东 北 大 学 2008 年 6 月
A Thesis in Control Theory and Control Engineering
Research on Fuzzy Control for Double Inverted Pendulum
By Chen Zewang
Supervisor : Professor Gao Xianwen
分类号 UDC
密 级
学 位 论 文
二级倒立摆系统的模糊控制研究
作 者 姓 名 ： 陈泽望 指 导 教 师 ： 高宪文 教授 东北大学信息科学与工程学院 申请学位级别： 硕士 学 科 类 别 ：工学
学科专业名称： 控制理论与控制工程 论文提交日期： 2008 年 6 月 学位授予日期： 评 阅 人 ： 李界家 教授 论文答辩日期： 2008 年 7 月 答辩委员会主席：王建辉 教授 王小刚 副教授
关键词：倒立摆；模糊控制；融合函数；T-S 模型；逐级控制
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Research on Fuzzy Control for Double Inverted Pendulum
Abstract
Inverted pendulum is a typical high order system that is fleet, multivariable, nonlinear, strong coupling and absolutely instable. The research on theories and methods of the inverted pendulum's control is of extensive significance in many fields such as walking of biped robots, launching process of rockets and flying control of helicopters. Several fuzzy control strategies are employed to solve the contradiction between the control performance and the number of fuzzy rules, aiming to control double inverted pendulum effectively in this thesis. Firstly, the development situation and trend of fuzzy control are discussed briefly and the development course and research status of inverted pendulum are summarized in this thesis. The structure and work principle of double inverted pendulum are introduced. Nonlinear mechanism model of it and its linearization model in equilibrium are obtained by means of Lagrange equation. Performances, such as stability, are analyzed for linearization model. Secondly, linear quadratic optimum control, fuzzy control, and their mutual combination are discussed systematically. Several fuzzy control strategies are studied. Information fusion which is based on fuzzy control strategy reduces the dimension of its input vectors and solves the problem of rule number's explosion by combining the linear system theory with information fusion technique. Takagi-Sugeno based gradual fuzzy control strategy, which has fewer and more effective rules and can greatly simplify the design process of fuzzy controller, is adopted to stabilize the double inverted pendulum. Finally, the simulation model of double inverted pendulum system is edited by compiling S function in Matlab/Simulink and some simulations are carried out. Simulation results indicate that the fuzzy control strategies proposed in this thesis can not only solve the problem of fuzzy rule number's explosion and simplify the design process of fuzzy controller, but also obtain better performance in control of the double inverted pendulum.
Key words: Inverted Pendulum; Fuzzy Control; Fusion Function; T-S Model; Gradual Control
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东北大学硕士学位论文
目 录
目 录
独创性声明 .................................................................................................................................I 摘 要 ......................................................................................................................................... II ABSTRACT ............................................................................................................................ III 第 1 章 绪论 .............................................................................................................................. 1 1.1 课题的研究背景和意义 ..................................................................................................... 1 1.2 模糊控制的研究概况 ......................................................................................................... 1 1.2.1 模糊控制的产生 ...................................................................................................... 1 1.2.2 模糊控制的研究现状与发展趋势 .......................................................................... 2 1.3 倒立摆控制系统研究概况 ................................................................................................. 4 1.3.1 倒立摆控制系统的产生 .......................................................................................... 4 1.3.2 倒立摆控制系统的研究现状与发展趋势 .............................................................. 5 1.4 本文的主要工作 ................................................................................................................. 7 第 2 章 倒立摆系统建模与现代控制策略分析 ...................................................................... 9 2.1 二级倒立摆系统的结构及工作原理 ................................................................................. 9 2.2 二级倒立摆系统的数学建模 ............................................................................................. 9 2.2.1 倒立摆系统建模假设 .............................................................................................. 9 2.2.2 符号说明 .................................................................................................................. 9 2.2.3 系统建模 ................................................................................................................ 11 2.3 二级倒立摆系统的运动模态 ........................................................................................... 15 2.4 二级倒立摆非线性模型的线性化 ................................................................................... 15 2.5 二级倒立摆系统的性能分析 ........................................................................................... 17 2.6 二级倒立摆系统的最优状态反馈控制 ........................................................................... 19 2.7 基于线性化模型的仿真 ................................................................................................... 20 2.8 本章小结 ........................................................................................................................... 22 第 3 章 模糊控制方法研究 .................................................................................................... 23 3.1 模糊控制理论简介 ........................................................................................................... 23 3.1.1 模糊控制的特点 .................................................................................................... 23 3.1.2 模糊控制器的工作原理 ........................................................................................ 24 3.2 模糊融合技术与融合函数 ............................................................................................... 24 3.2.1 融合技术 ................................................................................................................ 25 IV