一阶直线双倒立摆系统的可控性研究.doc

摘 要

一阶直线双倒立摆是一种欠驱动机械系统，此次设计的目的是能否在保持两个摆杆不倒的前提下，实现小车的位置伺服控制。在设计中通过对一阶直线双倒立摆系统的工作机理及其数学模型的建立，了解可控性的含义和Fcn模块的应用。通过恒等变形的方法来消除代数环，减少迭代计算量使仿真的速度更快。通过Matlab/Simulink软件对控制系统建模，并用Simulink绘制系统动态结构图分析两摆杆质量相同，摆角< （摆角的初始值为 ），摆长变化时的仿真结果。论证了一阶直线双倒立摆系统的可控性只与两个摆的摆长有关，对于形状不规则的摆杆而言也同样适用。

关键词：一阶倒立摆；线性化；可控性；仿真


 


 


 


 


 


 


 


 


 


 


 


 


 




Abstract


First-order linear double inverted pendulum is an underactuated mechanical system, The purpose of this design is achieving the car's position servo control whether keeping both of the pendulum booms is stand. Through building the mathematical model and working mechanism of the first-order linear double inverted pendulum system, understanding the meaning of controllability and applying of Fcn module. In order to reducing the amount of iterative calculation to make the simulation faster, through the method of identical deformation to eliminate the algebraic loop. Through Matlab / Simulink software to building the control system model and drawing the dynamic structure of system with Simulink to analysis the simulation results when the double pendulums in the same quality and swing angle less than ten angle (the initial value of swing angle is zero angle). Demonstrating the first-order linear double inverted pendulum system’s controllability only related to  the length of the pendulums and the same to irregular shape pendulums.

Keywords: first-order inverted pendulum; linear; controllability; simulation


 


 


 


 


目 录

引  言 1

第一章 倒立摆系统概述 2

1.1 单倒立摆概述 2

1.2 双倒立摆概述 3

第二章 MATALAB概述 5

2.1 MATLAB简介 5

2.2 MATLAB主要特点 6

第三章 可控性概述 8

第四章 一阶直线双倒立摆系统的可控性研究 10

4.1 一阶直线双倒立摆系统数学模型的建立 10

4.2 系统数学模型的线性化 12

4.3 模型验证 13

4.3.1 精确模型的验证 14

4.3.2 模块封装 17

4.3.3 仿真验证 21

4.4 线性化之后的模型的验证 22

4.5 仿真实验 25

结  论 26

参考文献 27

谢  辞 28