本文運用狀態空間平均法對具有柔性切換之雙併式降壓轉換器進行模型分析並推導其平均線性動態態方程式，再以此為模型應用一可變動操作點之線性二次調節器 (Linear Quadratic Regulator, LQR) 設計一最佳化控制器。

雙併式降壓轉換器的調變方式是 PFM(Pulse-Frequency Modulation) ，且因為雙併式降壓轉換器的柔性切換特性，其開關有諸多限制使得在此種調變方式下降壓比，也就是控制力，無法小於 0.5 。為了擴展轉換器的控制力範圍，本文以 PWM/PFM 混合調變的方式調變雙併式降壓轉換器，同時，為了使同步開關達到零電流截止，需計算同步開關的放電時間，供控制器回授使用。本文最後以 MATLAB 模擬與撰寫 Verilog 硬體描述語言經 FPGA (Field Programmable Gate Array) 實現驗證此控制器與調變方式的可行性。

In the thesis, we apply the state average method to model the time-average linear dynamic equation, which is used to design a gain scheduled linear quadratic optimal controller. Because the standard modulation method of the twin-buck converter is PFM(Pulse-Frequency Modulation) and twin-buck converter owns the soft-switching characteristic, the voltage step-down ratio, that is, control force can not be lowered less than 0.5. For expanding the range of control force of converter, we modulate the converter by means of
mixed modulation of PWM/PFM. With the former odulation method, we have to calculate the discharging time of synchronous switch taken by controller to achieve zero-voltage-transition (ZVT).

In the last part of this thesis, we verify the practicability of the controller and modulation method through soft simulation coded by MATLAB and hardware implementation of FPGA driven by Verilog.

目錄
中文摘要ii
英文摘要iii
圖目錄vi
表目錄ix
第1章研究主題之背景與目的 1
1.1研究背景、動機與目的 . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻回顧 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 建立轉換器數學模型的方法 . . . . . . . . . . . . . . . . . . . 5
1.2.2 降壓式轉換器之調變模式. . . . . . . . . . . . . . . . . . . . 8
1.2.3 直流對直流轉換器控制器設計法回顧 . . . . . . . . . . . . . . 8
1.3 論文大綱與貢獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
第2章雙併式降壓轉換器11
2.1 直流對直流降壓轉換器. . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 基本降壓轉換器. . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 交錯式轉換器. . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.3 同步整流降壓轉換器. . . . . . . . . . . . . . . . . . . . . . . 15
2.1.4 具同步整流之雙併式降壓轉換器. . . . . . . . . . . . . . . . 16
2.1.5 結合基本降壓轉換器操作之雙併式降壓轉換器. . . . . . . . . 18
2.2 結合基本降壓轉換器操作之雙併式降壓電源轉換器之數學模型分析 . 19
2.2.1 狀態空間分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 狀態空間平均法 . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3 同步開關之零電流截止時間計算 . . . . . . . . . . . . . . . . 23
第3章應用LQR方法之適應控制器設計27
3.1 控制器設計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 增益規劃. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.2 LQR 控制器設計. . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.3 雙併式降壓轉換器之控制器設計. . . . . . . . . . . . . . . . 31
3.2 雙併式降壓轉換器控制器模擬 . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 控制系統架構 . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.2 模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
第4章控制器之實現與實驗結果42
4.1 雙併式降壓轉換器硬體架構介紹 . . . . . . . . . . . . . . . . . . . . 42
4.2 實驗結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
第5章結論與未來展望48
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2 未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
參考文獻49
附錄53
A.1 雙併式降壓轉換器實驗電路 . . . . . . . . . . . . . . . . . . . . . . . 53

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