直线一级倒立摆的PID和LQR控制及其仿真

KEY WORDS： Linear inverted pendulum, Control, PID, LQR, simulation
BY NB GONG
II
华北电力大学毕业设计（论文）
目
录
摘 要 ........................................................................................................................................... I ABSTRACT ..................................................................................................................................... II 第 1 章：绪论 .................................................................................................................................. 1 1.1 倒立摆简介......................................................................................................................... 1 1.1.1 倒立摆分类.............................................................................................................. 2 1.1.2 倒立摆的特性......................................................................................................... 2 1.1.3 倒立摆的控制目标................................................................................................. 3 1.1.4 倒立摆的控制方式................................................................................................. 3 1.2 倒立摆控制研究的发展及其现状.................................................................................... 4 1.3 本文的主要内容................................................................................................................ 7 第 2 章：直线一级倒立摆系统数学模型....................................................................................... 8 2.1 直线一级倒立摆系统的物理模型.................................................................................... 8 2.2 直线一级倒立摆系统的数学模型.................................................................................... 9 2.3 直线一级倒立摆系统的系统分析.................................................................................. 12 2.3.1 直线一级倒立摆系统的系统稳定性分析 ........................................................... 12 2.3.2 直线一级倒立摆系统的系统能控性、能观性分析 ........................................... 14 第 3 章：直线一级倒立摆系统的 PID 控制及仿真..................................................................... 16 3.1 PID 控制概述 .................................................................................................................... 16 3.2 PID 的控制规律、原理 .................................................................................................... 17 3.3 PID 参数整定 .................................................................................................................... 17 3.4 直线一级倒立摆双闭环 PID 控制算法 ........................................................................... 18 第 4 章：直线一级倒立摆系统的线性二次最优控制及仿真..................................................... 24 4.1 线性二次最优控制简介.................................................................................................. 24 4.2 直线一级倒立摆 LQR 控制算法及仿真 ......................................................................... 26 结 论 ........................................................................................................................................ 35 参考文献 .......................................................... 36 致 谢 ........................................................................................................................................ 38
Inverted pendulum system is a typical fast, multivariable, nonlinear, unstable system, and many abstract concepts of control theory can be inverted pendulum through the visual show. Therefore, the inverted pendulum system is often used to test the practical effect of control strategies. Application, the inverted pendulum control is widely used in aerospace, robots, acrobatic performances mandrill areas of precise control of inverted pendulum control of the industrial complex object also has important engineering applications. In this paper, solid line of high-level company as the research object inverted pendulum on an inverted pendulum model of linear modeling, control algorithm simulation comparison, and conclusions are drawn. This paper introduces the classification of inverted pendulum, characteristics, control objectives, control methods and the development of an inverted pendulum control and the status quo. Using Newton mechanics pushed to the linear inverted PU pendulum dynamic model, find the transfer function and state space equation. E C N ir.inverted The establishment of a system model basis, we study the pendulum n e v u control strategy, on the first line uses a classic inverted d so pendulum control algorithm, e t a the design of conventional PID controller, du dual loop PID controller, and use a r g MATALAB / Simulink simulation ce- software, with varying control results. Then the u d o use of advanced modern Pr control methods, design based on second-order LQR e c i l controller o optimal ya control theory, with MATALAB simulation, by changing the state R LQR space module and the module parameters in the simulation debugging, the best control effect. By comparing the PID control method and the LQR control method of control in the simulation results, the paper obtained under the conditions permit, the modern control methods to control than classical control better than many.
PU E C ir.N n e 在建立了系统模型的基础下，本文还研究了倒立摆系统的控制策略，对直线 v ou s d e 一级倒立摆首先采用了经典控制算法，设计了常规 PID 控制器、双闭环 PID 控制 uat d a r e-g 器，并且利用 MATALAB/Simulink 软件进行仿真，取得了不同的控制效果。然后 c u d o Pr 采用先进的现代控制方法，设计了基于二阶最优控制理论的 LQR 控 制 器 ， 借 助 e c i l a y o R MATALAB 仿真，通过改变 LQR 模块及状态空间模块中的参数，在仿真调试中，得
华北电力大学毕业设计（论文）
摘
要
倒立摆系统是一个典型的快速、多变量、非线性、不稳定系统，许多抽象的 控制理论概念都可以通过倒立摆实验直观的表现出来。因此，倒立摆系统经常被 用来检验控制策略的实际效果。应用上，倒立摆广泛应用于航空航天控制、机器 人、 杂技顶杆表演等领域， 研究倒立摆的精确控制对工业复杂对象的控制也有着 重要的工程应用价值。 本文以固高公司直线一级倒立摆为研究对象，对直线一级倒立摆模型进行了 建模，控制算法的仿真对比，并得出了相应结论。 文中介绍了倒立摆的分类、特性、控制目标、控制方法等以及倒立摆控制研 究的发展及其现状。 利用 Newton 力学方法推到了直线一级倒立摆的动力学模型，
求出其传递函数及其状态空间方程。 到最好的控制效果。 件允许的情况下，现代控制方法比经典控制方法控制效果要好很多。
通过对比 PID 控制方法和 LQR 控制方法在仿真中的控制效果，本文得到在条
关键词：直线一级倒立摆、控制、PID、LQR、仿真
BY NB GONG
I
华北电力大学毕业设计（论文）
ABSTRACT