本論文針對一升壓式轉換器搭配電池電源模組 (Battery Power Modules, BPMs) 輸出串聯架構設計具平衡放電性質之輸出穩壓控制器。輸出串聯架構之優點在於能夠提供較高的輸出電壓，且各模組均可以行獨立放電控制。

本文先針對電池電源模組輸出串聯架構，運用狀態空間平均法進行模型分析，推導一平均非線性動態模型。之後，吾人在針對特定操作點對模型線性化，導出一線性非時變之近似模型。吾人應用線性二次調節器 (Linear Quadratic Regulation, LQR) 方法，並藉特定的權重函數來設計一個強健的穩壓控制器。最後，為了達到平衡放電的功能，吾人在設計一個回授機制，利用各模組之個別電壓與平均電壓之差異調節個別模組參與放電的程度，來達到平衡放電的目的。本文最後以數值模擬軟體MATLAB驗證其是否具備平衡放電，且達到穩定輸出電壓，對於負載改變時仍可按參考指令穩定輸出吾人所欲之端電壓。

In this thesis, we consider the control design problem of output voltage regulation with balanced discharge for a boost converter with battery power modules (BPMs) in output series connection. One of the advantages of the output series connection is that such circuits are able to provide a higher collective output voltage, while at the same time each battery modules can be regulated to discharge independently.

In this thesis, we first apply the state-space averaging approach to establish a nonlinear average dynamical model. Furthermore, we linearize the model around a given operating point to derive a linear time invariant approximation for the nonlinear model. Linear Quadratic Regulation (LQR) approach is then applied to design a robust output voltage regulator based on an integral weighting function. Lastly, to achieve balanced discharge, an additional feedback mechanism for each BPM is introduced. The mechanism is linear feedback based on the difference between the voltage of the individual module and the average voltage among the modules. The effectiveness of our design is verified by numerical simulations using the software package MATLAB. The results of our numerical experiments indicate that our design is robust against load variation, and the controller is indeed able to regulate the output voltage to a given desired value while maintaining balanced discharge among the BPMs.

誌謝 i
中文摘要 ii
Abstract iii
目錄 iv
圖次 vii
表次 ix
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機、目的與貢獻 2
1.3 論文架構 3
第二章 預備知識 4
2.1 建立轉換器數學模型的方法 4
2.1.1 電流注入法 4
2.1.2 電路平均法 6
2.1.3 狀態空間平均法 6
2.2 轉換器之調變模式 7
2.2.1 脈波寬度調變 7
2.2.2 脈波頻率調變 8
2.3 平均相位移控制 8
2.4 線性化 9
第三章 電池電源模組 12
3.1 直流對直流轉換器 12
3.1.1 基本型升壓轉換器 12
3.2 建立電路模型 17
3.3 電池電源模組輸出並聯架構 18
3.4 電池電源模組輸出串聯架構 19
3.4.1 多組升壓式電池電源模組輸出串聯運轉之連續導通模式. 20
3.5 升壓式電池電源模組輸出串聯之數學模型分析 22
3.5.1 平均相位移分析 22
3.5.2 狀態空間分析 28
3.5.3 狀態空間平均法 44
3.5.4 無限多組升壓式電池電源模組輸出串聯架構之模型 53
第四章 應用LQR 設計具備平衡放電之升壓式電池電源模組輸出串聯之控制器 55
4.1 LQR 控制器設計 55
4.1.1 LQR 控制器設計與分析 55
4.1.2 升壓式電池電源模組輸出串聯之LQR 控制器設計 57
4.2 電池電源模組輸出串聯之平衡放電控制器設計 62
4.2.1 電池電壓量測 62
4.2.2 平衡放電控制器設計方法 63
4.3 升壓式電池電源模組輸出串聯控制器模擬 64
4.3.1 控制系統架構 64
4.3.2 模擬結果 65
第五章 結論與未來展望 74
5.1 結論 74
5.2 未來展望 74
參考文獻 75

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