## 二阶倒立摆系统的控制问题研究

Abstract Inverted pendulum control system is a nonlinear, complex, strong coupling, natural unstable system. Study of inverted pendulum system can effectively solve typical problems in control system, such as robustness, tracking. Main problem of the inverted pendulum control is to make the swinging rod with the fastest speed to achieve an equilibrium position, and let the pendulum rod no oscillation and excessive speed and Angle. When swinging rod reaches the equilibrium position, the system can effectively overcome random disturbance and maintain in a stable position.
In order to realize the steady pendulum control, it uses the state space pole assignment and LQR theory, so as to design the first-order inverted pendulum system of two kinds of controller. And then the two kinds of controller use MATLAB simulation, and compare the result of the simulation data. These two kinds of control theory can be very good to control.

Keywords: Inverted pendulum   Nonlinear   LQR   State-space                                                                        Pole allocation    Simulation

Abstract    II
1 绪 论    1
1.1 相关研究背景    1
1.1.1 倒立摆系统的控制目标    1
1.1.2 倒立摆的实际应用    1
1.1.3 倒立摆系统稳定性研究的意义    1
1.2 倒立摆系统研究现状    2
1.3 倒立摆的相关特点    3
2 倒立摆系统的建模与定性分析    5
2.1 了解单级倒立摆系统    5
2.2 一级倒立摆系统模型的建立    5
2.2.1 微分方程的推导    6
2.2.2 状态空间的推导    8
3 基于LQR的一级倒立摆的稳摆控制    11
3.1 引言    11
3.2 LQR理论    11
3.3 LQR控制算法分析    12
3.4 倒立摆LQR控制器的设计    13
4 状态空间极点配置理论    16
4.1 引言    16
4.2 能控性和能观性    16
4.2.1 能控性判据    17
4.2.2 能观性判据    18
4.3 基于状态反馈的极点配置理论    19
4.3.1 问题的提法    19 源`自<六:维*论-文>网/www.lwfree.cn
4.3.2 单输入反馈极点配置    20
4.3.3 多输入反馈极点配置    22
5 设计一级倒立摆控制器    24
5.1 引言    24 二阶倒立摆系统的控制问题研究:http://www.lwfree.cn/zidonghua/20191013/40795.html
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