順滑模態理論應用於有限元素法模式之撓性臂控制

Abstract

在本篇論文中，我們研究如何穩健控制撓性臂頂端位置的問題。首先以有限元素法推導撓性臂的數學模型，將非線性的撓性臂的高階模式省略，求出一個近似的線性數學模型。而這些被省略的高階撓性臂模式，與系統結構的不確定項一起當成系統外在的擾亂。知名的穩健順滑模式理論可以對付這些擾亂，做有效的控制。模擬以及實驗的結果顯示順滑控制理論的穩健以及在控制結果上的優越。

This thesis studies the robust problem of the tip position control of a physical flexible arm. Its linear model is mathematically derived by the finite element method (FEM), which is approximate to the nonlinear flexible arm by neglecting the higher order modes. As a result, these higher order modes are considered as the disturbances of the linear model of the flexible arm. In addition, uncertainties subject to the structure and payload variations are also included in the linear model. To cope with these disturbances and uncertainties, the well-known robust control technique, the sliding-mode control, is employed to effectively control the tip position of the flexible arm. Finally, simulation and experimental results are used to demonstrate the robustness and superiority of the sliding mode control.