本論文運用資料取樣模型分析法對新型具有柔性切換功能之雙併式降壓轉換器進行分析，推導出線性誤差動態方程式作為閉迴路控制器設計的基礎，並根據此線性誤差動態模型設計一個離散 LQR 控制器，使雙併式降壓轉換器輸出電壓在輸入電壓或負載變動的情況下擁有良好的暫態響應和強韌性。
　　為了使雙併式降壓轉換器在穩定輸出電壓同時達到開關柔性切換，控制器必須計算所需的開關導通率以及同步開關電流為零時間，以便利用脈波頻率調變 (PFM) 技術控制切換週期。
　　本論文所提出之控制器，吾人藉 MATLAB 套裝軟體模擬驗證其可行性後，以現場可程式邏輯閘陣（FPGA）達成硬體實現。實驗結果顯示閉迴路系統之輸出表現與對輸入電壓或負載變動的強韌性跟理論預期吻合，驗證了本控制設計方法在實際上運用的可行性。

　　We consider output voltage regulation of a novel twin-buck switching power converters with so-called zero voltage switching (ZVS) and zero current switching (ZCS). In order to observe the constraints imposed by ZVS and ZCS, it is necessary to adopt the pulse frequency modulation (PFM) technique, which lead to a switching system with aperiodic operating cycles. The control design is based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the at-sampling behaviour into account. The applicability of the proposed controller is validated via numerical simulations written in MATLAB and SIMULINK. The controller is realized using Field Programmable Gate Array (FPGA). The experimental results indicate that the feedback system have good transient response and adequate robustness margin against source and load variation, which verify the applicability of the proposed control design approach.

第一章 緒論 1
1.1 研究背景、動機與目的 1
1.2 文獻回顧 3
第二章 雙併式降壓轉換器 6
2.1 雙併式降壓轉換器之基本電路架構與工作原理 6
2.2 雙併式降壓轉換器之同步整流架構與工作原理 10
2.3 同步整流之雙併式降壓轉換器的狀態空間分析 15
第三章 轉換器之模型分析 19
3.1 資料取樣模型分析法 19
3.2 系統說明 21
3.3 系統離散化 23
3.4 系統線性化 26
3.4.1 問題描述 26
3.4.2 小訊號干擾模型 27
第四章 轉換器之控制器設計 29
4.1 離散 LQR 控制器設計 29
4.2 同步開關電流為零的時間計算 33
4.3 轉換器之控制器模擬 36
4.3.1 控制系統架構 36
4.3.2 模擬結果 37
第五章 控制器之硬體實現 42
5.1 控制硬體架構 42
5.2 實驗結果 43
第六章 結論與未來展望 47
6.1 結論 47
6.2 未來展望 47
參考文獻 49
附錄 53
A.1 FPGA 內部程式架構 53

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