摘要倒立摆系统是一个典型的多变量、非线 性、强耦 合和快 速运动的自然不稳定系统。研究双足机 器 人直立行走、火箭发射的姿态调整和直升机飞行控制领域的倒立摆系统具有重要的现实意义。在航天、机器人学习及我们平时生活中很多方面都有运用，这也就是倒立摆具有如此重要现实意义的原因。75059

本文运用极 点配 置的方法，实现用状 态反 馈对一级倒立摆的控制。运用相关原理等建立一级倒立摆的状态反馈系统的数学模型，分别对小车和摆进行受力分析，并应用等效小车概念，将状态方程写出，然后进行线性化处理，最后运用极点 配 置，得到变 量 系 数阵。设计状 态控 制 器，应用Matlab来设计一个一级倒 立摆的状态反馈系统的仿 真，最后进行详细分析。得出最终结论，仿真结果证明控制器不仅使得倒立摆系统稳定，还能使小车定位在特 定位 置。

该论文有图7幅，表4个，参考文献20篇

毕业论文关键词：倒立摆  状态反馈  极点配置

The Investigation of the inverted pendulum based on state-feedback control

Abstract Inverted pendulum system is a typical multi variable, nonlinear, strong coupling and fast movement of the natural unstable system。 The research on the vertical walking of biped robot, the attitude adjustment of rocket launching and the inverted pendulum system in the field of helicopter flight control has important practical significance。 In aerospace, robotics and our usual life in many aspects of the application, which is inverted pendulum has such an important practical significance。

In this paper, the method of pole assignment is used to realize the control of a single inverted pendulum with state feedback。 Based on relevant theories, such as the establishment of an inverted pendulum state feedback system mathematical model, carries on the stress analysis respectively of the cart and pendulum, and the application of the concept of equivalent car, the state equations are written out, then linearization treatment。 Finally, using pole allocation, the variable coefficient matrix are obtained。 Design of state controller, the application of Matlab to design an inverted pendulum state feedback system simulation, and finally a detailed analysis。 Finally, the simulation results show that the controller can not only make the inverted pendulum system stable, but also make the car positioned in a specific location。 

This paper has 7 figures,4tables,20 references。

Key Words: Inverted pendulum  State feedback  Mole placement

目  录

摘  要 I

Abstract II

目  录 III

图清单 IV

表清单 IV

变量注释表 V

1 绪论 1

  1。1 倒立摆系统的研究意义 1

  1。2 倒立摆系统的国内外现状 2

  1。3 本文的主要内容 3

2 一级倒立摆数学模型的建立 4

  2。1 倒立摆系统的物理结构与建模 4

  2。2 倒立摆的控制方法 8

3 状态反馈控制器的设计 12

  3。1 系统参数设定 13

  3。2 系统能观性和能控性 14

  3。3 极点配置理论