Based on Fuzzy Basis Function of Model Reference Adaptive Controller Design

基於模糊基底函數之參考模式適應控制器之設計

蔡樸生(Pu-Sheng Tsai) ； 陳珍源(Jen-Yang Chen)

《中華技術學院學報》 27期 (2003/05) Pp. 72-82

https://doi.org/10.7095/JCIT.200305.0072

摘要

本文將提出一種基於模糊基底函數的參考模式適應控制器之架構。首先以模糊基底函數來學習與逼近未知或不確定的非線性系統，然後結合適應控制與強健控制的理論，在李雅普諾夫穩定條件下設計控制法則，使得系統響應能夠追隨參考模型的軌跡。根據Stone Weierstrass定理証實模糊基底函數可近似任何一個連續函數之特性，本文嘗試以模糊基底函數來代表系統模型中的未知參數，並且將適應控制中的鑑別問題由系統模式參數轉為基底函數的線性組合參數。利用這些線性組合參數，以系統與參考模型間的追蹤誤差與參數估測誤差作為李雅普諾夫函數，所推導的控制法則與適應律對於時變的非線性系統確可獲得良好的追蹤效果。此外，當歸屬函數訂得不夠多時，系統參數的估測將會產生近似誤差，這些近似誤差加上外界的干擾將直接影響控制精度。有鑑於此，在控制法則中將引入強健控制的觀念，企圖涵蓋所有不確定因素與雜訊源。經由電腦模擬顯示，本文所提出的參考模式適應控制器之架構不僅能夠有效地追蹤參考模型的軌跡，並可將近似誤差與外來干擾的影響衰減至容忍的範圍之內。

關鍵字

模糊基底函數 ； 參考模式適應控制器 ； 李雅普諾夫穩定條件 ； 強健控制

並列摘要

This paper presents the structure of model reference adaptive control based on fuzzy basis function. Initially, the techniques of fuzzy basis function are introduced to approach uncertain (or unknown) nonlinear systems. In addition, a heuristic adaptive algorithm, which is robust feature under the Lyapunov stability criterion so that the output of the plant tracks a reference model output or follow another signal. As a result, the linear combination of the fuzzy basis function can approximate any nonlinear continuous function to any arbitrary accuracy that is substantiated by the Stone Weierstrass theorem. We use the linear combination coefficients to represent unknown system parameters and change the identification problem from identifying the original unknown parameters to the combination coefficients. The adaptive law based on tracking error and prediction error is presented and performance better can be expected than traditional MRAC in a time-varying nonlinear system. Furthermore, the effect of fuzzy logic approximation error will appear gradually when the number of the membership function is not enough. Therefore, a desired tracking performance cannot be guaranteed for a class of uncertain systems with external disturbances. In view of this, we impose a robust law in order to eliminate the influence of uncertain sources and approximation error. Two examples are given to illustrate the performance of the proposed method. Computer simulation results confirm that the proposed method not only satisfied tracking performance, but it also is vigorously robust.

並列關鍵字

Fuzzy Basis Function ； Model Reference Adaptive Control ； Lyapunov Stability Criterion ； Robust Control