倒立摆系统的模糊控制仿真研究

摘要倒立摆作为一个被控对象，具有高阶次、不稳定、多变量、非线性、强耦合的特性，也因此成为自动控制实验中验证控制算法优劣的极好的实验装置。本文采用了模糊控制对一级倒立摆系统进行控制，对于倒立摆的建模，本文采用分析力学中的拉格朗日方程来建立其动力学方程，相较于传统的牛顿力学定律建模，模型复杂度降低。而对于模糊控制器的设计，本文采用了 TS模糊模型，由于其后件采用线性函数的形式，类似于多模型的结构使得其在物理意义上更容易让人理解，而且相对于其他模糊模型，其每条规则包含更多的信息，对于倒立摆这种复杂系统能够采用更少规则来表达系统更多特性。最后，本文采用了Matlab进行了仿真，并与状态反馈控制进行对比，经过分析可以发现该控制方法对倒立摆的控制效果良好。 22523
毕业论文关键词倒立摆模糊控制 TS模糊模型 Matlab仿真
Title    Simulation and research on fuzzy control for inverted   pendulum system
Abstract
Inverted pendulum is a controlled object with higher-order, unstable,
multivariable, nonlinear and strong coupling features. Thus it has become
an excellent experimental device to test the merits of the control
algorithm in automatic control experiments.
In this paper, fuzzy control method is used to control a single inverted
pendulum system. For the model of inverted pendulum, this paper uses the
Lagrange equations of analytical mechanics to build its kinetic equations.
Compared to the traditional laws of Newtonian mechanics modeling, model
complexity is reduced. As for the fuzzy controller design, this paper uses
the TS fuzzy model, because the subsequent pieces is not only in the form
of a linear function, so that similarity to multi-model structure makes
it easier for the people to understand the physical sense, but also relative
to other fuzzy models, each rule contains additional information, so that
a complex system like inverted pendulum is able to express more features
with fewer rules. Finally, using the Matlab simulation, and compared with
conventional control method, the simulation results show that the control
method has good control effectiveness on inverted pendulum.
Keywords    inverted pendulum fuzzy control TS fuzzy model Matlab simulation
目   次

1 绪论 . 1
1．1 倒立摆系统的研究意义 . 1
1．2 倒立摆研究现状 . 1
1．3 本文内容概述    2
2 倒立摆的数学模型 . 4
2．1 理论分析 . 4
2．2 状态空间方程    7
2．3 系统性能分析    8
3 模糊控制系统设计 . 9
3．1 T-S模糊模型简介    9
3．2 倒立摆的T-S模糊模型    11
3．3 模糊控制器设计    13
4 控制系统的仿真 .. 15
4．1 Matlab计算状态空间方程 . 15
4．2 局部线性化状态空间方程的可控性 .. 18
4．3 局部线性状态空间方程反馈增益的求解 . 18
4．4 模糊控制器设计    19
4．5 Simulink仿真 .. 27
结论 . 36
致谢 . 37
参考文献 .. 38
1 绪论
1．1 倒立摆系统的研究意义倒立摆系统的模糊控制仿真研究:http://www.751com.cn/zidonghua/lunwen_15199.html