離散型T-S模糊系統的穩定設計條件放寬之研究

機構典藏 > College of Engineering > Graduate Institute & Department of Mechanical and Electro-Mechanical Engineering > Research Paper > Item 987654321/47061

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Title:	離散型T-S模糊系統的穩定設計條件放寬之研究
Other Titles:	Relaxed Stabilization Criteria for T-S Fuzzy Discrete Systems
Authors:	孫崇訓
Contributors:	淡江大學機械與機電工程學系
Keywords:	T-S 模糊系統;穩定條件放寬;控制輸入限制;T-S fuzzy system;relaxed stability conditions;control input constraint
Date:	2009
Issue Date:	2010-04-15 16:11:08 (UTC+8)
Abstract:	基於T-S 模糊模型（T-S fuzzy model）與李亞普諾夫定理（Lyapunov Theorem）的模糊控制設計已被廣泛的分析與應用在許多實際系統。一般來說，用較多的模糊規則來表示的T-S 模糊模型會與實際系統更為近似。但是當模糊系統中的規則數過多時，即使是使用線性矩陣不等式的軟體工具，也不一定能找到適合的李亞普諾夫函數。換句話說，太多的模糊規則數會導致穩定條件太過嚴格。之前的研究已證實，在穩定性分析方面，藉由離散模糊系統中觸發規則群的觀念和最大狀態間距的分析，能夠放寬穩定性條件。然而在穩定性設計中，由於最大狀態間距的分析與控制器設計並沒有辦法同時進行，因此現有的解決方法常將最大狀態間距分析與控制器設計以疊代的方法反覆計算以求出適合的解。為了解決此控制設計的缺點，本計劃目標為提出一個在考慮觸發規則群與最大狀態間距的前提下能一次求出控制器增益值的方法，取代最大狀態間距分析與控制器設計的疊代計算，並同時符合控制輸入的限制需求。最後我們將此研究結果以電腦模擬貨運拖車的倒退控制，證明能在較寬鬆的穩定條件下設計控制器，並保證系統隨時在滿足控制輸入限制。 Recently, based on T-S fuzzy model and Lyapunov theorem, the fuzzy control issues have been extensively investigated. In general, the more rules there are, the smaller modeling error is. However, while the number of rules of a fuzzy system is large, the Lyapunov function may not be found even by LMI tool. It means that large fuzzy rules induce conservative stability conditions. By adopting ideas of group-fired rules and the maximal width of states step, we have derived more relaxed stability criteria for discrete T-S fuzzy models in previous studies. However, in stabilization issue, the analysis of maximal states step width and controller design cannot be done simultaneously. Presently, scholars solve this problem by computing the maximal states step width and control gains iteratively. In the other hand, some studies design the fuzzy controller with control input constraint. In practical applications, indeed, the driver circuit limits control gains. The limitation of control gains can estimate the maximal states step width. Therefore, if the controller design is with control input constraint, one should reduce the iterative computing efforts of the maximal states step width and control gains. This project is trying to propose a novel methodology to design the controller with ideas of group-fired rules and the maximal width of states step. This novel methodology can reduce the computing effort of present stabilization method. Finally, we will demonstrate the effectiveness of this idea by the simulation of backing up control of truck.
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