平面运动n级倒立摆的鲁棒保成本模糊控制  

Robust Guaranteed Cost Fuzzy Control for Planar n-order Stage Inverted Pendulums

作　　者：苗志宏[1] 李洪兴[2] 

机构地区：[1]中国人民武装警察部队学院消防工程系,河北廊坊06500 [2]大连理工大学电信学院,辽宁大连116024

出　　处：《模糊系统与数学》2014年第3期62-74,共13页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61374118)

摘　　要：针对参数不确定平面运动n级倒立摆系统,研究了鲁棒保成本模糊控制器设计问题。给出了将系统动力学模型转化为一种新型广义T-S模糊模型的方法,由此避免了求逆矩阵的过程。为获得保守性更低的系统稳定性设计条件,通过引入松弛变量矩阵来解耦Lyapunov函数中的系统矩阵,增加了设计条件的自由度。然后讨论了最优鲁棒保成本模糊控制器的设计条件,并将这些条件转换成了线性矩阵不等式(LMI)的凸优化问题。最后,在仿真实验中以平面运动二级倒立摆系统为例验证了本文方法的有效性。For a class of planar n-order inverted pendulums（PnIP） with parameter uncertainties, Design strategy of robust guaranteed cost fuzzy controller is discussed. Firstly, a new method which transform dynamic model of PnlP into a new-type fuzzy descriptor system is proposed, which avoids the complexities of matrix inversion. In order to reduce the conservativeness in stability analysis of fuzzy control systems, slack matrix variables are introduced to decouple the Lyapunov matrices from the system matrices, which provides extra degrees of freedom to the stability conditions. Then, the design conditions of optimal robust guaranteed cost fuzzy controller are obtained, and these are changed into a convex optimization problem in terms of linear matrix inequalities （LMI）. Finally, a numerical example for planar double inverted pendulums is given to illustrate the effectiveness of the proposed approach.

关 键 词：倒立摆 保成本控制 广义T-S模糊模型 线性矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]