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研究生:鄭元傑
研究生(外文):CHENG, YUAN-CHIEH
論文名稱:分數階粒子群演算法應用於 H2/H∞ PIMD 優化設計問題
論文名稱(外文):Optimal Design of H2/H∞ PIMD Controller by Using Fractional-order Particle Swarm Optimizer
指導教授:周至宏周至宏引用關係周阜毅
指導教授(外文):CHOU, JYH-HORNGCHOU, FU-YI
口試委員:蔡進聰周至宏何文獻周阜毅楊柏遠
口試委員(外文):TSAI, JINN-TSONGCHOU, JYH-HORNGHO, WEN-HSIENCHOU, FU-YIYANG, PO-YUAN
口試日期:2020-07-10
學位類別:碩士
校院名稱:國立高雄科技大學
系所名稱:電機工程系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:中文
論文頁數:60
中文關鍵詞:分數階粒子群演算法H2/H∞ PIMD控制器允差設計
外文關鍵詞:Fractional-order Particle Swarm OptimizerH2/H∞ PIMD ControllerTolerance Design
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本論文應用分數階粒子群演算法結合均勻設計於混合式H2/H∞最佳PIMD優化設計共分為兩大部分,第一部分為分數階粒子群演算法 (Fractional-order Particle Swarm Optimizer, FPSO) 以及均勻設計 (Uniform Design),其用途在於解決最佳化問題。粒子群演算法 (PSO) 是模仿動物行為的群智慧演算法中,最經典的演算法之一。近幾年,部分學者考慮到分數階結構的群智慧演算法,提出分數階粒子群演算法,可使FPSO增加多樣性的計算方法,節省大量複雜的計算程序步驟。由於FPSO內的參數將會影響演算成效,因此使用均勻設計以減少實驗數並使其能夠以最短的時間獲得更好的計算成果。第二部分為穩定強健和抗噪性能的H∞性能與強健最佳控制H2性能等之混合式H2/H∞最佳PIMD優化設計問題,以解決含有高頻雜訊的控制系統以及考慮允差優化問題的控制器設計為目標,使用新型的PIMD控制器並結合H2/H∞來達到模擬貼近實務層面的問題,使用結合均勻實驗設計之FPSO以及田口基因演算法 (Hybrid Taguchi-Genetic Algorithm, HTGA) 兩種演算法來優化處理並進行比較。從結果來看,FPSO所得到的H2/H∞ PIMD控制器參數之穩定性和收斂性皆優於HTGA。

關鍵詞:分數階粒子群演算法、均勻設計、允差優化設計、H2/H∞ PIMD控制器

This thesis applies a fractional-order particle swarm optimizer (FPSO) combined with uniform design for the hybrid H2/H∞ PIMD optimal design. The issue in this thesis can be divided into two parts. The first part is the FPSO and a uniform design to solve its optimization problems. Particle swarm optimizer (PSO) is one of the most classic algorithms among swarm intelligence that mimic animal behavior. In recent years, some scholars have considered the cluster intelligence algorithm of fractional-order structure and proposed the FPSO, which can increase the diversification of the FPSO calculation methods, save a lot of complex calculation procedures. The parameters in FPSO will influence the algometric performance. To obtain the suitable parameter combination of FPSO, the uniform design is used to deal with because the uniform design can reduce the number of experiments and a better result can be obtained in a short time. The second part is to optimize the hybrid H2/H∞ PIMD design which attempts to obtain the robust control H2 performance while the H∞ performance can be stable and anti-noise. This thesis focuses on searching an optimal controller design which can solve the control system containing high frequency noise and consider the tolerance. For reaching this target, a new type of PIMD controller is used in hybrid H2/H∞ to achieve a simulation practical problem. In the experiment, the FPSO with uniform design and the hybrid Taguchi genetic algorithm (HTGA) is used to design and compare their performance. From the results, the stability and convergence of the H2/H∞ PIMD controller parameters obtained by FPSO are better than HTGA.

Keywords: Fractional-order Particle Swarm Optimizer, Uniform Design, Tolerance Design, H2/H∞ PIMD controller

中文摘要--------------------------------------------------------------------I
英文摘要-------------------------------------------------------------------II
誌謝--------------------------------------------------------------------- IV
目錄-----------------------------------------------------------------------V
圖目錄--------------------------------------------------------------------VII
表目錄-------------------------------------------------------------------VIII
一、緒論--------------------------------------------------------------------1
1.1 前言-----------------------------------------------------------------1
1.2 研究動機及文獻回顧-----------------------------------------------------1
1.3 論文架構--------------------------------------------------------------5
二、分數階粒子群演算法與均勻設計----------------------------------------------6
2.1 粒子群演算法之發展背景--------------------------------------------------6
2.2 粒子群演算法-----------------------------------------------------------6
2.3 分數階粒子群演算法-----------------------------------------------------10
2.4 均勻設計---------------------------------------------------------------13
2.5 自適應均勻設計分數階粒子群演算法--------------------------------------20
三、混合式H2/H∞ PIMD控制器--------------------------------------------------22
3.1 PID控制器-------------------------------------------------------------22
3.2 PIMD控制器------------------------------------------------------------25
3.3 PIMD之允差設計問題----------------------------------------------------30
3.4 H2/H∞ 控制性能--------------------------------------------------------32
四、分數階粒子群演算法應用於混合式H2/H∞最佳PIMD設計問題------------------------35
4.1 應用AUFPSO於混合式H2/H∞最佳PIMD設計-------------------------------------35
4.2 實驗結果---------------------------------------------------------------35
五、結論與未來研究方向------------------------------------------------------47
5.1 結論------------------------------------------------------------------47
5.2 未來研究方向-----------------------------------------------------------47
參考文獻-------------------------------------------------------------------48

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