改进蛙跳算法的LQR控制器的优化设计

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Title:

Optimal design of the LQR controller based on the improved shuffled frog-leaping algorithm

作者:

彭勇¹, 陈俞强^1,2

1. 东莞职业技术学院 计算机工程系, 广东 东莞 523808;
2. 广东工业大学 自动化学院, 广东 广州 510006

Author(s):

PENG Yong¹, CHEN Yuqiang^1,2

1. Department of Computer Engineering, Dongguan Polytechnic, Dongguan 523808, China;
2. Faculty of Automation, Guangdong University of Technology, Guangzhou 510006, China

关键词:

LQR控制器; 倒立摆; 改进蛙跳算法; 优化设计; 权矩阵

Keywords:

LQR controller; inverted pendulum; improved shuffled frog-leaping algorithm; optimal design; weight matrices

分类号:

TP18

DOI:

10.3969/j.issn.1673-4785.201305055

摘要:

针对多变量、非线性、强耦合性的倒立摆系统, 运用牛顿-欧拉方法建立了倒立摆的数学模型, 然后对该模型分别进行LQR控制。在 LQR 控制中, 权矩阵 Q和 R 的选取直接影响着结构的动力反应和控制力。在标准蛙跳算法对权矩阵 Q 和 R 进行优化的基础上, 通过采取新的最差青蛙跳跃策略能有效提高算法的全局搜索能力, 同时加入自适应跳跃因子以加快算法的收敛时间。仿真实验表明, 该算法能有效地获得最优的权矩阵 Q 和 R, 使LQR控制效果能够满足结构性能要求。

Abstract:

Based on the inverted pendulum system which is multi-variable, nonlinear and strong coupling, a mathematical model of the inverted pendulum is established by utilizing the Newton-Euler method, and then the LQR control is implemented for the model. The weighted matrices Q and R have a direct impact on the dynamic response and control of the single inverted pendulum. During optimization of the matrices Q and R through use of the standard shuffled frog-leaping algorithm, the new worst frog jumping strategy can effectively improve the global search ability of the algorithm and the adaptive jump factor can speed up the convergence. The simulation experiment shows that the improved shuffled frog-leaping algorithm can effectively obtain the optimal weight matrices Q and R; as a result, the effect of the LQR controller meets the performance requirements of the single inverted pendulum.