基于动态补偿的线性系统最优干扰抑制(英文) 被引量：2

Optimal disturbance rejection via dynamic compensation for linear systems

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摘要本文针对受外部干扰的线性时不变系统研究了基于动态补偿的最优干扰抑制问题,其中干扰信号为已知动态特性的扰动信号.首先,将原系统与扰动系统联立构成增广系统,进而转化为无扰动的标准线性二次最优问题.其次,给出了经具有适当动态阶的补偿器补偿后的闭环系统渐近稳定并且相关的Lyapunov方程正定对称解存在的条件,进一步给定的二次性能指标可写成一个与该解和闭环系统初值相关的表达式.为了得到系统的最优解,将该Lyapunov方程转化为一个双线性矩阵不等式形式,并给出了相应的路径跟踪算法以求得性能指标最小值以及补偿器参数.最后,通过数值算例说明应用本文方法可以不仅能够最小化线性二次指标,而且能够使得系统的干扰得到抑制. We investigate the linear-quadratic optimal control by using dynamic compensation for the linear timeinvariant system affected by external persistent disturbances with known dynamic characteristics.By combining the system with the disturbance system,we transform this optimal disturbance rejection problem into the standard linear quadratic optimal control problem without disturbance,and develop the dynamic compensator with appropriate order to make the closed-loop system asymptotically stable with associated Lyapunov equation having a symmetric positive-definite solution.The quadratic performance index is formulated as a simple expression related to the symmetric positive-definite solution to the Lyapunov equation as well as the initial value of the closed-loop system.In order to solve the optimal control problem for the system,we transform the Lyapunov equation to a bilinear matrix inequality and develop a corresponding pathfollowing algorithm to minimize the quadratic performance index and obtain the optimal dynamic compensator.Finally,a numerical example is provided to show that the proposed method can minimize the linear quadratic performance index and reject the system disturbances.

作者刘蕾张国山

机构地区北京大学工学院力学与工程科学系天津大学电气与自动化工程学院

出处《控制理论与应用》 EI CAS CSCD 北大核心 2013年第7期808-814,共7页 Control Theory & Applications

基金 supported by the National Natural Science Foundation of China(Nos.60674019,61074088)

关键词线性系统动态补偿线性二次最优控制干扰抑制双线性矩阵不等式路径跟踪算法 linear systems dynamic compensator linear-quadratic（LQ） optimal control disturbance rejection bilinear matrix inequality（BMI） path-following method

分类号 TP273 [自动化与计算机技术—检测技术与自动化装置]

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