摘 要

一階直線雙倒立擺是一種欠驅(qū)動(dòng)機(jī)械系統(tǒng)，此次設(shè)計(jì)的目的是能否在保持兩個(gè)擺桿不倒的前提下，實(shí)現(xiàn)小車的位置伺服控制。在設(shè)計(jì)中通過(guò)對(duì)一階直線雙倒立擺系統(tǒng)的工作機(jī)理及其數(shù)學(xué)模型的建立，了解可控性的含義和Fcn模塊的應(yīng)用。通過(guò)恒等變形的方法來(lái)消除代數(shù)環(huán)，減少迭代計(jì)算量使仿真的速度更快。通過(guò)Matlab/Simulink軟件對(duì)控制系統(tǒng)建模，并用Simulink繪制系統(tǒng)動(dòng)態(tài)結(jié)構(gòu)圖分析兩擺桿質(zhì)量相同，擺角< （擺角的初始值為 ），擺長(zhǎng)變化時(shí)的仿真結(jié)果。論證了一階直線雙倒立擺系統(tǒng)的可控性只與兩個(gè)擺的擺長(zhǎng)有關(guān)，對(duì)于形狀不規(guī)則的擺桿而言也同樣適用。

關(guān)鍵詞：一階倒立擺；線性化；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 錄

引  言 1

第一章 倒立擺系統(tǒng)概述 2

1.1 單倒立擺概述 2

1.2 雙倒立擺概述 3

第二章 MATALAB概述 5

2.1 MATLAB簡(jiǎn)介 5

2.2 MATLAB主要特點(diǎn) 6

第三章 可控性概述 8

第四章 一階直線雙倒立擺系統(tǒng)的可控性研究 10

4.1 一階直線雙倒立擺系統(tǒng)數(shù)學(xué)模型的建立 10

4.2 系統(tǒng)數(shù)學(xué)模型的線性化 12

4.3 模型驗(yàn)證 13

4.3.1 精確模型的驗(yàn)證 14

4.3.2 模塊封裝 17

4.3.3 仿真驗(yàn)證 21

4.4 線性化之后的模型的驗(yàn)證 22

4.5 仿真實(shí)驗(yàn) 25

結(jié)  論 26

參考文獻(xiàn) 27

謝  辭 28