基于高阶PI观测器的不确定线性系统鲁棒故障检测设计

摘要

The problem of designing robust fault detection via high-order proportional integral (PI) obser-vers in uncertain linear systems with disturbances is investigated. Based on the parametric solutions of a class of Sylvester matrix equations, the problem of designing robust fault detection via high-order PI observers is changed into an optimal problem with multiple constraints. Based on the solution of the optimal problem, the necessary and sufficient existence condition of the high-order PI observer with the robust fault detection function is derived, and a design method of robust fault detection in uncertain linear systems with disturbances is pro-posed. Finally, a numerical example and its simulation results show that the proposed method is effective.%针对一类受干扰影响的不确定线性系统,研究了基于高阶比例积分(proportional integral,PI)观测器的鲁棒故障检测设计问题.通过对一类Sylvester矩阵方程的参数化解,将基于高阶PI观测器的鲁棒故障检测问题转化为具有多约束的优化问题.基于该优化问题的解,给出了具有鲁棒故障检测功能的高阶PI观测器存在的充要条件,并给出受干扰影响的不确定线性系统的鲁棒故障检测设计方法.最后,数值算例及仿真分析结果验证了所提方法的有效性.