基於片段式LYAPUNOV 函數的模糊動態系統 之H∞輸出迴授控制器設計

H∞ OUTPUT FEEDBACK CONTROLLER DESIGN OF FUZZY DYNAMIC SYSTEM BASED ON PIECEWISE LYAPUNOV FUNCTION

陳建宏(Chien-Hung Chen)

指導教授 ： 龔宗鈞

大同大學/電機資訊學院/電機工程學系所/碩士(2004年)

摘要

本論文提出一個基於片段式Lyapunov 函數的動態模糊系統之H∞輸出迴授控制器
設計。首先，我們使用動態模糊系統去表示一個複雜的連續時間系統。其次，基於這個
動態模糊系統，建構一個以觀察器為基礎的模糊H∞控制器使得片段式連續Lyapunov函
數能被用來建立全域穩定性而且具有要求的H∞排除外部擾動條件。根據所提出的解耦
合技巧以及兩個階段的步驟，整個以觀察器為基礎的模糊H∞控制器的問題，可以化成
兩個線性矩陣不等式的形式，一個是對控制器而言，另一個則是對觀察器而言。而線性
矩陣不等式的解是可以利用商業軟體得到非常有效的解答。
最後，我們應用此以觀察器為基礎的模糊¥ H 控制器去控制一個球及橫桿的系統，
以及一個倒單擺的系統。而模擬結果可以證明所提出的方法是有其應用性。

關鍵字

片段式LYAPUNOV函數 ； 模糊動態系統 ； H∞ 控制

並列摘要

This thesis presents an H∞ fuzzy output feedback control design method for fuzzy dynamic systems based on a piecewise Lyapunov function. First, we use the fuzzy dynamic model to represent a complex continuous-time system. Next, based on the fuzzy dynamic model, a fuzzy observer-based H∞ controller is developed to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous Lyapunov function can be used to establish the global stability with a desired H∞ disturbance rejection constraint. By the proposed decoupling technique and two-stage procedure, the overall fuzzy observer-based H∞ control problems are parameterized in terms of two linear matrix inequalities (LMIs)— one for controller and the other for observer. The LMIs can be solved very efficiently using commercially available
software.
Finally, we apply the fuzzy observer-based H∞ controller to control a ball-beam system (BB-system) and an inverted pendulum system, the simulation results demonstrate the applicability of the proposed method.

並列關鍵字

fuzzy dynamic system ； H∞ control ； piecewise lyapunov function

參考文獻

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