臺灣博碩士論文加值系統

本文說明如何最小化特徵值的幅度與相位靈敏度合成的量，再示以分析數位控制器封閉迴路系統的穩定性。控制器參數因四捨五入運算和計算誤差所造成的定點運算之不確定性可以表示為字長 (word length) ；我們可透過小增益定理以及 Bellman- Grownwall 定理於定點統計模型基礎上之封閉迴路穩態標準。此一結合了與控制器參數有關的封閉迴路特徵值的幅度與相位靈敏度之量測值，為最小化並建立在混合於matrix-2/ Frobenius 之規範中；接著我們便可以從建立於最小化量測的代數分析方法裡，取得最佳化的相似轉換；利用此相似轉換式以及穩態標準，我們可以得到最少的字長。

This note presents an approach to analyze the stability of the closed-loop system for digital controller implementations by minimizing a measure synthesized by the magnitude and phase sensitivities of eigenvalues.
First, uncertainties of the controller parameters using fixed-point arithmetic caused by roundoff and computational errors are expressed as a function of word length. Then, a stability criterion of the closed-loop system based on fixed-point statistical model is derived by means of small gain theorem and Bellman-Grownwall Lemma. Thus, a measure that combines the magnitude and phase sensitivities of the closed-loop system eigenvalues with respect to controller parameters is constructed and is minimized in the sense of mixed matrix-2/Frobenius norms.
Then an optimal similarity transformation is obtained from an analytically algebraic method based on this minimum measure. Using this transformation as well as the stability criterion, a least word length can be obtained. Finally, an example is performed to illustrate the effectiveness of the proposed scheme.

中文摘要 i
Abstract i
目錄 i
表目錄 i
第一章 緒論 1
1.1 前言 1
1.2 研究方法 1
1.3 論文架構 1
第二章 問題公式化以及定點運算 1
第三章 定點控制器執行穩態分析 1
第四章 封閉迴路系統裡幅度與相位靈敏度特徵值 1
第五章 最佳化控制器執行轉換式 1
第六章 實際的數值範例 1
第七章 結論 1
參考文獻 1
誌謝 1

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