臺灣博碩士論文加值系統

在考慮元件參數變動下，本論文研究降壓型DC-DC轉換器之強健PD控制器設計，使整個閉回路系統在參數變動時，其暫態及穩態規格仍能符合需求。
首先利用狀態空間平均法的觀念，建立轉換器之開迴路小訊號模型、脈波寬度調變器之轉移函數及回授分壓網路之轉移函數。然後，考慮在加入PD控制器之情形下，利用Kharitonov理論，並結合羅斯穩定準則就可以判定在參數變動下，讓整個閉迴路轉換器系統穩定下來的PD控制器參數範圍。由降壓型轉換器分析可知，系統阻尼比參數大於一時，可以獲得較佳之最大超越量及上升時間。因此，本論文藉由Sixteen Plants理論，求出滿足阻尼比之PD控制器參數範圍。透過上述步驟，找出同時滿足穩態及暫態規格之交集，即為所求之控制器參數範圍。除此之外，利用滿足暫態響應規格的阻尼比公式，本論文推導出相對應的LFT模型，再引入結構性奇異值的概念來驗證我們控制器參數的設計範圍是否正確。最後，轉換器加入強健PD控制器後之穩態和暫態響應，以電腦模擬來驗證其改善效果。另外，經由模擬發現，本論文所提之強健PD控制器亦能改善穩態誤差及聲頻感受度，也就是提高輸出電壓位準的準確度及加強抑制雜訊從輸入端耦合到輸出端的能力。

The objective of this thesis is to investigate the design of robust PD controller for the uncertain DC- DC buck converter, provided the transient and steady responses meet the
specifications while the component parameters vary.
At first, the concept of the state-space averaging method is adopted to establish the small signal model of the open-loop converter, and transfer functions of the PWM modulator and feedback voltage-sampling network are derived accordingly. When the PD controller is introduced in the loop, using Kharitonov theorem and Routh-Hurwitz Criterion, the range of the PD controller parameters is found over which the closed- loop converter keeps stability as component parameters vary. For the dynamic analysis of Buck converters, it is known that superior maximum overshoot and rise time can be obtained for the damping ratio of the system is one. Using this fact, Kharitonov Sixteen Plants theorem is applied to find out the range of the PD controller parameters over which the damping ratio is slightly larger than or equal to one. Consequently, the intersection of the obtained ranges indicates where the PD parameters can be assigned to meet the stability and transient specifications. In addition, the derived damping inequality that satisfies the transient specification is converted into the LFT formulation. Then we broach the concept of the structured singular value to verify whether our derived range of the controller parameters is correct or not.
Finally, by using Matlab/Simulink, the dynamic response of the converter with the proposed PD controller is simulated to demonstrate the practicality. The simulation also shows that the robust PD controller proposed in this thesis can improve the steady state error and the audiosusceptibility. It is mean that the robust PD controller improves the accuracy of the output voltage level and enhances the ability of suppressing the noise from input to output.

摘要 Ⅰ
Abstract Ⅱ
目次 Ⅳ
表目錄 Ⅵ
圖目錄 Ⅶ
第一章 緒論 1
1.1前言 1
1.2 研究動機與文獻回顧 2
1.3 論文架構 5
第二章 DC-DC轉換器原理及模型建立、分析 6
2.1 轉換器基本架構 6
2.2 轉換器動作原理 10
2.3 轉換器操作模式 12
2.4 轉換器的穩態和暫態分析 14
2.5 參數變動下轉換器的穩態和暫態分析 21
第三章 強健控制理論介紹 27
3.1 Kharitonov定理 27
3.2 線性分式轉換原理 30
3.3 結構化奇異值介紹 34
第四章 DC-DC轉換器強健PD控制器設計 36
4.1 應用Kharitonov理論於轉換器控制器設計 36
4.2 設計滿足轉換器暫態響應之控制器範圍 42
4.3 阻尼比之LFT建模及控制器參數強健性分析 45
4.4 加入PD控制器之小訊號轉換器性能分析 49
4.5 設計滿足轉換器穩態誤差之控制器範圍 64
4.6 轉換器聲頻感受度探討 69
4.7 加入PD控制器之大訊號轉換器性能分析 74
第五章 結論與未來研究方向 80
參考文獻 82

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