在真實生活中，風力發電系統可能受到各種因素的影響，例如外在的干擾、機器零件的耗損、重要參數的變化等，造成輸出行為並不如我們所預期的情況。本論文先以強韌控制理論的觀點來分析文獻[1]中所提出的新型風力發電系統，並建立系統的數學模型、不確定性的考量及H∞最佳化控制器的設計，再進一步探討系統電阻不匹配所造成輸出有弦波行為時，藉由二次積分限制的架構來解決這個問題。

本論文所預期達到的控制目標為風能最大功率追蹤控制和系統定轉速追蹤控制。當系統發生不匹配的情形下，我們先把原系統的系統矩陣做適當的轉換，將可能影響輸出行為的因子併入不確定性因素的一項，此時可得到一組新的系統矩陣，之後我們再利用二次積分限制的方法來規範輸出弦波的行為，並以適當的H∞最佳化控制器的設計來達到本論文的控制目標。根據實驗結果顯示，以二次積分限制方法所設計出來的控制器確實能有效抑制輸出所發生的弦波行為，使系統在發生不匹配的情況下，還是能達到良好的輸出表現。

In the real world, a wind turbine generator system may be affected by various uncertain factors, such as external disturbances, wear loss of the individual components, variation of critical parameters, etc., which may result in unexpected reduced performance. In this thesis, we consider control design problem if a new wind turbine generator system, which was introduced in [1]. Based on the robust control point of view, we establish a mathematical model with structured uncertainties for the system. A robust control is then designed based on the H∞ norm minimization principle. Moreover, the problem caused by the resistance mismatch is also addressed and handled under the integral quadratic constraint framework.

The principle design objective considered in this thesis is to ensure the maximal power tracking and maintaining a constant rotational
speed - and hence a constant frequency of the electrical power output. In case the resistance mismatch occurs, the system equations governing the power generation are transformed in such a way that the periodic time-varying terms appearing as part of the structured uncertainties in feedback interconnection with a nominal dynamics. Integral quadratic constraints are then utilized to characterized these uncertainties and an H∞ optimal controller is designed based on the resulting robust stability criterion. The simulation results shows that the H∞ optimal controller designed by this approach renders satisfactory performance.

論文審定書i
誌謝ii
中文摘要iii
英文摘要iv
目錄v
符號表vii
第 1 章 緒論 1
1.1 研究背景 1
1.2 研究動機、目的與貢獻 3
1.3 論文架構 4
第 2 章 預備知識 5
2.1 帕克轉換5
2.2 線性化 6
2.3 強韌控制理論 8
2.3.1 H∞範數 8
2.3.2 小增益定理(Small-gain theorem) 8
2.3.3 不確定性 9
2.3.4 線性分式變換 9
2.3.5二次積分限制(IQC) 11
2.3.6 H∞ 最佳化控制器 12
第 3 章 風力發電系統的數學模型 13
3.1 創新型激磁式風力發電系統簡介 13
3.2 各系統微分方程式 14
3.2.1 馬達電氣方程式 14
3.2.2 發電機電氣方程式 17
3.2.3 系統的整體機械方程式 18
3.3 解決方法 19
3.3.1 消除時變項 19
3.3.2 消除非線性項 20
3.3.3 不確定性因子 23
第 4 章 控制器設計與模擬驗證 27
4.1 設計架構 27
4.2 iqc muti harmonic 37
4.3 Simulink模擬與結果 43
第 6 章 結論與未來展望 50
5.1 結論 50
5.2 未來展望 50
參考文獻 51

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