臺灣博碩士論文加值系統

本論文是有關單節橈性臂的設計與控制。研究工作包括，建立單節橈性臂的數學模式，分析其動態響應並進行模式簡化的驗證，然後依據簡化後的數學模式進行控制器的設計。另外，我們使用田口法技術，對單節橈性臂結構進行最佳參數設計。
首先，由進行數學模式簡化分析結果得知，當單節橈性臂承受一反正向扭矩測試時，真實模式與省略縱向變形模式兩者的位移響應與偏位量響應幾乎完全相同，因此我們先以省略縱向變形模式來代替真實模式。進一步，在低轉速條件下，我們再比較單節橈性臂的線性模式與省略縱向變形模式的差別；其結果顯示，兩者之位移響應、偏位量響應差異性也不大，所以我們可採用線性模式做為單節橈性臂控制器設計的參考模式。
接著，依據此單節橈性臂參考模式，我們進行PD控制器與LQR兩種控制器的設計與分析。由電腦程式模擬結果顯示，PD控制器對單節橈性臂的自由端位置響應，若要達到終值的2%內的安定時間要求，需要較長的時間；而LQR控制器對於單節橈性臂，則可以較快的達成。此結論也驗證了LQR控制器係利用最佳控制法則，並在適當的穩定邊限(stability margin)要求下，所設計出的單節橈性臂全狀態回授控制系統，當然具有更佳的動態響應。
最後在使用田口法技術，以進行多次控制系統的模擬與分析，於規劃單節橈性臂結構設計上；我們針對三種不同材質材料進行最佳參數設計，依滿足最小扭矩控制量的要求下，求得單節橈性臂結構設計的最重要參數。

This thesis is about a design and control of a single link flexible arm (SLFA). The research work includes establishing a SLFA mathematical model, analyzing its dynamic response and model simplification verification, and performing controller design using the simplified model. Furthermore, we performed an optimal parameter design for the SLFA structure using the Taguchi Techniques.
At first, from the model simplification verification, we found when the SLFA model was subjected to a test torque, a negative pulse followed by a positive pulse, the truth model and the model without considering longitudinal deformation, both of the models have almost the same displacement responses and deflection responses. Moreover, under a small rotating speed, the model can be further simplified. The simulation showed that when the linear model was compared with the previous simplified model, the displacement responses and deflection responses have only small variations. Therefore, It is concluded that we can use the linear model for the SLFA controller design.
Next, using the SLFA linear model, we started analyzing and designing of a PD controller and a LQR controller for the SLFA feedback control system. And, the simulation results show that the SLFA free-end response for a PD controller has a longer settling time using 2% criterion. Nevertheless, the LQR controller can achieve a much better response. This concludes and verifies that a LQR controller with a proper stability margin, using full states feedback, can achieve a fast and better response.
Finally, using Taguchi Techniques to perform many control system simulations and analysis were carried out, to optimize design parameters of a SLFA structure. We use three different materials and a minimum control torque requirement, to realize the SLFA structure major design parameters.

摘要…………………………………………………………… Ⅰ
英文摘要………………………………………………………. Ⅲ
誌謝……………………………………………………………. Ⅳ
目錄……………………………………………………………. Ⅴ
圖目錄…………………………………………………………. Ⅷ
表目錄………………………………………………………. ⅩⅢ
第一章 緒論
1.1 研究動機……………………………………. 1
1.2 文獻回顧……………………………………. 1
1.3 研究方法與步驟……………………………. 5
第二章 動態數學模式之建立
2.1 前言…………………………………………. 9
2.2 單節橈性臂的假設模式……………………. 9
2.3 縱向變形和橫向變形之動態方程式……... 14
2.4 省略縱向變形之動態模式………………. 21
2.5 動態模式轉換為狀態方程式表示法……... 23
2.6 模擬分析…………………………………. 25
2.7 結果與討論………………………………... 27
第三章 PD 控制器設計
3.1 前言………………………………………... 37
3.2 PD控制法則……………………………….. 37
3.3 PD控制器參數之選定…………………….. 38
3.4 模擬分析…………………………………... 42
3.5 結果與討論………………………………... 43
第四章 最佳控制器設計
4.1 前言………………………………………... 48
4.2 最佳控制理論……………………………... 48
4.3 線性狀態回授控制………………………... 50
4.4 模擬分析…………………………………... 51
4.5 結果與討論………………………………... 54
第五章 應用品質工程技術田口法分析
5.1 前言………………………………………... 65
5.2 田口法實驗程序設計……………………... 65
5.3 田口法實驗………………………………... 66
5.4結果與討論………………………………… 75
第六章 結果討論與未來研究
6.1結果討論…………………………………… 79
6.2未來研究…………………………………… 81
參考文獻………………………………………………………. 84
符號索引………………………………………………………. 89
作者簡介………………………………………………………. 91
著作……………………………………………………………. 92

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