摘要：倒立摆是一种强耦合、多变量、非线性的不稳定系统，被作为典型的被控对象，一直广受控制界学者的研究。本课题分别采用基于牛顿力学的动力学建模方法与基于Lagrange方程的动力学建模方法对一级倒立摆系统进行数学建模，并对两种建模方式进行了比较。课题采用基于Mamdani模糊控制方法对倒立摆系统的摆杆角度和小车位移进行控制，其中模糊控制器设计为有四个输入变量一个输出变量，模糊控制器的输入变量依次为摆角、角速度、小车位移、小车速度；输出变量为作用在小车上的控制力。同时研究了量化和比例因子对倒立摆系统控制效果的影响，并利用Matlab对该控制策略进行了离线仿真实验，通过仿真波形，可以知道该控制策略有较好的控制效果，具有控制器响应速度快、超调量较小、鲁棒性强、稳定性好等优势，得到的动态和静态的效果都较好。但是，在采用基于Mamdani模糊控制方法对一级倒立摆系统进行实时控制时，得到的控制效果还有待改进。6440
关键词：一级倒立摆；数学建模；模糊控制；Matlab仿真
Design of Single-stage inverted pendulum fuzzy control system
Abstract: Inverted pendulum is a strong coupling, multivariable, nonlinear and unstable system, which is used as a typical controlled object and has been popular with scholars of control industry. The dynamic modeling method based on Newton's mechanics and dynamics modeling method based on Lagrange equations to mathematical modeling of single inverted pendulum system are used in this issue, and the comparison between the two kinds of modeling methods is proposed. The fuzzy control method which is based on the Mamdani is used to control the swinging rod angle and displacement of car of single inverted pendulum system in this issue. The fuzzy controller contains four inputs and one output, the inputs are :pendulum Angle, angular velocity, and displacement of the car, vehicle speed; and the output is the control force to the car. Meanwhile  the effect of quantification and proportion factors is also considered. Then used Matlab to simulate offline, from the simulation waveform, the control effect is showed,  this control strategy has faster response speed, smaller overshoot, stronger robustness, better stability and other advantages, the dynamic and static effects are better. However, when using this fuzzy control method to control single inverted pendulum in real time, the control effect remains to be improved.
Keywords: single inverted pendulum；mathematical modeling；fuzzy control；Matlab simulation
目 录
1 绪论    1
  1.1 本课题的研究意义    1
  1.2 倒立摆的工作原理    1
  1.3 倒立摆的研究发展概况    2
  1.4 倒立摆控制策略综述    2
2 倒立摆系统建模    4
  2.1 倒立摆系统的建模    4
  2.2 基于牛顿力学的动力学建模    5
  2.3 基于Lagrange方程的动力学建模    9
  2.4 两种建模方式的比较    10
  2.5 倒立摆实际系统模型    11
3 模糊控制的基本理论    13
  3.1 模糊控制理论简介    13
    3.1.1模糊控制理论的发展简介    13
    3.1.2模糊控制理论的基本概念    13
  3.2 模糊控制器原理    17
  3.3 模糊控制器的设计    18
  3.4 模糊控制器的特点与局限性    19
  3.5 模糊控制改进方法    19
    3.5.1自校正模糊控制    19 Matlab一级倒立摆的模糊控制系统设计仿真:http://www.751com.cn/zidonghua/lunwen_3990.html