环形二级倒立摆H∞鲁棒控制器设计及仿真

王东云， 廖雷， 王海泉, 张强

（中原工学院 电子信息学院，河南 郑州 450007）

摘要：研究了环形二级倒立摆的平衡控制，首先利用拉格朗日动力学方法建立了环形二级倒立摆的数学模型，分析了系统的稳定性及能控能观性；接着引入H∞回路成形鲁棒方法设计其控制器，但考虑到H∞控制器阶次过高的问题，因此采用最小信息损失方法对设计的控制器进行了降阶。通过仿真验证，证实了降阶后的H∞回路成形控制器对于环形二级倒立摆平衡控制有良好效果。

关键词：环形二级倒立摆； 平衡控制； H∞回路成形； 控制器降阶

中图分类号： TP 273     文献标志码： A

H∞ Robust Controller Design and Simulation for  Double Inverted Pendulum

WANG Dongyun， LIAO Lei， WANG Haiquan， ZHANG  Qiang

 (School of Electric and Information Engineer, Zhongyuan University of Technology, Zhengzhou 450007, China)

Abstract:  The paper is mainly focused on the balance control of rotary double inverted pendulum. Firstly, the mathematical model of rotary double inverted pendulum is established based on the Lagrange dynamic method, the stability, controllability and observability of system are also analyzed. Secondly, the H∞ loop shaping robust method is introduced to design the controller, and considering that the order of the controller is too high, the minimum information loss method is proposed to reduce the order of the designed controller. Finally, numerous simulations verify that the order reduced H∞ loopshaping controller is effective for the balance control of rotary double inverted pendulum.

 Key words: rotary double inverted pendulum; balance control; H∞loop shaping; the orderreduction of the controller

 收稿日期： 20130922

基金项目： 国家自然科学基金项目（61074022，61304115）；科技部国际科技合作项目（2010DFA22770）.

 作者简介： 王东云（1963—），男，教授，博士.