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研究生:林耿源
研究生(外文):Geng-Yung Lin
論文名稱:具時變不確定量伺服系統之強健模式追隨控制
論文名稱(外文):Design of Robust Model-Following Servo Systems with Time-Varying Uncertainties
指導教授:鄭良安
指導教授(外文):Liang-An Zheng
學位類別:碩士
校院名稱:國立高雄應用科技大學
系所名稱:機械與精密工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:73
中文關鍵詞:模式追隨伺服系統卡曼濾波器線性矩陣不等式二次線性調節器混合田口基因演算法
外文關鍵詞:Model-following servo system、Kalman Filter、LMI、LQR、HTGA
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本論文的主要目地是探討模式追隨伺服系統具時變不確定量狀況下之強健模式追隨控制。首先針對模式追隨伺服系統建立數學模型與分析其動態特性,使用狀態回授的設計方法,將控制輸入經由最佳控制法則設計出最佳回授控制,取得控制系統的初步性能與穩定度;另一方面,使用卡曼濾波器(Kalman Filter)來估測系統的狀態變數,以作為回授之用。其次,考慮系統具有時變不確定量時之強健穩定性;文中應用一線性矩陣不等式(linear matrix inequality, LMI)的穩定性條件,來確保系統具有時變不確定量時,仍能達到良好的追隨效果並同時保有強健穩定性。再者最佳回授控制器與估測器之增益值,文中使用二次線性調節器(linear quadratic regulator, LQR)控制法與混合田口基因演算法(hybrid taguchi-genetic algorithm, HTGA)兩種方法分別設計。最後舉出自動繞捲系統與模式追隨伺服系統之工程例子來分別說明及驗證文中所提設計方法之可行性。
This paper proposes a robust design approach for model-following servo systems with time-varying perturbations. In the approach, the control law is obtained from optimal control method and the observer state is estimated by using the Kalman filter. A sufficient condition in terms of linear matrix inequalities (LMIs) is employed to guarantee that the resulting control system not only can follow the step response of a given model plant, but also is asymptotically stable in the presence of time-varying parameter perturbations. Furthermore the game of the optimal control and the observer , in this paper, is designed by the linear quadratic regulator (LQR) and hybrid Taguchi-Genetic algorithm (HTGA). In the end, two engineering examples (one is wilding shaping systems of auto belt and the other is model-following servo systems) are given to demonstrate the use of the proposed design method.
目錄

中文摘要......................................................................................................................Ⅰ
Abstract........................................................................................................................Ⅱ
誌謝..............................................................................................................................Ⅲ
目錄..............................................................................................................................Ⅳ
圖目錄..........................................................................................................................Ⅷ
表目錄..........................................................................................................................Ⅹ

第一章 緒論…………………………………………………………………………1
1.1 研究動機………………………………………………………………….1
1.2 文獻回顧…………………………………………………………….……3
1.3 研究方法與目的……………………………………………………….…4
1.4 研究流程…………………………………………………………….……6
1.5 論文架構……………………………………………………………….…7

第二章 具時變不確定量伺服系統之強健模式追隨控制………………………8
2.1 前言…………………………………………………………………….…8
2.2 模式追隨伺服系統描述………………………………………………….8
2.3 模式追隨控制系統之設計…….……...………..…………………….…11
2.3.1 最佳控制法則………………………………………....…….…….11
2.3.2 狀態觀測器的設計…………………………………....………..…14
2.4 強健追隨控制系統……………………………………….…..…..……..15

第三章 工程實例模擬………………………………………………………..…..…19
3.1實例一:自動捲繞系統之張力追隨控制…………………………..……19
3.1.1 前言……………………………………………………………......19
3.1.2 自動捲繞系統的參數特性…………………………………......…20
3.1.3 自動捲繞系統之數學模型建立……………….………..……...…21
3.1.3-1 建立自動捲繞系統之微分方程式………………..…….…22
3.1.3-2 建立自動捲繞系統之狀態方程式……………………...…23
3.1.4 自動捲繞系統模擬之參數設定…………………………………24
3.1.5 自動捲繞系統之張力追隨控制模擬響應……………….……….27
3.2實例二:伺服系統之強健模式追隨控制……….……………………….29
    3.2.1前言……………………………………………………………...…29
    3.2.2伺服系統之模式追隨描述……………………………………...…29
3.2.3伺服系統之模式追隨模擬的參數設定……………………...........30
3.2.4伺服系統之模式追隨控制模擬響應…………………………...…32

第四章 應用基因演算法與田口品質工程搜尋最佳化控制參數………………....33
   4.1 前言………………………………………………………...…………....33
   4.2 基因演算法(GA)...……….…………...………….…………..…………33
4.2.1 基本概念…………………………………………………….….…34
4.2.1-1 複製…………..………………………..……………...……35
4.2.1-2 交配…………………………………………………...……36
4.2.1-3 突變…………..……………………………………….……37
4.2.2 主要特性………………………………………………………..…38
4.3 田口品質工程………………………………………………………...…40
4.3.1 田口實驗法步驟………………………………………………..…40
4.3.2 品質特性的種類……………………………………………..……41
4.3.2-1 S/N比……...……………….…………………………….…41
4.3.2-2 直交表…………………………………………………...…43
4.4 混合田口基因演算法(HTGA)……….…………….......……………….45
4.4.1 基因演算法之實驗參數設定………. ………………………..…..47
4.4.2 基因演算法之編碼與初始族群…………………………….…….47
4.4.3 適應函數設定…………………………………………………..…49
4.4.4 選擇………………………………………………………….….....50
  4.4.5 交配操作………………………………………………………..…50
4.4.6田口方法於基因演算法的運用……………………………...…..51
4.4.7 突變操作………………………………………………..…………54
4.4.8 終止條件……………………………………………..………...….55

第五章 應用HTGA搜尋工程實例模擬之最佳控制器與估測器的增益值………56
5.1 實例一:應用HTGA搜尋自動捲繞系統之最佳控制器與估測器的
增益值…………………………………………………......…56
5.1.1 前言………………………………………………………………..56
5.1.2 自動捲繞系統搜尋最佳控制器與估測器的增益值之參數設定..56
5.1.3 自動捲繞系統之張力追隨控制模擬響應…………………….….59
5.2 實例二:應用HTGA搜尋模式追隨伺服系統之最佳控制器與估測
器的增益值……………………………………………..……61
5.2.1 前言…………………………………………………………..……61
5.2.2 模式追隨伺服系統搜尋最佳控制器與估測器的增益值之參數
設定………………………………………………………………61
5.2.3 模式追隨伺服系統模擬響應…………………………...…...……64

第六章 結論……………………………………………………………………....…65
6.1 總結…………………………………………………………………...…65
6.2 未來展望…………………………………………………………...……66
參考文獻……………………………………………..………………………………68
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