李亞普諾夫函數應用於倒單擺車之控制

Lyapunov-Function Application to Car-Pole Inverted Pendulum Control

黃政嘉(Cheng-Chia Huang)

指導教授 ： 陳大道

崑山科技大學/工程學院/電機工程研究所/碩士(2007年)

https://doi.org/10.6828/KSU.2007.00001

摘要

這篇論文介紹一種模糊邏輯控制器(FLC)，其為滑動模式控制(SMC)和狀態回授控制(SFC)架構的結合，並且應用它控制倒單擺車系統。模糊控制器將狀態空間劃分成3個子系統，在FLC裡的每個控制法便是一個閉回路子系統。FLC的每個規則在後件部裡不是SMC就是SFC。如此設計的控制架構能降低模糊控制法則數目，並且克服FLC穩定性分析的缺點，並改善滑動控制在狀態空間原點處的抖動現象。如果每個子系統在共通的Lyapunov函數下是Lyapunov意義上穩定的，則整體系統在Lyapunov意義上也是穩定的。因為不含有描述授控體的模糊模型，產生的子系統的數量相當小，並且共通Lyapunov函數能更容易被求得。經過倒單擺控制模擬實驗證明，所提方法是有效且優越的。

關鍵字

李亞普諾夫 ； 模糊邏輯控制 ； 滑動模式控制

並列摘要

This thesis introduces one kind of fuzzy logic controller (FLC) combined by sliding mode control (SMC) and state feedback control (SFC) structure, and applies it to controlling the car-pole inverted pendulum system. State space is partitioned into three subsystems, each rule in the FLC refers to a stable closed-loop subsystem. Each rule in this FLC has a SMC or a SFC in the consequent part. The role of the FLC is to schedule the final control under different antecedents. Thus the controller structure designed can reduce the fuzzy rule numbers, and overcome the disadvantages of stability analysis. If each subsystem is stable in the sense of Lyapunov under a common Lyapunov function, the overall system is also stable in the sense of Lyapunov. Since no fuzzy plant model is involved, the number of subsystems generated is relatively small, and the common Lyapunov function can be found more easily. The effectiveness of the proposed approach is demonstrated under experiment of a car-pole inverted pendulum system.

並列關鍵字

Lyapunov ； sliding mode control ； fuzzy logic control

參考文獻

[1] C. C. Hwang, and S. C. Lin, “A stability approach to fuzzy control design for nonlinear systems,” Fuzzy Sets and Systems 48 (1992)

[2] C. C. Lee, “Fuzzy logic in control systems: Fuzzy logic controller Parts I and II,” IEEE Trans. Syst., Man, Cybern., Vol. 20, pp.

404-435,Mar./Apr. 1990

[3] C. W. Park, and M. Park, “Adaptive parameter estimator based on T-S fuzzy models and its applications to indirect adaptive fuzzy control design,” Information Sciences 159 (2004) 125-139

[5] L. K. Wong, F. H. F. Leung, and P. K. Tam, “Lyapunov Function Based Design of Fuzzy Logic Controllers and Its Application on Combining Controllers,” IEEE Trans. Ind. Electron., Vol. 45, pp.