倒立摆论文：倒立摆 粒子群 LQR 模糊控制 实时控制

【关键词】倒立摆 粒子群 LQR 模糊控制 实时控制

【英文关键词】Inverted pendulum PSO LQR Fuzzy control Real-time control

倒立摆论文：基于粒子群优化的二级倒立摆控制研究

【中文摘要】倒立摆系统是一个多变量、强耦合、自然不稳定的高阶非线性系统，研究它的控制设计具有很大的意义。一方面可以反映许多控制理论中的经典问题，如系统鲁棒性问题、镇定问题、跟踪问题；另一方面对于军事工业、航天仪器、机器人领域和一般工业进程也有着很高的理论指导意义，是控制理论与实际应用的桥梁；倒立摆系统作为检验各种控制算法和控制理论的典型实验装置，为检验控制器设计方法的有效性做了重要贡献。本文以直线二级倒立摆系统为研究对象，将粒子群算法应用到传统控制理论和智能控制理论当中，设计了基于粒子群优化的二级倒立摆LQR最优控制器和基于粒子群优化的二级倒立摆模糊控制器，并对倒立摆实物系统进行了实时控制。具体研究内容如下：1）介绍倒立摆系统的和研究现状，运用拉格朗日方程建立二级倒立摆系统的数学机理模型，并在平衡点附近进行线性化处理得到其状态空间方程，运用线性控制理论对其进行定性分析，证明了直线二级倒立摆系统的自然不稳定性和平衡位置附近的能控能观性。2）介绍LQR最优控制和粒子群算法的基本原理。利用粒子群算法所具有的智能式搜索、渐进式优化，快速收敛等特点，获

取Q、R的全局最优解，从而设计状态反馈控制律K，实现基于粒子群算法优化的二级倒立摆LQR控制器设计，并仿真验证了控制方法的有效性。3）利用LQR控制器设计的状态反馈控制率K，设计信息融合函数，将系统输入变量降维，然后将粒子群算法的强大优化功能应用到比例因子和加权因子的选取当中，实现了基于粒子群优化的二级倒立摆模糊控制器设计，并通过仿真验证了控制方法的有效性。最后对所设计的两种控制器进行了仿真对比分析，结果表明基于粒子群算法优化的模糊控制器具有更好的稳定性和鲁棒性。4）在MATLAB实验平台上运用所设计两种控制器对二级倒立摆进行实时控制，结果表明两种控制器都能够很好的镇定实物系统，都具有一定的鲁棒性。

【英文摘要】The inverted pendulum system is a multi-variable, strong coupling, natural instability and higher ordernonlinear system. On the one hand, the inverted pendulum system control can reflect classic problems ofcontrol theory, such as the robustness, stabilization and tracking problem. On the other hand, it has a hightheoretical guiding significance for the military industry, aerospace equipment, robotics and general industrialprocesses. Moreover, it sets up a bridge between control theory and practical application. Inverted pendulumsystem is the typical experimental setup for testing various control algorithms and control theory, so it

makesan important contribution to the effectiveness of the test controller design method.In this thesis, we have studied the linear double inverted pendulum system. By using the traditionalcontrol theory and the theory of intelligent control with particle swarm optimization (PSO), we

haverespectively designed the LQR optimal controller and the fuzzy controller based on particle swarmoptimization for double inverted pendulum. Finally, the real-time control test is made for inverted pendulumphysical system. The detailed contents are as follows:1) Firstly, we introduce the research background and status quo for inverted pendulum system andestablish the mathematical mechanism of the double inverted pendulum model by using the Lagrange equation.Then based on the linear processing, we get the state space equation at the neighborhood of the equilibriumpoint and have qualitative analysis using the linear control theory. Finally, the natural instability of a straightline double inverted pendulum system is proved as well as the controllability and observe-ability near theequilibrium position.2) The basic principle of the LQR optimal control and PSO is described in this paper. By using theintelligent search, incremental optimization and fast

convergence characteristics of the PSO, we can get theglobal optimal solution of Q and R and then design state feedback control K to achieve the double invertedpendulum controller design based on particle swarm optimization LQR. Simulation results have shown theeffectiveness of the design method.3) Based on the state feedback control K, we have designed information fusion function in order to reducethe dimension of the system input variables. Then the powerful optimization features of the PSO can beapplied to the selection of the scale factor and weighting factor. Therefore, a fuzzy controller is designed fordouble inverted pendulum based on particle swarm optimization and the effectiveness of the control method isverified by simulation. Finally, by simulating comparative analysis on the two controllers, results have shownthat the fuzzy controller based on particle swarm optimization has better stability and robustness than another.4) We have carried out the real-time control in MATLAB experiment platform for the two controllers. Theresults suggest that both of the two controllers can stabilize the double inverted pendulum system and haverobustness as well.

【目录】基于粒子群优化的二级倒立摆控制研究

摘要

3-4ABSTRACT4第一章 绪论7-111.1 倒立摆

系统的研究背景和意义77-8

1.2 倒立摆系统的研究现状

1.4 本文结

1.3 倒立摆系统的主要控制方法8-9

9-11

构及主要研究内容及性能分析11-2211-15

第二章 二级倒立摆数学模型的建立

2.1 二级倒立摆数学模型的建立

2.3

2.2 二级倒立摆数学模型的线性化15-18

二级倒立摆线性模型的性能分析18-22化的二级倒立摆 LQR 控制器设计22-38原理22-2626-29

第三章 基于 PSO 优3.1 LQR 最优控制的

3.2 LQR 控制反馈系统的稳定性分析3.3 粒子群算法的基本原理29-31

3.4 基于

PSO 对加权矩阵 Q,R 的选取31-34立摆 LQR 控制器仿真实验34-38二级倒立摆模糊控制器设计38-5738-40函数39-40

3.5 基于 PSO 优化的倒第四章 基于粒子群优化的4.1 信息融合技术39

4.1.2 构造融合4.2.1 定义输

4.1.1 信息融合技术的原理

4.2 模糊控制器设计40-45

40-41

入输出变量及其论域41-43过程4545-47

4.2.2 定义隶属度函数

4.2.4 精确化

4.2.3 确定模糊推理规则43-45

4.3 基于粒子群算法优化模糊控制器参数4.4 运用 matlab 软件设计控制器47-49

4.5 4.6 仿

基于 PSO 优化的二级倒立摆模糊控制仿真结果49-51真结果对比分析51-57

4.6.1 控制效果对比

51-534.6.2 鲁棒性能对比53-57第五章 倒立摆系统

参考文献

的实时控制57-6162-64

附录

第六章 结论与展望61-6264-66

致谢66