本論文針對結構主動控制文獻中最常被利用到LQG最佳控制理論作延伸性的拓展與探討。本文將LQG最佳控制器的應用拓展至LQG/LTR強健控制器，和現有的文獻相比可以看出LQG/LTR強健控制器應用在結構主動控制上可以對系統提供較佳的穩定裕度。 近來，H2 和 H¥ 最佳控制理論被應用在結構主動控制上，文獻記載應用H2 和 H¥ 最佳控制理論可有效的減低結構在強風與地震下的反應。本文將闡述在適當選擇權重函數下，定義於時間域的LQG最佳控制器和定義於頻率域的H2 最佳控制器可以在數學上全等。除了將LQG最佳控制器的應用拓展至LQG/LTR強健控制器外，本論文所探討另一個重點是嘗試將H¥ 最佳控制的理論精神融入LQG或說是H2 最佳控制器的設計考慮中。此時吾人不再緊守著LQG、H2 和H¥ 最佳控制理論中成本函數必須最佳化的要求，而是在這些成本函數求取適當的妥協。從本文的結果可以知道，不同最佳化控制理論中成本函數間的妥協可以使控制器的設計更有彈性。傳統的LQG、H2 和H¥ 最佳控制器可以由兩項聯立的Riccati Equation求得，但是不同最佳化控制理論中成本函數間的妥協問題卻不能由簡單的聯立的Riccati Equation求得。近來，interior-point method的出現與應用使得LMIs(Linear Matrix Inequalities)成為一套有用的數學工具。本文中，利用單一的Lyapunov函數將不同最佳化控制理論成本函數間的妥協問題轉換成LMIs並實際求解出控制器。吾人將此控制器設計法則應用到ASCE Committee on Structural Control提出的受風力影響高樓結構主動控制標準問題上可以得到滿意的結果。 The LQG optimal control theory used extensively in the literatures for active structural control is extended in this dissertation. Since the LQG controller provides no guarantee for robust stability, we extend the LQG controller to the LQG/LTR controller. Simulations show that LQG/LTR controllers provide better stability margin than those presented in the published literatures. Recently, H2 and H¥ optimal control techniques were introduced for active structural control problem, which results in effectual approaches in the design of controllers for seismic and wind excited buildings. Since LQG optimal control criteria defined in time domain can be numerically equivalent to the H2 optimal control criteria defined in frequency domain with appropriate selection of design weightings. In this dissertation, we present a control strategy that is the simultaneous treatment of both H2 and H¥ criteria and this control strategy quantitatively demonstrates design tradeoffs. Thus, we extend the popular LQG controller to the mixed LQG/H¥ or H2/H¥ controller. This mixed control problem can be formulated by linear matrix inequalities in terms of a common Lyapunov function. Solving linear matrix inequalities is a convex optimization problem. Simulation and design results demonstrates that decreasing H¥ attenuation constraint can be used to reduce the structural response under wind excitations at the expense of increasing H2 performance index and control efforts of the actuator.
