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題 名 | On Determining the Robust Pole Locations of Uncertain Systems: An LMI Approach=基於線性矩陣不等式法的不確定系統強健極點判定 |
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作 者 | 楊錫凱; | 書刊名 | 中國機械工程學刊 |
卷 期 | 33:2 2012.04[民101.04] |
頁 次 | 頁169-176 |
分類號 | 448.942 |
關鍵詞 | 線性矩陣不等式法; 不確定系統; 強健極點; LMI; Robust pole location; Structured uncertainty; Uncertainty bound; |
語 文 | 英文(English) |
中文摘要 | 本文探討具結構化不確定性系統的強健極點落點,不同於一般系統極點使用線性矩陣不等式區域(LMI-region)進行系統極點落在凸集區域內的判別,本文所研究的強健極點叢集包含著個別的常態極點,因此可以更明確的了解不確定系統的動態。結合了矩陣的譜半徑性質與線性矩陣不等式(LMI)技術,本文針對極點叢集落點問題,建立成為一個LMI的廣義特徵值問題(GEVP),透過Matlab的LMI工具箱,可以迅速得到包圍個別極點叢集的等半徑圓群。接著提出另一種基於LMI最佳化問題的改善步驟,可以更精確的估計出包含個別極點叢集的獨立圓盤半徑。同時亦將此法延伸至不確定系統強健極點落在指定圓盤群所容許不確定參數的變動界限,並將其求解過程建立成另一個LMI的廣義特徵值問題,最後並以一範例驗證運用所提出的方法的可行性。 |
英文摘要 | This paper addresses the problem of determining the robust pole locations of systems with structured uncertainties. Different from the researches using methods based on the LMI-region, the bound of the pole cluster around each nominal system pole is studied, which can provide more clear dynamic information of uncertain systems. Utilizing the matrix spectral radius property and the linear matrix inequality (LMI) method, the problem of determining the discs of equal radius which contain the pole clusters of the uncertain system is formulated as an LMI generalized eigenvalue problem (GEVP). An improved method is then proposed for obtaining a more accurate estimate of the individual discs containing each pole cluster using an LMI eigenvalue optimization approach. Finally, the problem of determining the perturbation bounds which ensure that the robust pole clusters remain within certain pre-specified discs is formulated as another LMI GEVP. The validity of the proposed approach is demonstrated by way of a numerical example. |
本系統中英文摘要資訊取自各篇刊載內容。