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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.
In this paper, the optimal interference suppression based on dynamic compensation is studied for linear time-invariant systems subject to external disturbances, where the disturbing signals are disturbing signals with known dynamic characteristics.Firstly, the original system and disturbance system are combined to form an augmented system, And then transformed into a perturbed standard linear quadratic optimization problem.Secondly, given the conditions for the asymptotic stability of the closed-loop system compensated by the compensator with appropriate dynamic order and the positive definite symmetric solution of the related Lyapunov equation, The quadratic performance index can be written as an expression related to the initial value of the solution and the closed-loop system.In order to obtain the optimal solution of the system, the Lyapunov equation is transformed into a form of bilinear matrix inequalities and the corresponding path Tracking algorithm to obtain the minimum performance index and the compensator parameters.Finally, numerical examples show that the proposed method can not only minimize the linear quadratic index, but also make the system interference suppressed.