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研究了一类受随机扰动影响的线性时不变系统的故障诊断滤波器(Faultdiagnosisfilter,简称FDF)设计问题。分别应用从扰动、故障到残差的传递函数的H2范数作为残差系统对扰动的鲁棒性和对故障信号的灵敏度度量指标,以最小化基于鲁棒性/灵敏度的性能指标函数为目标,将FDF设计问题归结为H2优化问题。推导并证明了问题可解的充分条件,给出了一种FDF设计的迭代线性矩阵不等式(IterativeLinearMatrixInequality,ILMI)算法,并进一步讨论了残差的评价问题。算例验证了该算法的有放性。
A class of fault diagnosis filter (FDF) design problem for linear invariant systems subject to stochastic disturbances is studied. The H2 norm of the transfer function from disturbance to fault to the residual is used as the robustness of the residual system to the disturbance and the sensitivity measure to the fault signal, respectively. The objective is to minimize the performance index function based on robustness / sensitivity , The FDF design problems attributed to the H2 optimization problem. A sufficient condition for the solvability of the problem is derived and proved. An iterative linear matrix inequality (ILMI) algorithm for FDF design is given, and the evaluation of residuals is discussed. The example shows that the algorithm is decoupled.