臺灣博碩士論文加值系統

本論文探討具有傳輸與狀態延遲的不定奇異系統之模糊多重迴路保證成本控制器設計，其適用於具傳輸延遲的網路控制系統或狀態延遲的化工程序。所提出的設計法則不僅有較好的設計彈性，還可以藉由降低成本函數的上界，當不定參數變動時仍能使性能維持在一定的水準。
本研究運用type-2 T-S模糊理論建立數學模型，以平行分佈補償概念結合李亞普諾夫理論設計出保證成本模糊控制器。首先，選擇包含傳輸延遲與狀態延遲的李亞普諾夫泛函。求出泛函導數後，引入成本函數的被積分項，再利用自由權重矩陣與線性矩陣不等式運算技巧，得出穩定度分析與控制器設計的充分條件。多重迴路保證成本控制器所造成的交乘項，則是利用舒爾補數將其線性化。最後，結合最佳化方法，本論文推導出具有最佳化保證成本上界的控制器設計演算法。
本論文得到的保證成本控制器充分條件中的線性矩陣不等式，可以用Matlab LMI toolbox求解出對應的多重迴路保證成本控制器增益矩陣。將上述增益矩陣代入Simulink所建構的非線性系統後，進行數值範例模擬以驗證控制器效能。根據模擬結果，所設計的最佳化保證成本控制器在控制系統同時出現不定參數以及傳輸與狀態延遲的情形之下，有較好的設計彈性，並可使閉迴路系統強健穩定且保證成本上界下降92%。

This thesis investigates the T-S fuzzy multiple feedback-loop guaranteed cost controller design for uncertain singular systems with transmission and state delays. The controller is applicable for the networked control systems with transmission delays or the chemical processes with state delays. The proposed approach has better design flexibility and is able to reduce the upper bound of the cost function in the presence of uncertainties.
Based on the Type 2 T-S fuzzy theory, this work constructs a mathematical model. Using the parallel distributed compensation concept with Lyapunov theory, the robust guaranteed cost fuzzy controller is designed. First, we choose the Lyapunov functional taking in account the transmission and state delays. After differentiating the Lyapunov functional, the integral term of the cost function is added to the derivative. Adopting the free-weighting matrix method and the linear matrix inequality technique, we conduct the sufficient conditions for stability analysis and controller synthesis. Multiplication terms caused by using the multiple feedback-loop guaranteed cost controller are decomposed and linearized by the Schur complement. Finally, an optimal guaranteed cost fuzzy controller design algorithm is presented.
This work uses the Matlab LMI toolbox to find multiple feedback-loop guaranteed cost controller gain matrix. Numerical examples with the obtained controller are simulated to verify the performance of the controller by Simulink software. According to the simulation results, when parametric uncertainties and transmission and state delays exist simultaneously, it shows that the proposed guaranteed cost controller demonstrates better design flexibility. Also, the close-loop system is robust stable and the upper bound of guaranteed cost is decreased by 92%.

摘 要 i
ABSTRACT iii
誌 謝 v
目 錄 vi
圖目錄 viii
第一章 緒 論 1
1.1 研究動機及目的 1
1.2 文獻探討 2
1.3 研究方法與貢獻 3
1.4 論文架構 4
第二章 背景知識介紹 5
2.1 前言 5
2.2 奇異系統 5
2.3 系統不定參數 6
2.4 區間型type 2 T-S模糊控制系統 6
2.5 多重迴路控制器 10
2.6 保證成本控制 11
2.7 結語 12
第三章 系統穩定度分析與控制器設計 13
3.1 前言 13
3.2 預備引理 13
3.3 問題描述 14
3.4 系統穩定度分析 15
3.5 保證成本控制器設計 23
3.6 保證成本上限最佳化 35
3.7 結語 39
第四章 數值模擬與討論 40
4.1 前言 40
4.2 數值範例 40
範例一 定理2與上限最佳化比較 40
範例二 設計彈性與保證成本上界比較 51
4.3 模擬結論 54
第五章 結論與未來研究方向 55
5.1 結論 55
5.2 未來展望 55
參考文獻 57
附錄 62

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