本論文目的是設計一廣義預測控制器 (Generalized Predictive Control, GPC) 控制輸入燃料電池的氫氣流量，使得氫氣流量能在燃料電池輸出功率不同時，依然能快速地到達其適合的大小，一可節省氫氣流量，二可避免輸入過少的氫氣而損害到燃料電池內部。
　　首先吾人定義一指標函數氫氣過量比為 [ (供給的氫氣質量速率) 除以 (消耗的氫氣質量速率) ] 並以此當做輸入氫氣流量的依據，設計控制器的目的是使氫氣過量比能快速追蹤到設定值。吾人將輸給流量控制器的電壓對氫氣過量比之間複雜的動態假設為一簡單的線性模型，並利用最小平方法確定系統模型，之後經由線上估測系統模型參數並同時由控制器做運算得到控制力。本論文在實際燃料電池系統上證實，在燃料電池輸出功率變動時，經由此方法氫氣過量比仍可快速追蹤到設定值。

This thesis proposes an adaptive control approach to regulate the hydrogen feed of a fuel cell. The goal of the controller is to maintain the so-called hydrogen excess ratio, defined as the ratio between the hydrogen fed to the cell stake and those consumed in the stake, at a desired level when the fuel cell is under load variation. Maintaining the hydrogen excess ratio
at an appropriate level would avoid hydrogen starvation, which is crucial for slowing degeneration of the fuel cell membranes and prolonging the life of the cell stake.

The control approach we propose is based on the receding horizon linear quadratic optimal control algorithm with an on-line turning scheme which updates the plant model according to real-time measurement. To ease the computational complexity and make real-time turning realizable, we adopt a simple autoregressive with external disturbance (ARX) model to approximate the complicate chemical/electrical process of the fuel cell. The proposed adaptive control approach is implemented
on an experimental platform. The experimental results show that the proposed control works with reasonably good performance.

中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . .i
英文文摘要. . . . . . . . . . . . . . . . . . . . . . . . . .ii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iii
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .v
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii
符號表. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .viii
第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . .1
1.1 研究背景、動機和目的 . . . . . . . . . . . . 1
1.2 文獻回顧 . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 研究成果與貢獻. . . . . . . . . . . . . . . . . . 5
第二章燃料電池簡介與數學模型. . . . . . . .7
2.1 燃料電池的歷史 . . . . . . . . . . . . . . . . . . 7
2.2 質子交換膜燃料電池的原理與構造 . . 7
2.3 燃料電池的數學模型. . . . . . . . . . . . . . 9
2.3.1 電池堆電壓模型. . . . . . . . . . . . . . . . 10
2.3.2 燃料電池陰極流場模型. . . . . . . . . . 14
2.3.3 燃料電池陽極流場模型. . . . . . . . . . 15
2.3.4 薄膜水滲透模型. . . . . . . . . . . . . . . . 17
2.3.5 氫氣過量比 . . . . . . . . . . . . . . .. . . . . 17
第三章系統識別. . . . . . . . . . . . . . . . . . . . .20
3.1 系統識別的目的 . . . . . . . . . . . . . . . . . 20
3.2 系統識別的步驟 . . . . . . . . . . . . . . . . . . 21
3.3 實驗架構與設備 . . . . . . . . . . . . . . . . . . 22
3.4 系統識別實驗. . . . . . . . . . . . . . . . . . . . 25
3.4.1 實驗設計. . . . . . . . . . . . . . . . . . . . . . 25
3.4.2 輸入輸出數據的收集與處理 . . . . . 26
3.4.3 模型結構識別. . . . . . . . . . . . . . . . . . 27
3.4.4 模型參數辨識. . . . . . . . . . . . . . . . . . 28
3.4.5 實驗結果. . . . . . . . . . . . . . . . . . . . . . 29
3.5 線上估測系統模型參數. . . . . . . . . . . . 37
第四章控制器設計. . . . . . . . . . . . . . . . . . . .39
4.1 預測控制的簡介. . . . . . . . . . . . . . . . . . 39
4.2 廣義預測控制理論推導 . . . . . . . . . . . . 41
4.3 廣義預測控制之程序控制 . . . . . . . . . . 45
4.4 控制器模擬 . . . . . . . . . . . . . . . . . . . . . . 46
第五章實驗設計與結果討論. . . . . . . . . . . .51
5.1 實驗設計. . . . . . . . . . . . . . . . . . . . . . . . 51
5.2 實驗結果. . . . . . . . . . . . . . . . . . . . . . . . 53
第六章結論與未來展望. . . . . . . . . . . . . . . .63
6.1 結論. . . . . . . . . . . . . . . . . . . . . . .. . . . . . 63
6.2 未來展望. . . . . . . . . . . . . . . . . . . . . . . . 63
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . .64

