Set-membership Fault Detection Observer Design in Finite-Frequency Domain for Linear Discrete-Time System
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摘要: 本文针对线性离散系统, 提出了一种新的有限频域执行器故障检测方法.利用中心对称多胞体近似未知扰动边界, 本文提出的中心对称多胞体集员故障检测观测器可实时估计残差范围.通过观测零点是否脱离残差生成的中心对称多胞体的范围, 判断故障是否发生.为了提高对干扰的鲁棒性和对故障的敏感性, 基于P半径准则和广义Kalman-Yakubovich-Popov引理, 本文给出了故障检测观测器的设计条件, 并将其转化为便于求解的矩阵不等式形式.最后, 车辆横向动态系统的仿真结果验证了所提方法的有效性.Abstract: This paper proposes a novel finite-frequency domain actuator fault detection method for discrete-time linear system. By considering disturbances are unkown but bounded by zonotopes, a zonotopic set-membership fault detection obsever is presented to estimate the bounds of residual. Faults can be detected by checking whether the zero value is included by the zonotopes of residual or not. To improve the robustness to disturbance and sensitivity to fault, sufficient design conditions are derived based on the P radius criterion and the generalized Kalman-Yakubovich-Popov lemma. Moreover, the design conditions are converted as linear matrix inequalities, which can be solved easily. Finally, simulation results of vehicle lateral dynamic systems are given to show the effectiveness of the proposed method.
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Key words:
- Fault detection /
- set-membership estimation /
- zonotopes /
- finite-frequency domain
1) 本文责任编委 孟凡利 -
图 1 考虑有限频域特性的残差生成中心对称多胞体$ \mathcal{Z}_r $的变化过程
Fig. 1 Zonotopes $ \mathcal{Z}_r $ generated by residual considering the finite-frequency characteristics
图 2 考虑有限频域特性的故障检测结果
Fig. 2 Result of fault detection by considering the finite-frequency characteristics
图 3 不考虑有限频域特性的残差生成中心对称多胞体$ \mathcal{Z}_r $的变化过程
Fig. 3 Zonotopes $ \mathcal{Z}_r $ generated by residual without considering the finite-frequency characteristics
图 4 不考虑有限频域特性的故障检测结果
Fig. 4 Result of fault detection without considering the finite-frequency characteristics
表 1 集合$\Theta $与矩阵$\Xi $在不同频域的取值
Table 1 $\Theta $ and $\Xi $ for different frequency ranges
$\Theta $ $\Xi $ 低频 $|\theta | \le {\vartheta _1}$ $\left[ {\begin{array}{*{20}{c}} { - P}&Q\\ Q&{P - 2{\rm{cos}}{\vartheta _l}Q} \end{array}} \right]$ 中频 ${\vartheta _1} \le \theta \le {\vartheta _2}$ $\left[ {\begin{array}{*{20}{c}} { - P}&{{e^{j\theta }}cQ}\\ {{e^{ - j\theta c}}Q}&{P - 2{\rm{cos}}{\vartheta _w}Q} \end{array}} \right]$ 高频 $|\theta | \ge {\vartheta _h}$ $\left[ {\begin{array}{*{20}{c}} { - P}&{ - Q}\\ { - Q}&{P + 2{\rm{cos}}{\vartheta _h}Q} \end{array}} \right]$ 
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