文档介绍：摘要
一阶直线倒立摆是一个典型的“快速、多变量、非线性、自不稳定系统”,对一阶倒立摆系统的稳定性研究在理论上和方法上具有深远的意义。对一阶倒立摆的研究可以归结为对非线性、多变量、不稳定系统的研究。在应用上,一阶倒立摆广泛应用于控制理论研究、航空航天控制等领域,在自动化领域中具有重要的价值。
本文首先是建立一阶倒立摆的数学模型,并且采用的是双闭环控制系统,通过对一阶倒立摆的双闭环控制系统数学模型的分析,将模糊控制方法应用于一阶倒立摆的控制问题,其中,内环控制倒立摆的摆角,外环控制倒立摆的位置。采用模糊控制器的设计包括隶属函数及模糊控制规则、解模糊,最后利用MATLAB软件进行仿真实验。模糊控制方法应用于一阶倒立摆系统的控制中,能够发挥模糊控制在非线性系统的控制、复杂对象系统控制方面的优势,简化设计,提高系统的鲁棒性。
关键词:一阶倒立摆,数学模型,模糊控制,MATLAB
Abstract
The first-order linear inverted pendulum is a typical “fast, multivariable, nonlinear, unstable system”, for an inverted pendulum system stability research in theory and method has the profound significance. For an inverted pendulum can boil down to the research on nonlinear, multivariable, unstable system research. In application, an inverted pendulum is widely used in control theory, aerospace control and other fields, in the field of automation has important value.
This paper is to establish a mathematical model of the inverted pendulum, and using the double closed-loop control system, through the inverted pendulum double closed-loop control mathematical model analysis, a fuzzy control method is applied to an inverted pendulum control, Wherein, the inner control of the inverted pendulum swing angle, the outer loop controls the position of inverted pendulum. Fuzzy controller design including the membership function and fuzzy control rule, fuzzy solution, finally using the Matlab software simulation. The fuzzy control method is applied to an inverted pendulum control system, fuzzy control can play in the control of nonlinear system, complex object systems control advantages, simplify the design, improve the stability of system.
Key words: Inverted pendulum,Mathematical model,Fuzzy control,Matlab
目录
摘要 I
Abstract II
1 绪论 1
一阶倒立摆系统研究的意义 1
一阶倒立摆系统在国内外研究综述 1
本论文的研究内容和所用方法 2
2 一阶倒立摆数学模型的建立与控制系统 3
一阶倒立摆的数学模型 3
一阶倒立摆系统的动力学分析 4
系统微分方程的线性化 5
系统微分方程状态空间表示 6
一阶倒立摆定性分析 7
系统的稳定性、能控性和能观测性判据 7
基于状态方程的系统定性分析 8
一阶倒