一级倒立摆的设计

论文编号:ZD992    论文字数:15898,页数:44

摘   要
 倒立摆系统是一种典型的复杂难控系统，对倒立摆的研究可归结为对非线性多变量、绝对不稳定系统的研究，其控制方法和思路无论对理论或实际的过程控制都有很好的启迪，是检验各种控制理论和方法的有效的“试金石”。倒立摆系统是机电一体化系统，其机械部分遵循牛顿的力学定律，电气部遵循电磁学的基本定理。因此，我们可以先通过机理建模方法得到较为准确的数学模型对其进行仿真，通过实验测量来获取系统模型参数。本次实验运用反馈控制原理，对输出量于参考量进行比较，并且将它们的偏差量作为控制手段。采用极点配置法，配置到理想极点使得系统的主导闭环节点具有所期望的阻尼比和无阻尼自然频率。
 本次实验利用Matlab求得系统的状态反馈增益矩阵，通过Simulink对倒立摆系统进行建模仿真。再利用Labview作为反馈控制系统的界面设计开发工具，执行倒立摆系统各程序功能。
 
 
 关键词：倒立摆，数学模型，反馈控制，极点配置，Matlab，Simulink仿真，Labview
 

 Abstract
   Inverted Pendulum System（IPS）is a type of typical complex hard-control system. The research on it can be representative of that on a nonlinear, multivariable, absolute unstable system. The method and thought for controlling it is very useful to the control theory and process control. It can check control theories and methods effectively. IPS is an inte- gration of mechanical and electrical systems, which the mechanical part of Newton''s mechanics to follow the law, the Department of Electrical Electromagnetic follow the basic theorem. Therefore, we may first obtain the more accurate mathematical modeling through the mechanism modeling method to carry on the simulation to it, gains the system model parameter through the experimental survey. The experiment use the feedback principle, compare with the output in the reference quantity, and the deviation of them as a means of control. Based on pole-placement, the pole will deploy an expectative point, making the leading closed-loop system nodes have the desired damping ratio and non-damping natural frequency.
  This experiment use the Matlab obtained a system designed by the state feedback gain matrix, stands upside IPS on the modeling and simulation by Simulink. Labview selected as a feedback control system interface design and development tools, carries out IPS various program function.
 
 
 Keywords: Inverted Pendulum System, mathematical modeling, pole-placement, feedback control, matlab，Simulink simulation, Labview.

 摘要  
 Abstract…………………………………………………………………………Ⅱ
 第一章 引言…………………………………………………………………….1
 1.1倒立摆的系统及其研究意义…………………………………………………….1
 1.2倒立摆系统的研究状况………………………………………………………....2
 1.3倒立摆系统控制研究的特点及难点……………………………………………...3
 1.4本次试验的内容…………………………………………………………...........4
 第二章 倒立摆系统及硬件设计………………………………………………..5
 2.1倒立摆的系统结构结构与分类…………………………………………………..5
 2.2系统的整体设计框架…………………………………………………………....6
 2.3倒立摆实验装置及工作原理……………………………………………………..7
 第三章 数学模型推导及建立………………………………………………......9
 3.1模型推导的理论依据…………………………………………………………….9
 3.2一级倒立摆数学建模的建立……………………………………………………..9
 3.3 倒立摆系统开环稳定性判断……………………………………………………13
 第四章  一级倒立摆系统的控制设计…………………………………….......15
 4.1控制方法——状态反馈控制…………………………………………………….15
 4.2可控性与可观性判断……………………………………………………………15
 4.3达到性能指示的方法……………………………………………………………16
 4.4反馈矩阵的求得………………………………………………………………...16
 4.5系统闭环的仿真与响应…………………………………………………………17
 4.6线性二次型最优控制……………………………………………………………21
 第五章  LabVIEW软件介绍………………………………………………….23
 5.1 LabVIEW简介………………………………………………………………….23
 5.2 LabVIEW程序介绍……………………………………………………………..24
 第六章 一级倒立摆LabVIEW设计及外部连线……………………………..26
 6.1在labVIEW中创建A、B、C矩阵………………………………………………26
 6.2数据的采集……………………………………………………………………..26
 6.3数据的分析与处理……………………………………………………………...28
 6.4数据输出及显示………………………………………………………………...28
 6.5控制器界面与程序框图…………………………………………………………29
 第七章 实验倒立摆装置……………………………………………………….32
 7.1外部结构……………………………………………………………………….32
 7.2微分电路……………………………………………………………………….32
 7.3检测电路……………………………………………………………………….33
 7.4功率放大电路与运放调零电路…………………………………………………..34
 7.5直流稳压电源………………………………………………………………......34
 第八章 调试实现……………………………………………………………….36
 8.1硬件和软件设置………………………………………………………………...36
 8.2调试步骤……………………………………………………………………….36
 第九章 倒立摆的问题及误差分析…………………………………………….37
 9.1倒立摆系统非线性问题…………………………………………………………37
 9.2倒立摆系统的误差分析…………………………………………………………38
 第十章 总结………………………………………………………………………………39
 致谢……………………………………………………………………………...40
 参考文献：………………………………………………………………………40