Fuzzy Control Design Based on Fuzzy Modeling

基於模糊辨識之模糊控制器設計

吳德豐(Ter-Feng Wu) ； 蔡樸生(Pu-Sheng Tsai) ； 陳珍源(Jen-Yang Chen)

《宜蘭技術學報》 9期電機資訊專輯 (2002/12) Pp. 191-200

https://doi.org/10.6179/nit.eec.2002.09.29

摘要

本文首先利用蘇吉諾的模糊模型對一非線性系統中的輸入與輸出資料進行辨識，其根據Stone-Weierstrass定理證實，透過模糊推論的過程，模糊系統可精確地逼近任何連續函數。進而提出一套系統之辨識流程，包括以Fuzzy C Mean進行空間分割、以最小平方法作為初始參數之粗調、採用最陡梯度法進行參數微調、最後以一個性能指標函式作為模型評估之標準。最終目標在滿足模型最簡化以及精度上的兩大需求。接著，如何針對一個模糊模型的受控區間來設計一個模糊控制器是本文的第二個研究目的。藉由李雅普諾夫穩定條件與線性矩陣不等式所推導的穩定條件是目前研究的熱門課題，但如何有系統的尋找共同P解，以保證系統在李雅普諾夫下為漸近穩定仍是模糊控制器設計上之瓶頸。本研究將控制器之設計分為兩大步驟，首先將模糊模型中的每一條規則視為一個區域線性狀態方程式，針對每一個線性狀態模型設計相對應的狀態回授控制器。其次是建立一個全域穩定之條件，來取代共同P之求解，並保證所設計之模糊系統為全域穩定之系統。

關鍵字

模糊建模 ； 李雅普諾夫穩定條件 ； 結構辨識 ； 參數辨識 ； 最陡梯度法 ； 線性矩陣不等式

並列摘要

In this paper, we first develop a procedure for constructing Takagi-Sugeno fuzzy systems from input-output pairs to identify nonlinear dynamic systems. The fuzzy system can approximate any nonlinear continuous function to any arbitrary accuracy that is substantiated by the Stone Weierstrass theorem. A learning-based algorithm is proposed in this paper for the identification of T-S models. Our modeling algorithm contains four blocks: fuzzy C-Mean partition block, LS coarse tuning, fine turning by gradient descent, and emulation block. The ultimate target is to design a fuzzy modeling to meet the requirements of both simplicity and accuracy for the input-output behavior. In the second part, we propose a discrete time fuzzy system ”that is composed of a dynamic fuzzy model and a fuzzy state feedback controller. This requires that for all the local linear models, a common positive-definite matrix P can be found to satisfy the Lyapunov stability criterion, although this is an extremely difficult problem for all systems. Thus in this paper, Fuzzy controller design is divided into two procedures. In the first step, we express the fuzzy model by a family of local state space models, and the controller is designed by state feedback control law for each local linear state space model. In the second step, we establish a global stability condition to guarantee the stability of the global closed loop system in order to circumvent the problem of determining the common P.

並列關鍵字

Fuzzy Modeling ； Lyapunov Stability Criterion ； Structure Recognition ； Parameter Identification ； Maximum Gradient Descent ； Linear Matrix Inequality