## 倾斜导轨上直线倒立摆的智能控制方法研究

Title  Study on the intelligent control method of the linear inverted
pendulum on the inclined rail
Abstract
In this paper, the intelligent stable control of the inverted pendulum on the inclined rail is studied.
Firstly, based on the single and double inverted pendulum system of GoogolTech Company, the inclined single inverted pendulum system is modeled by Newton Euler method and the double is modeled by Lagrange method, and the stability and controllability of the inclined model is analyzed. On this basis, the stable pendulum control of the inclined single and double inverted pendulum system is carried out by using LQR algorithm. The optimal control of different inclination angels is obtained. After simulation in MATLAB environment, the design algorithm is applied to the inclined single inverted pendulum system, the validity of the algorithm is tested. The paper also designs the fuzzy stable controller for the inclined single inverted pendulum system. And the MATLAB simulation and actual system experiments are carried out for various inclination angels of the rail, to verify the validity of the control algorithm. Finally, the results of the simulation and experiment are compared and analyzed. 源`自*六)维[论*文'网www.lwfree.cn
Keywords  Inclined inverted pendulum  Modeling  LQR  Fuzzy control
目   次
1  绪论 1
1.1  倒立摆系统的研究意义 1
1.2  倒立摆系统的常用控制方法与现状 1
1.3  本文的主要研究内容 2
2  倾斜倒立摆的建模和分析 3
2.1  固高倒立摆系统概述 3
2.2  倾斜一级倒立摆的建模及分析 4
2.3  倾斜二级倒立摆的建模及分析 8
2.4  本章小结 12
3  线性二次调节器（LQR） 13
3.1  线性二次调节器（LQR）的简介 13
3.2  倾斜一级倒立摆的线性二次调节器（LQR）设计 14
3.3  倾斜二级倒立摆的线性二次调节器（LQR）设计 20
3.4  本章小结 27
4  模糊控制 28
4.1  模糊控制的简介 28
4.2  倾斜一级倒立摆的模糊控制器设计 30
4.3  本章小结 35
5  倾斜一级倒立摆实验 36
5.1  基于LQR的倾斜一级倒立摆实验 37
5.2  基于模糊控制器的倾斜一级倒立摆实验 41
5.3  本章小结 45

1  绪论
1.1  倒立摆系统的研究意义

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