北京航空航天大学学报 ›› 2016, Vol. 42 ›› Issue (10): 2231-2237.doi: 10.13700/j.bh.1001-5965.2015.0556

• 论文 • 上一篇    下一篇

基于LMI的输出反馈μ控制器求解

李喆, 高元楼, 李佩林   

  1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100083
  • 收稿日期:2015-08-31 出版日期:2016-10-20 发布日期:2016-01-04
  • 通讯作者: 高元楼,Tel.:010-82339757,E-mail:gaoyuanlou@263.net E-mail:gaoyuanlou@263.net
  • 作者简介:李喆,男,硕士研究生。主要研究方向:控制工程。Tel.:010-82339513,E-mail:dzztlz@163.com;高元楼,男,博士,副教授,硕士生导师。主要研究方向:机电控制。Tel.:010-82339757,E-mail:gaoyuanlou@263.net

Solution of output feedback μ controller based on LMI

LI Zhe, GAO Yuanlou, LI Peilin   

  1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2015-08-31 Online:2016-10-20 Published:2016-01-04

摘要: D-K算法是结构奇异值(μ)方法的主要实现方式,存在着求解条件较苛刻、系统适用性差的问题,针对D-K算法应用的局限性,提出将线性矩阵不等式(LMI)用于D-K算法的改进,即通过Schur引理与有界实引理得到了结构奇异值上界的LMI判据,利用消元法得到了输出反馈的H控制器,在此基础上通过D-K迭代解出输出反馈μ控制器,避免了因求解Riccati方程受到求解条件的限制以及待定参数选择好坏的影响,增强了D-K算法对一般系统的适用性并提高了求解效率。数值结果表明,该方法得到的输出反馈系统的鲁棒稳定性及鲁棒性能均优于传统D-K算法。

关键词: 结构奇异值, 线性矩阵不等式(LMI), 输出反馈, 控制器, 鲁棒性能

Abstract: D-K iteration is the main implementation method of structured singular value (μ), which has problems of strict solution conditions and poor system suitability. Aimed at overcoming limitation shortage of D-K iteration application, the linear matrix inequality (LMI) was proposed to improve D-K iteration, which uses Schur's lemma and bounded real lemma to get LMI criterion of upper boundary of structured singular value, and elimination method was developed to obtain H controller in output feedback system. Based on improvements related to LMI, D-K iteration was adopted to solve μ controller in output feedback system, which avoids solution limitation of Riccati equation and influence by selection quality of some uncertain parameters, enhances its applicability in general system, and improves the solution efficiency of controller in output feedback system. Numerical results show that this method gets not only robust stability but also robust performance superior to the traditional D-K iteration of output feedback system.

Key words: structured singular value, linear matrix inequality (LMI), output feedback, controller, robust performance

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