引用本文:张宝琳, 唐功友.含正弦扰动奇异摄动时滞系统的最优减振控制[J].控制理论与应用,2007,24(2):255~260.[点击复制]
ZHANG Bao-lin, TANG Gong-you.Optimal damping control for singularly perturbed time-delay systems with sinusoidal disturbances[J].Control Theory and Technology,2007,24(2):255~260.[点击复制]
含正弦扰动奇异摄动时滞系统的最优减振控制
Optimal damping control for singularly perturbed time-delay systems with sinusoidal disturbances
摘要点击 1548  全文点击 882  投稿时间：2005-06-13  修订日期：2006-03-14
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DOI编号  10.7641/j.issn.1000-8152.2007.2.016
  2007,24(2):255-260
中文关键词  奇异摄动系统  时滞  最优控制  摄动法  正弦扰动
英文关键词  singularly perturbed systems  time-delay  optimal control  perturbation method  sinusoidal disturbances
基金项目  国家自然科学基金资助项目(60574023);山东省自然科学基金资助项目(Z2005G01);青岛市自然科学基金资助项目(05-1-JC-94).
作者单位
张宝琳, 唐功友 中国海洋大学~信息科学与工程学院, 山东 青岛 266071
中国计量学院 数学与信息科学系, 江苏 杭州 310018 
中文摘要
      研究奇异摄动时滞系统在正弦扰动下的最优减振控制问题.基于奇异摄动的快慢分解理论,将原最优控制问题转化为无时滞快子问题和受扰线性时滞慢子问题,通过摄动法和前馈补偿技术求解时滞慢子系统的最优控制问题,得到了系统的前馈反馈组合控制(FFCC)律及其存在唯一性条件.FFCC律由线性解析项和共态向量无穷级数和表示的时滞补偿项组成, 其中线性解析项可通过求解Riccati方程和Sylvester方程得到,时滞补偿项通过递推求解共态向量方程得到. 仿真算例表明了方法的有效性.
英文摘要
      The optimal damping control design for singularly perturbed time-delay systems affected by external sinusoidal disturbances is considered. Based on the slow-fast decomposition theory of singular perturbation, the system is firstdecomposed into a fast subsystem and a slow time-delay subsystem with disturbances. Then, the perturbation method is proposed to solve the slow time scale time-delay optimal control problem, and the feedforward compensation technique is used to reject the disturbances. The conditions of existence and uniqueness of the feedforward and feedback composite control (FFCC) law are also obtained. The FFCC law consists of linear analytic terms and a time-delay compensation term which is a series sum of adjoint vectors. The linear analytic terms can be found by solving Riccati matrix equation and Sylvester equation respectively. The compensation term can be approximately obtained by a recursion formula of adjoint vector equation. Finally, numerical examples are presented to illustrate the effectiveness of the proposed design method.