连续非线性系统的模糊控制

连续非线性系统的模糊控制

摘要

与传统控制相比，模糊控制具有两大不可比拟的优点：其一，它在许多应用中可以有效且便捷的实现人的控制策略和经验；其二，它可以不需要被控对象的数学模型即可实现较好的控制。在控制领域，模糊系统主要用来作为非线性函数的逼近工具。日本学者Takagi和Sugeno在1985年提出的Takagi-Sugeno(T-S)模糊模型，给模糊控制理论研究及应用带来了深远的影响，使模糊系统稳定性分析上升到新的理论高度，且有许多结果已经应用于实际对象中。T-S模糊模型的优点在于它充分运用了Lyapunov稳定性理论来进行系统分析和控制器设计，通过对非线性系统进行T-S模糊建模，建立起相应的模糊T-S模糊系统。在此基础上，调整选取合适的模糊规则及隶属度函数，使得模型逼近原非线性系统。

采用Lyapunov稳定性原理对系统的稳定性进行分析，得到系统稳定的充要条件。通过Matlab工具箱中的LMI工具箱，得到系统控制器的解。

关键词：非线性系统，模糊控制，并行分布补偿算法（PDC），稳定性，线性矩阵不等式（LMI），

Fuzzy Control of Continuous Nonlinear Systems

ABSTRACT

Compared with the tradition control, fuzzy control's having two greatly can not compare of merit: firstly, it can be effective in many applications and conveniently she carries out the person's control strategy and experience; secondly, it need not be charged the mathematical models of object can immediately carry out better control affection. In control realm, the fuzzy system mainly usage is an approaching of non- liner function tool. Japanese scholar Takagi and Sugeno in 1985 suggested Takagi-Sugeno (T-S) fuzzy pattern, give fuzzy control theory the search and application brought profound impact and made the misty system stability analysis up to a new theory high, and have many result have already been applied to actual object amid. The merit of T-S fuzzy pattern lay in it to make the most of Lyapunov stability theory to carry on systematic analysis and control T-S model based fuzzy logic system is composed of Japanese scholars Takagi T and Sugeno M made in 1985. T-S fuzzy system has many attractive features: the system part of the antecedent of fuzzy rules is ambiguous; the latter part is determined by piece. The proposal to make such systems theory of fuzzy systems has been strengthened, and the precision of such systems can approximate a n arbitrary nonlinear system.

Uses the lyapunov stable principle to carry on the analysis to system's stability, obtains the system stable necessary and sufficient condition. Through Matlab's LMI toolbox, obtains system controller's solution.

KEY WORDS: Nonlinear system, Fuzzy control, Parallel Distributed Compensation (PDC), Stability, Linear Matrix Inequality (LMI)

目录

前言 (1)

第1章引言 (4)

1.1模糊控制的产生及其发展 (4)

1.1.1 模糊控制理论的产生 (4)

1.1.2 模糊控制技术的发展 (5)

1.1.3 模糊控制应用领域及现状 (8)

1.1.4 模糊控制的研究成果 (9)

第2章T-S模糊模型建模 (12)

2.1 T-S模型建模 (12)

2.1.1T-S模糊模型简述 (12)

2.1.2 T-S模糊模型建模 (12)

第3章T-S模糊模型控制器设计 (15)

3.1 T-S模糊模型控制器设计 (15)

3.1.1 PDC并行分布补偿算法 (15)

3.1.2模糊控制器的设计 (16)

第4章系统渐近稳定条件 (17)

4.1李雅普诺夫稳定性理论 (17)

4.1.1稳定性的几个定义 (17)

4.1.2Lyapunov第一法 (17)

4.1.3 Lyapunov第二法 (19)

4.2连续时间T-S模糊系统的稳定性分析 (22)

第5章仿真实验 (25)

5.1 MATLAB及LMI工具箱简介 (25)

5.1.1 MA TLAB软件简介 (25)

5.1.2 LMI工具箱简介 (28)

5.2算例仿真实验 (30)

结论 ................................................................ 错误！未定义书签。谢辞 (38)