[1] J. Pukrushpan, A. Stefanopoulou, and H. Peng, “Control of fuel cell breathing,”
IEEE Control Systems Magazine, vol. 24, no. 2, pp. 30–46, 2004.
[2] 丁寶蒼, 預測控制的理論與方法. 機械工業出版社, 2008.
[3] 林昇佃{,}余子隆{,}張幼珍,翁芳柏,李碩仁,林育才,吳和生,魏榮宗,林修正,賴子珍,曾盛恕,詹世弘, 燃料電池 新世紀能源. 滄海書局, 2006.
[4] Y. Yang, F. Wang, H. Chang, Y. Ma, and B. Weng, “Low power proton exchange
membrane fuel cell system identification and adaptive control,” Journal
of Power Sources, vol. 164, no. 2, pp. 761–771, 2007.
[5] Y. Yang, Z. Liu, and F. Wang, “Model reference adaptive control of a low
power proton exchange membrane fuel cell,” in IEEE Conference on Decision
and Control, pp. 1314–1319, 2007.
[6] F. Wang, Y. Yang, C. Huang, H. Chang, and H. Chen, “System identification
and robust control of a portable proton exchange membrane full-cell system,”
Journal of Power Sources, vol. 164, no. 2, pp. 704–712, 2007.
[7] F. Wang, H. Chen, Y. Yang, H. Chang, and J. Yen, “Multivariable system identification
and robust control of a proton exchange membrane fuel cell system,”
in IEEE Conference on Decision and Control, pp. 6118–6123, 2007.
[8] F. Wang, H. Chen, and J. Yen, “Multivariable lqg control of a proton exchange
membrane fuel cell system,” in The International Federation of Automatic Control,
2008.
[9] R. Mann, J. Amphlett, M. Hooper, H. Jensen, B. Peppley, and P. Roberge, “Development
and application of a generalised steady-state electrochemical model
for a pem fuel cell,” Journal of Power Sources, vol. 86, no. 1-2, pp. 173–180,
2000.
[10] S. Yerramalla, A. Davari, A. Feliachi, and T. Biswas, “Modelling and simulation
of the dynamic behavior of a polymer electrolyte membrane fuel cell,” Journal
of Power Sources, vol. 124, no. 1, pp. 104–113, 2003.
[11] M. Ceraolo, C. Miulli, and A. Pozio, “Modelling static and dynamic behaviour
of proton exchange membrane fuel cells on the basis of electro-chemical description,”
Journal of Power Sources, vol. 113, no. 1, pp. 131–144, 2003.
[12] J. Gruber, C. Bordons, and F. Dorado, “Nonlinear control of the air feed of a
fuel cell,” in IEEE American Control Conference, pp. 1121–1126, 2008.
[13] M. Danzer, S. Wittmann, and E. Hofer, “Prevention of fuel cell starvation
by model predictive control of pressure, excess ratio, and current,” Journal of
Power Sources, vol. 190, no. 1, pp. 86–91, 2009.
[14] J. Gruber, M. Doll, and C. Bordons, “Design and experimental validation of a
constrained mpc for the air feed of a fuel cell,” Control Engineering Practice,
vol. 17, no. 8, pp. 874–885, 2009.
[15] W. Garcia-Gabin, F. Dorado, and C. Bordons, “Real-time implementation of
a sliding mode controller for air supply on a pem fuel cell,” Journal of Process
Control, vol. 20, no. 3, pp. 325–336, 2010.
[16] A. Vahidi, A. Stefanopoulou, and H. Peng, “Model predictive control for starvation
prevention in a hybrid fuel cell system,” in IEEE American Control
Conference, vol. 1, pp. 834–839, 2004.
[17] C. Bordons, A. Arce, and A. Del Real, “Constrained predictive control strategies
for pem fuel cells,” in IEEE American Control Conference, pp. 6–pp, 2006.
[18] A. Arce, D. Ramirez, A. del Real, and C. Bordons, “Constrained explicit predictive
control strategies for pem fuel cell systems,” in IEEE Conference on
Decision and Control, pp. 6088–6093, 2007.
[19] P. Thounthong and P. Sethakul, “Analysis of a fuel starvation phenomenon of
a pem fuel cell,” in IEEE Power Conversion Conference-Nagoya, pp. 731–738,
2007.
[20] J. Kang, D. Jung, S. Park, J. Lee, J. Ko, and J. Kim, “Accelerated test analysis
of reversal potential caused by fuel starvation during pemfcs operation,”
International Journal of Hydrogen Energy, vol. 35, no. 8, pp. 3727–3735, 2010.
[21] A. Taniguchi, T. Akita, K. Yasuda, and Y. Miyazaki, “Analysis of electrocatalyst
degradation in pemfc caused by cell reversal during fuel starvation,”
Journal of Power Sources, vol. 130, no. 1-2, pp. 42–49, 2004.
[22] 黃鎮江, 燃料電池(第三版). 滄海書局, 2008.
[23] 王曉宏,黃宏, 燃料電池基礎. 全華圖書股份有限公司, 2008.
[24] 韓曾晉, 適應控制系統. 科技圖書股份有限公司, 1992.
[25] 龐中華,崔紅, 系統辨識與自適應控制MATLAB仿真. 北京航空航天大學出版社, 2009.
[26] 趙清風, 使用MATLAB控制之系統識別. 全華圖書股份有限公司, 2001.
[27] K. Astrom and B. Wittenmark, Adaptive control. Addison-Wesley Publishing
Company, 1995.
[28] E. Camacho and C. Bordons, Model predictive control. Springer Verlag, 2000.
[29] D. Clarke, C. Mohtadi, and P. Tuffs, “Generalized predictive control–part i. the
basic algorithm,” Automatica, vol. 23, no. 2, pp. 137–148, 1987.
[30] D. Clarke, C. Mohtadi, and P. Tuffs, “Generalized predictive control–part ii
extensions and interpretations,” Automatica, vol. 23, no. 2, pp. 149–160, 1987.
[31] Q. Song and F. Liu, “The direct approach to unified gpc based on armax/
carima/carma model and application for pneumatic actuator control,” in IEEE
First International Conference on Innovative Computing, Information and Control,
vol. 1, pp. 336–339, 2006.
[32] D. Clarke and C. Mohtadi, “Properties of generalized predictive control,” Automatica,
vol. 25, no. 6, pp. 859–875, 1989.