基于 LMI 的不确定系统鲁棒故障检测观测器设计

摘要

针对系统模型同时具有未知输入扰动和模型不确定性，提出了一种鲁棒故障检测观测器的设计方法。在不考虑系统模型误差的情况下，为降低设计的保守性，利用描述残差对故障灵敏度的 H -指数和表示残差对未知输入鲁棒性的 H ∞范数以及一种新的迭代线性矩阵不等式（linear matrix inequality，LMI）算法解决 H ∞/H -的优化问题，设计了参考残差模型和自适应门限，并将观测器设计转化为 LMI 表述的标准 H ∞模型匹配问题，减小故障检测过程中误报、漏报率。仿真结果表明，设计的故障检测观测器对故障的灵敏度高，对不确定因素的鲁棒性强。%Considering both unknown inputs and modeling errors of system models,a design method for ro-bust fault detection observers is presented.Assuming that there are no modeling errors and in order to reduce the design conservativeness,the H - index and the H ∞ norm,which measure the sensitivity of the residual to the fault and the robustness of the effect of the unknown inputs on the residual respectively,as well as a new iterative linear matrix inequality(LMI)algorithm are used to deal with the H ∞/H - optimization problem.The reference residual model and the adaptive threshold generators are also designed.Then the robust fault detection observer design as a standard H ∞ model-matching problem is presented via an LMI formulation to decrease the rate of false alarming and miss probability.Simulation shows that the designed fault detection observer has high sensitivity to faults and strong robustness to uncertain factors.