以座標轉換為基礎的多目標控制器合成方法

淡江大學機構典藏 > 工學院 > 電機工程學系暨研究所 > 學位論文 > Item 987654321/52493

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Title:	以座標轉換為基礎的多目標控制器合成方法
Other Titles:	Coordinate- transformation-based multi-objective controller synthesis
Authors:	朱彥碩;Chu, Yen-shou
Contributors:	淡江大學電機工程學系碩士班周永山
Keywords:	座標轉換;H2/H∞ 控制;降階;多目標;線性矩陣不等式;coordinate transformation;H2/H∞ control;reduced order;Multi-Objective;linear matrix inequality
Date:	2010
Issue Date:	2010-09-23 17:51:23 (UTC+8)
Abstract:	本論文主要研究H2/H∞多目標控制器合成問題。1997年Scherer等人所提出的連續時域LMI解法是為人稱道的有效方法，但其受限於單一的李亞普諾夫變數，有所謂的共同P問題。目前的最新技術，在離散時域有學者Oliveira等人，引進額外的變數，即所謂的參數相關李亞普諾夫函數方法，證實可減少多目標控制問題LMI解法的保守性，但並沒有完全脫離共同P問題的窘境。另外也有演化計算的方法，利用大量的計算，來逼近全域最佳解。此方法雖然沒有上述共同P問題，但是必須耗費大量的運算時間與成本。本論文提出一種新型方法，稱為「以座標轉換為基礎的多目標控制器合成方法。此方法無上述共同變數的限制，而與一般熟知的雙線性矩陣不等式(Bilinear Matrix Inequality, BMI)解法相比較，求解新控制器時，有一額外的自由變數可協同求解，故可搜尋其未能搜尋的解空間。當以這些現存方法之最佳解作為本文方法之初始控制器，此方法可作為提昇現有方法性能之用。另外，本論文提出的座標轉換技術，在很容易滿足的假設條件下，可將BMI問題轉換為含特殊格式座標轉換的“LMI問題”，可作為各種系統性能的新型有解條件。本論文提供數個數值例子，包括連續時域H2/H∞多目標控制與H∞降階控制、離散時域多目標控制問題。模擬結果驗證了本文方法使用不同初始控制器的影響、效能，並與前述方法作完整的比較。 This thesis revisits the H2/H∞ multi-objective control problem. The continuous-time LMI method developed by Scherer at al. in 1997 is well recognized as a powerful tool for solving these sorts of problems. However, this approach suffers from the constraint of a single common Lyapunov function for the multiple performance specifications, known as the common P problem. One of the state-of-the-art techniques includes the method developed by Oliveira et al.,known as the Parameter-Dependent Lyapunov Function method. The method introduces a slack variable into the condition which has been proven to be useful for reducing conservatism. But it is known that the problem remains. Alternatively, there is an approach using evolution algorithm to search for a good solution at the expense of a large amount of computation cost, though no aforementioned problem exists. The thesis proposes a new method, named Coordinate-Transformation-based Multi-objective Controller Synthesis (CTMCS), which is free of the aforementioned common variable constraint. When compared with the well-known BMI method, an additional free variable exists in the step of searching for new controllers. This degree of freedom is useful for exploring the solution space which has never been touched by the aforementioned LMI methods. As a result, the proposed method can serve as a performance-enhanced approach when the solutions of the aforementioned methods are used as initial controllers. In addition, this thesis presents a coordinate-transformation technique which, under mild assumption, transforms a BMI problem into a LMI problem. Consequently, the resulting conditions serve as new solvability conditions for the various system performance analysis problems. In this thesis several numerical examples involving the continuous-time H2/H∞ control problem, H∞ educed-order controller design, and the discrete-time control problem are provided for illustration. A thorough comparison with the aforementioned methods is made.
Appears in Collections:	[電機工程學系暨研究所] 學位論文

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