- 學位論文
模糊控制之全域穩定分析與追蹤控制
Global Stability Analysis for Fuzzy Systems and Tracking Control
摘要
T-S 模糊模式(T-S fuzzy model)，是近幾年來廣泛使用於處理非線性系統的控制方法之一。此種模糊模式可將非線性系統以模糊理論中的IF-THEN規則庫來取代且其推論部為線性方程式的型式為他的主要特色，而且此模式化方式可近似或完整的表示原非線性系統。在設計控制器上使 用所謂平行分布補償(PDC)的概念並利用線性系統的方法，最後將穩定性分析的問題轉換為線性矩陣不等式(LMIs)的型式並用Matlab 去求解。在討論T-S 模糊模式時，我們所探討的大都僅僅限於區域穩定，在討論區 域穩定時，首先提出線性矩陣不等式(LMIs) 有解並不代表整個模式區域皆穩定，隨後提出如何找出這個穩定的區域，最後並提出全域穩定的條件。在追蹤控制上，我們藉由一些技巧可將原本複雜的追蹤系統轉換成比較簡單的型式。在此追蹤控制上，我們知道要量測所有的狀態在實際 的系統中是不太可能，所以在此我們使用估測器來量測這些不可量測的狀態。在現實的情況中，系統的內部部分狀態如果不可得知，可能會造成控制器或估測器的前件部的變數狀態跟著無法得知，而這變數狀態必須取決於估測器，這是我們最後探討的課題。
並列摘要
Recently, there has been a rapid growing interesting in using T-S fuzzy model to approximate nonlinear system. The T-S fuzzy model which originates from Takagi and Sugeno mainly deals with the nonlinear systems. With using this model, the nonlinear system is represented by several fuzzy subsystems in fuzzy IF-THEN rules where the con-sequent part is linear dynamical equation. Blending these IF-THEN rules, we can exactly represent the original nonlinear system. When consider the controller and observer design, we use the conception of parallel distributed compensation (PDC) to carry out these designs. We discuss the stability analysis of T-S fuzzy systems by using the Lyapunov's direct method. The sufficient conditions are formulated into linear matrix inequalities (LMIs). Typically, the stability analysis is investigated in local region due to the local sector nonlinearity. We introduce the concept of region of model and region of stability to characterize the stability property. The stability region can be obtained by using the level set of Lyapunov function. In addition, a global stability condition is addressed. As a second part of thesis, we discuss the tracking control of nonlinear systems by using T-S fuzzy model. To cope with the problem of immeasurable states, the observer-based fuzzy controller is our main concern. An H 1 performance criterion is proposed to attenuate the disturbance due to immeasurable premise variables. Furthermore, an asymptotical tracking can be achieved when the disturbance is with a Lischitz-type property. All the stability conditions and the derivation of control gains are converted into LMIs problems which can be solving by Matlab’s toolbox.