本論文旨在討論具有端點質量的單軸撓性機械手臂之端點力量控制。一開始我們先建立撓性機械手臂端點與限制面的模型系統，且推導出角度，振動以及限制力之間相關的動態方程式。利用漢米頓原理(Hamilton principle)來求得其相關的邊界條件，再以拉格朗日運算子(Lagrange multiplier)對手臂的端點與接觸面作力量的分析。由Galerkin’s方法推導出系統對時間相依函數的二階常微分方程式。在此我們選取系統前五個模態來進行控制器的設計以及系統的模擬。控制器我們採取直接參考模式適應性控制(Direct model reference adaptive control, DMRAC)，其主要架構分為參考模式以及受控系統。由於利用這種控制器，系統必須為完全正實數系統(Strictly positive real, SPR)，所以我們分別在參考模式以及受控系統加入前饋補償器，使得我們的受控系統能滿足接近完全正實數(Almost strictly positive real, ASPR)的條件。
實驗裡我們所使用的撓性機械手臂材質為彈簧鋼，致動器是利用交流伺服馬達，感測器的部分我們採用力量感測器以及應變規來做端點力量以及端點位移的量測。我們分別對步階、弦波以及方波函數來做端點力量控制的模擬以及實驗。在實驗的結果可以發現，端點力量在步階函數的控制效果不錯，在弦波函數時的輸出結果會有產生明顯的振動現象，而在方波函數輸出部分，當目標值輸出較大時會有較大的振盪產生。

This thesis investigates force control of one-link flexible arms with a tip mass. First, we derive the dynamic equations of the joint angle, vibration of the arm and constraint force, and use the Hamilton’s principle to obtain boundary conditions. The Galerkin’s method is used to develop the reduced order model of the flexible arm. We choose the system’s first five vibration modes for controller design and computer simulation. The robust direct model reference adaptive control(DMRAC) is adopted for the tip to track a desired force. The frame contains the plant and reference model. Because the plant must be almost strictly positive real(ASPR), we add the feedforward compensator to the plant and reference model, enabling the plant to meet the ASPR condition. In the experiment, we used the flexible arm made of stainless steel, an AC servo motor as an actuator, a force sensor for sensing the tip force, and a strain gauge for sensing the tip deflection. We control the tip force controlled to track the step, sinusoidal function and square wave function with the simulation and experiment. The results show that the tip force can track the step function quite well. The force response has the obvious fluctuation phenomenon when tracking the sinusoidal function. When tracking the square wave function, there will be severe fluctuation at the larger force.

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