文档介绍：基于PSO的LQR最优控制器设计及其在倒
立摆控制中的应用
院 系 自动化学院
专 业 自动化
班 级
学 号
姓 名
指导教师
负责教师
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，在研究双足机器人直立行走、火箭发射过程的姿态调整和直升机飞行控制领域 中有重要的现实意义，相关的科研成果己经应用到航天科技和机器人学等诸多领 域。LQR最优控制以其较好的稳定性在倒立摆控制中常被应用。该方法的关键在于 如何选取Q、R加权矩阵，通常要需要多次的反复试探才能得到较满意的结果，极 大地影响了其有效的应用。本文在建立二级倒立摆数学模型基础上，采用粒子群算 法设计Q、R阵，利用其具有的快速收敛、不易陷入局部最优、所需参数少且易于 实现等特点，获取Q、R阵及状态反馈控制率K。二级倒立摆的实验结果表明，该 方法响应速度快、超调小，优化获得的参数使实际控制稳定，证实该方法的有效性 和实用性。
关键词：二级倒立摆；LQR；粒子群算法；控制
Abstract
Inverted pendulum system is multivariable, nonlinear, strong-coupling and naturally unstable. The research of inverted pendulum has many important realistic meaning such as, the upright walking of biped robot, the attitude adjustment of rocket lunching process and the field of helicopter flight control. Related results of scientific research has been applied to space science and technology, and in many fields such as robotics. In the control of inverted pendulum, the LQR optimum control is often applied because of its better stability. The key of this method is that how to select Q and R weighting matrix which usually costs lots of time to obtain satisfying results by trial and efforts. So its effective application is restricted. In this paper, the Particle Swarm Optimization is applied to design Q and R weighting matrix based on the mathematical model of inverted pendulum. With its characteristics of rapid convergence, not a local optimum, the fewer necessary parameters, and easy to achieve, the Q, R weighting matrix and the state feedback control rate K are obtained. Experiments of the double inverted pendulum indicate that this method has quick response speed and small overshoot. The optimized parameters make the actual control stable. Therefore this method has good validity and applicability.
Keywords: double inverted pendulum; LQR; particle swarm optimization; control
符号表
M
小车质量
Mg
摆杆1的质量
mg
摆杆2的质量
Mg
叫
质量块的质量
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摆杆1中心到转动中心 的距离
M
摆杆2中心到转动中心 的距离
m
q
摆杆1与竖直方向的夹 角
m/s
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