本論文以質子交換膜燃料電池作為研究對象，目的為藉由設計強韌 PID 控制器調節氫氣流量，使得當燃料電池輸出不同功率時，將定義的氫氣過量比迅速追蹤到設定值，達到節省氫氣與避免由於輸入氫氣量過少而對電池造成傷害。
　　燃料電池系統為一非線性系統，但在其一固定的操作點上可以將之近似為一線性系統。如此，本文針對不同的操作點以系統識別方法獲得系統轉移函數。首先，在 Labview 平台圖控環境下，採用掃頻訊號 (chirp signal) 激發系統低頻到高頻響應，以頻譜分析法獲得系統波德圖，再藉由 Matlab 模擬分析軟體的曲線擬合功能獲得系統轉移函數。最後，設計一H∞PID 控制器，並實際驗證燃料電池於負載變動時，λH2能迅速追蹤到設定值。

In this thesis we propose a robust PID controller to regulate the hydrogen flow of proton exchange membrane fuel cells. The controller allows the so-called hydrogen excess ratio to track a desired value rapidly in order to achieve saving hydrogen and to avoid damage of the fuel cell when the power output of
the fuel cell varies from one level to another.

The fuel cell system is governed by a set of complicated nonlinear dynamical equations. To ease the control design task, we model the system, at each operating point, as a feedback interconnection of
a linear time-invariant nominal part with a norm-bounded perturbation. We use the technique of system identification to acquire the transfer
function representation of the nominal part and the size of the perturbation. To do this, the chirp signal is adopted to excite the system and the observed response is analyzed using spectral analysis
to obtain the model. Based on the model, a $H_{infty}$ PID controller is designed for the fuel cell system. The design is tested on an experimental platform. The experimental results verify that the proposed
controller can regulate the hydrogen excess ratio rapidly under load variation, and effectively reject the influence of external disturbances.

中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . ii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iii
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . vi
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .viii
符號表. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ix
第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 1
1.1 研究背景、動機與目的. . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻回顧 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 燃料電池相關回顧 . . . . . . . . . . . . . . . . . . . . . . . .2
1.2.2 系統識別相關回顧 . . . . . . . . . . . . . . . . . . . . . . . .2
1.2.3 PID控制相關回顧. . . . . . . . . . . . . . . . . . . . . . . . .3
1.3 研究貢獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
第二章燃料電池簡介與模型. . . . . . . . . . . . . . . . . . . . . 4
2.1 燃料電池歷史 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
2.2 燃料電池特點 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4
2.3 燃料電池種類 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.4 質子交換膜燃料電池工作原理. . . . . . . . . . . . . . . . .6
2.5 質子交換膜燃料電池動態模型. . . . . . . . . . . . . . . . .7
2.5.1 陰極流道模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.5.2 陽極流道模型. . . . . . . . . . . . . . . . . . . . . . . . .. . . . 9
2.5.3 薄膜水滲透模型. . . . . . . . . . . . . . . . . . . . . . . . .. . 11
2.5.4 電池電壓模型. . . . . . . . . . . . . . . . . . . . . . . . . . .. . 12
2.6 氫氣過量比. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
第三章系統識別. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .17
3.1 系統識別目的與原理. . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 頻譜分析法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 實驗設備 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4 實驗規劃與步驟 . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4.1 實驗規劃 . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 23
3.4.2 實驗步驟 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.5 實驗結果與曲線擬合 . . . . . . . . . . . . . . . . . . . . . . . 26
第四章強韌控制器理論與控制器設計. . . . . . . . . . . . ..34
4.1 H∞控制理論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1.1 範數定義 . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 34
4.1.2 回路系統穩定性 . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.3 系統的不確定性 . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1.4 系統的強韌穩定性與性能規格 . . . . . . . . . . . . . 37
4.2 控制器設計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.1 PID控制器基礎理論介紹 . . . . . . . . . . . . . . . . . . 39
4.2.2 權重函數(W2)的選擇與與不確定性(△)計算. . . 40
4.2.3 強韌PID控制器設計. . . . . . . . . . . . . . . . . . . . . . . 41
第五章控制器模擬與實驗結果. . . . .. . . . .. . . . .. . . . .. . 48
5.1 PID控制器的離散化與模擬結果. . . . . . . . . . . . . . .. 48
5.2 實驗規劃與結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
第六章結論與未來展望. . . . .. . . . .. . . . .. . . . .. . . . .. . . 55
6.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55
6.2 未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .56

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