臺灣博碩士論文加值系統

本篇論文結合強健穩定條件，正交函數法(OFA)，田口滑動微分進化演算法(TSBDEA)，使得設計具低軌跡靈敏度強健穩定二次最佳有限範圍靜態輸出回授平行分散補償(PDC)控制器，例如(i) 例如 Takagi-Sugeno (TS)模糊模型系統在參數不確定性影響下的強健穩定，以及(ii)二次有限時間積分性能指標能為最小值。本論文中提出線性矩陣不等式(LMIs)做為強健穩定性分析條件。使用正交函數法及強健穩定條件，TS模糊動態系統之強健穩定二次最佳有限範圍靜態輸出回授平行分散補償控制器設計問題可以轉換成以代數型式方程式的限制條件的靜態最佳化問題。對於靜態最佳化設計的計算問題，利用田口滑動微分進化演算法(TSBDEA)來搜尋在模糊模型系統在參數不確定性影響下具低軌跡靈敏度之強健穩定二次有限範圍最佳靜態輸出回授平行分散補償控制器。最後，用一個例子具低軌跡靈敏度非線性不確定周式電路之強健二次有限範圍最佳靜態輸出回授平行分散補償控制器來說明提出整合方法的應用性。

In this paper, an integrative method, which combines the robust stabilizability condition, the orthogonal-functions approach (OFA), and the Taguchi-sliding-based differential evolution algorithm (TSBDEA), is presented to design the robust-stable and quadratic-finite-horizon-optimal static output feedback parallel-distributed- compensation (PDC) controller with low trajectory sensitivity such that (i) the Takagi-Sugeno (TS) fuzzy control system with elemental parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite-time integral performance index including a quadratic sensitivity term for nominal TS fuzzy control system can be minimized. The robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). By using the OFA and the robust stabilizability condition, the robust-stable and quadratic-finite-horizon-optimal static output feedback PDC control problem for the TS fuzzy dynamic systems is transformed into a static constrained-optimization problem represented by the algebraic equations with constraint of LMI-based robust stabilizability condition; thus greatly simplifying the optimal static output feedback PDC controller design problem. Then, for the static constrained-optimization problem, the TSBDEA is applied to find the robust-stable and quadratic-finite-horizon-optimal static output feedback PDC controllers with low trajectory sensitivity of the TS fuzzy control systems with elemental parametric uncertainties. A design example of robust-stable and quadratic-finite-horizon-optimal static output feedback PDC controllers with low trajectory sensitivity for uncertain nonlinear Chua circuit is given to demonstrate the applicability of the proposed integrative approach.

中文摘要…………………………………………………………………………………I
英文摘要…………………………………………………………………………………II
誌謝…………………………………………………………………………………………III
目錄…………………………………………………………………………………………IV
圖目錄………………………………………………………………………………………VI
表目錄………………………………………………………………………………………VII

第一章 緒論 1
1.1 研究動機與文獻 1
1.2 論文架構 3
第二章 強健穩定性分析 5
2.1 前言 5
2.2 強健穩定條件推導 5
2.3 強健穩定定理 9
第三章 強健最佳控制器設計 13
3.1 前言 13
3.2 具軌跡靈敏度之T-S模糊模型為基礎的動態系統 13
3.3 二次有限時間積分性能指標 14
3.4 強健最佳回授控制器設計(OFA) 15
第四章 田口滑動微分進化演算法 19
4.1 前言 19
4.2 田口實驗設計方法基本概念 19
4.3 微分進化演算法 24
4.4 田口滑動微分進化演算法(TSBEDA) 27
第五章 案例模擬結果與分析 31
5.1 前言 31
第六章 結論 42
6.1 總結 42
6.2 未來展望 43

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