臺灣博碩士論文加值系統

本文對非剛性機器手臂之連續分散式參數系統將輪軸（Hub）半徑及端點荷重列入考慮，作動態分析與控制系統設計，以達到非剛性機器手臂之精確軌跡控制。
首先，以漢米頓原理（Hamilton principle）推導得到此系統的非線性動態方程式（一非線性四階偏微分方程式）及相關邊界條件，經線性化及拉式轉換（Laplace transform）求得此系統開迴路轉移函數，利用Fortran for IMSL求出無限多組極零點位置分佈，然後利用根軌跡穩定分析法則使受控系統得以穩定並設計控制器，並比較當致動器與感測器考慮輪軸半徑及不考慮時對系統穩定度的差異，最後利用假設模態法（Assumed-mode method）推導出分離化後對時間相依函數的二階常微分方程式，再結合數值分析中的Runge-Kutta method 模擬線性及非線性運動方程式之暫態響應結果。
根據以上電腦程式模擬結果，我們可以看出此系統不論是線性或是非線性經由所設計的控制器，其響應結果皆可呈現出良好的穩定度及軌跡控制。

The stability and tracking control is discussed within a flexible robot arm system. The flexible robot arm is considered as a Bernoulli-Euler beam with tip-payload. At the same time, the position of the actuator and sensor are also taken into account.
In this thesis, first, the dynamic equation of the flexible robot arm is derived from Hamilton priciple. This equation is a fourth-order partial differential equation. Second, the open loop transfer function of the system is obtained from the dynamic equation and related boundary conditions. Third, the Fortran for IMSL subroutines is used to find all of the poles and zeros of the system in the s-plane. The root-locus method is applied to analyze the stablity of the accurately infinite poles and zeros’ locations. Then, in order to find the dynamic response, the assumed mode method is adopted and a very reasonable numer of vibration modes of the system is selected for computer simulations.
From the computer simulations, it can be seen that both the linear system and the nonlinear system have good stability property and tracking control response. The designed controller is quite effective to the flexible robot arm system.

誌謝
中文摘要…………………………………………..…………………Ⅰ
Abstract…………………………………………….………………..Ⅱ
目錄………………………………………………..…………………Ⅲ
圖索引……………………………………………….…………………Ⅴ
第一章 緒論……………….……………………………………………1
1.1 前言………………………………………………..……….….1
1.2 研究動機………………………………………..…….…...….2
1.3 文獻回顧………………………………………..………….….3
1.4 研究步驟………………………………………..….….…….6
第二章 非剛性機器手臂之數學模式推導…….…………………….…8
2.1 引言………………………………………………………..….8
2.2 非剛性機器手臂模型之建立…….……………………….….8
2.3 非剛性機器手臂動態方程式推導…..……………….…….….12
2.4 非剛性機器手臂自然頻率與形狀函數…………..……...…...17
第三章 轉移函數推導與控制器設計………………………..………..21
3.1 引言………………………………………………….………...21
3.2 非剛性機器手臂之開迴路系統之轉移函數………..………...21
3.3 對開迴路系統之轉移函數分析穩定度…………………….….27
3.4 致動器與感測器因兩者間輪軸之半徑不同對系統根軌跡之改變評估……………………………………………….…….…32
3.5 控制器設計、分析……..……………………..………………..38
3.6 非剛性機器手臂模擬之振動模態………..…..………………..47
第四章 結果與分析……………..….………………………………….54
4.1 引言………………………………………….…..….…………..54
4.2 系統運動過程中的輸出響應結果………………...….………..54
4.2.1 響應軌跡之追蹤……………………..………………..54
4.2.2 加入比例微分控制器輸出響應結果…………...…….63
4.2.3 加入比例積分微分控制器輸出響應結果………...….71
4.2.4 比較線性與非線性系統模型之回授控制模擬………78
第五章 結論與建議……………………..………………………… .…81
參考文獻……………………………………………..….…………… ..83

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