空氣彈力系統為一非線性系統，相對於系統的動態模型有兩個自由度，分別是俯仰狀態和振幅狀態。其機翼模型在結構力、慣性力和空氣動力的交互作用影響，導致飛行器產生非預期的動態。在文獻中常見到的升力力矩模型有兩種：擬似穩態流和非穩態流。本文將介紹這兩種升力力矩模型的不同，以便日後分析。
本文考慮了單控制面的機翼系統模型，並利用此模型做了兩次座標轉換。在第一次座標轉換後，因為系統為單控制面，因此產生了非匹配式的部分。在非匹配式的部分，利用兩狀態之間的關係，設定其關係矩陣，使非匹配式的部份穩定，再利用此關係矩陣，做第二次的座標轉換。而第二次的座標轉換引入了順滑函數，並利用等效控制將非線性項和不確定項穩定，最後利用切換控制將外擾消除。
在設計等效控制時，通常會利用Lyapunov法來推導控制律，但是在空氣彈力系統中，其非線性項的影響非常大，所以利用此方法所推導出來的控制律並不實用。因此本文改用了線性矩陣不等式，降低其保守性，找出最佳的控制律。最後從模擬結果可以看出所推導出來的控制律可以壓制住顫振現象。

Aeroelastic system is a nonlinear system. The dynamic model describes the plunge and the pitch motion of a wing. The interaction of nonlinearity of structural, inertial force and aerodynamic force will lead to wing instability in forms of flutter and limit cycle oscillation. There are two kinds of lift-moment model in the literature. One is the quasi-steady flow, the other is the unsteady flow. This thesis will derivate the unsteady flow lift-moment model, and compare with quasi-steady flow lift-moment model.
In this thesis, we consider the wing system with one control surface. And we transform the coordinate into two part of the system. One part of the system is the mismatch term, another is the match term. We determine the matrix to stabilize the mismatch term. Then transform the coordinate again by the matrix. In this coordinate transformation, we introduce the sliding function into the system. And we use the equivalent control to eliminate the nonlinear term and uncertain term. Then the switching control is introduced to eliminate the external disturbance. The Lyapunov method is usually used to design the equivalent control. In this system, the nonlinear term is too large to find an applicable control matrix. Therefore, the linear matrix inequality method is applied to find the optimal control matrix. Numerical studies demonstrate that the proposed we find the control law can suppress the flutter phenomenon effectively.

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