臺灣博碩士論文加值系統

本論文結合了QFT的設計觀念與H∞最佳控制的設計方法。針對具有參數變動的SISO受控系統，將系統所期望的性能規格轉換成適當的權重函數，利用H∞的計算設計內部的控制器，不再以傳統QFT的方法在尼可士圖做迴路整形，避免了煩瑣的作圖過程。在內部的控制器設計完成之後，就和原始的QFT方法一樣，只要再加上前置濾波器做適當的修正，就能讓系統的輸出響應符合規格要求。

This thesis presents a design method which combines the QFT design concept and H∞-optimal control technique. For an SISO plant with parameter variations, we choose appropriate weighting functions to reflect the system performance objectives and solve the controller inside the loop by H∞-norm optimization. This design procedure is different from the classical QFT method. There is no tedious graphical loop-shaping on the Nichols Chart. When the inner loop controller is obtained, an appropriate prefilter is designed so that the output response can satisfy the system specifications.

中文摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
表列 vii
圖列 viii
第一章 緒論 1
1.1 研究動機與目的 1
1.2 論文架構 2
第二章 QFT設計問題簡介 3
2.1 二維自由度反饋系統 3
2.2 受控體的不確定性 4
2.3 量化設計 4
2.4 系統規格 5
2.4.1 時域規格 5
2.4.2 頻率規格 6
2.4.3 干擾抑制規格 7
2.4.4 靈敏度規格 8
2.5 時域規格轉換 8
2.6 QFT方法的設計步驟 12
2.6.1 建立受控體樣板與選取標稱點 13
2.6.2 在尼可士圖上建立滿足頻域規格的邊界 14
2.6.3 迴路整形 17
2.6.4 前置濾波器的設計 17
第三章 H∞設計問題簡介 20
3.1 範數 20
3.1.1 範數的定義 20
3.1.2 連續函數的範數 21
3.1.3 向量的範數 21
3.1.4 系統的H∞範數 22
3.2 反饋系統的設計考量 23
3.3 含權重的反饋系統設計考量 25
3.4 線性分式轉換 27
3.5 含有權重的反饋結構轉換成LFT結構 29
3.6 H∞控制器設計 30
3.6.1 線性矩陣不等式 31
3.6.2 LMI為基礎的H∞控制器 32
第四章 結合QFT/H∞的設計方法 34
4.1 設計步驟 34
4.2 受控體不確定性的乘法性模型與權重函數WT 36
4.3 靈敏度函數與權重函數WS 39
4.4 高頻雜訊抑制與權重函數WUN 44
4.5 求解控制器K和前置濾波器F 45
4.6 設計流程圖 47
第五章 模擬與分析 48
5.1 範例一 48
5.1.1 問題描述 48
5.1.2 規格轉換 48
5.1.3 決定權重函數WT 50
5.1.4 決定權重函數Wun與WS 50
5.1.5 利用H∞求解控制器K(s) 53
5.1.6 檢查頻率響應是否落在上、下邊界之內 53
5.1.7 設計前置濾波器F(s) 55
5.1.8 QFT/H∞與QFT設計比較 57
5.2 範例二 58
5.2.1 問題描述 58
5.2.2 規格轉換 58
5.2.3 決定權重函數WT 59
5.2.4 決定權重函數Wun與WS 60
5.2.5 利用H∞求解控制器K(s) 61
5.2.6 檢查頻率響應是否落在上、下邊界之內 62
5.2.7 設計前置濾波器F(s) 63
5.2.8 QFT/H∞與QFT設計結果比較 64
5.3 範例三 66
5.3.1 問題描述 66
5.3.2 規格轉換 66
5.3.3 決定權重函數WT 66
5.3.4 決定權重函數Wun與WS 67
5.3.5 求解控制器K(s)與前置濾波器F(s) 68
5.3.6 將類比控制器轉換成數位控制器 69
第六章 結論 71
參考文獻 72

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