R. A.Tondl, F.Verhulst, and R.Nabergoj, Autoparametric resonance in mechanical systems, 2000.