连续切换系统H_∞/H_-故障检测滤波器设计  

Design of H_∞/H_- fault detection filter for continuous switching system

作　　者：刘玉忠[1] 杨蒙[1] LIU Yuzhong;YANG Meng(College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院

出　　处：《沈阳师范大学学报（自然科学版）》2019年第4期356-361,共6页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省科技厅自然科学基金资助项目(20170540823)

摘　　要：针对连续切换系统的故障检测问题,设计了满足H∞/H-性能指标的故障检测滤波器。首先,通过构造故障检测滤波器得到残差,并引入了一种能同时体现残差对扰动的鲁棒性和对故障的敏感性的性能指标,利用H∞理论把求解滤波器的问题转化为H∞优化问题;其次,应用线性矩阵不等式(LMI)技术,对此性能指标进行优化。接着,利用Lyapunov函数方法和平均驻留时间技术验证所设计的增广滤波误差切换系统是指数稳定的,并且具有H∞性能水平;最后,在此基础上给出并证明了该滤波器设计问题解的存在性条件和被设计的滤波器的增益矩阵和权值矩阵的求解方法,并将其表示为线性矩阵不等式形式,以便利用Matlab工具箱求解并验证结果的有效性。较少的决策变量和较多的计算使所得的结果具有较小的保守性。In order to solve the problem of the fault detection of continuous switching system,a fault detection filter satisfying the H∞/H-performance index is designed.Firstly,a fault detection filter is constructed to obtain the residual,and a performance index which can reflect the robustness of the residual on the disturbance and the sensitivity of the fault is introduced,and the problem of the solution filter is converted into the H∞optimization problem by using the H∞theory.Secondly,the performance index is optimized by using the linear matrix inequality(LMI)technique.Next,the designed augmented filtering error switching system is exponential and has the H∞performance level,which is verified by using the Lyapunov function method and the average dwell time technique.Finally,on the basis of this,the existence conditions of the solution of the filtering design problem and the method of solving the gain matrix and the weight matrix of the designed filter are given,and the solution is expressed as a linear matrix inequality,so as to use the Matlab toolbox to solve and verify the validity of the results.Less decision variables and more calculations make the results less conservative.

关 键 词：切换系统 故障检测滤波器 H∞优化 平均驻留时间 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O231[自动化与计算机技术—控制科学与工程]