本文係在對撓性機械手臂分散式參數系統作動態分析與控制系統設計之研究，探討撓性機械手臂系統的穩定性分析與定位控制。即對撓性機械手臂的撓性問題做深入的探討，首著於撓性機械手臂之振動抑制下設計控制器，除須控制其剛體模態，而且必須抑制其撓性模態之振動行為，以期達到精確的軌跡控制。
首先以漢米頓原理(Hamilton’s principle)推導系統運動方程式來建立模型，經拉普拉斯轉換(Laplace transformation)以求出撓性機械手臂之受控系統轉移函數，得出系統精確之極零點位置，在據以根軌跡法分析選擇控制器設計。然後利用假設模態法(Assumed-mode method)對撓性機械手臂作模態分析，將偏微分方程式化成無窮多個振動模態之聯立二階常微分方程式，可將連續系統以無窮多個單自由度系統組合，並轉換成狀態空間表示式，方便於撓性機械手臂系統之動態模擬分析與控制系統設計。分析自然頻率方程式所得之自然頻率與極點位置相對照，驗證所取模態數以構成撓性機械手臂系統模擬上之精確性。最後結果顯示，藉由實用的PD控制器與速度回饋設計即可使閉迴路系統穩定，並結合基因演算法於控制器參數之調整，引入誤差準則的概念訂定適應函數，能更有效率地搜尋控制器參數，避免以試誤法的方式需要較多的嘗試時間，並有利於排除陷入到參數局部最佳值的問題。

In order to meet the requirements for higher productivity and efficiency, the trend toward using faster, lighter and more accurate manipulators in industrial and space application are apparent. Many control system design methods for a flexible manipulator are either based on reduced order model or require distributed actuators, which are not available in reality. This thesis is concerned with some topics in the dynamic modeling and control of a flexible manipulator system with infinite dimensional system. First, Hamilton’s principle is used to derive the equations of motion and boundary conditions of the flexible manipulator arm. Then, the system transcendental transfer function is obtained from the actuator and sensor’s locations. The extended root-locus is used to analyze the exact infinite dimensional pole and zero positions. Next, in order to simulate this distributed parameter system, the Assumed-mode method is adopted and its accuracy is proved in advance. Because the control design and the computer simulation are based on the concept of the infinite dimensional system, there will not “control and observation spillover problems” happen and computational error concern which are encountered in most of the control of flexible structures. In this thesis, by using a discrete set of actuator and sensor without involving truncation of the higher frequency modes, it can be seen from computer simulation, the designed PD and velocity feedback control system for flexible manipulator arm can not only stabilize all the vibration modes but also can provide good tracking properties.

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