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摘要: 针对具有未知扰动与测量噪声的线性离散时间系统, 提出了一种传感器故障检测方法. 首先, 将传感器故障视为增广状态, 将原始系统转化为一个等效的新线性动态系统. 然后, 基于鲁棒观测器设计和极点配置方法构造了一个故障检测观测器, 使得生成的残差能够同时满足对扰动与噪声的鲁棒性和对故障的敏感性. 此外, 设计了一种基于椭球分析的残差评价方法, 该方法可通过判断残差是否被无故障残差椭球包含来检测故障. 最后, 通过一个二阶RC电路模型的仿真算例验证了所提出方法的有效性与优越性.Abstract: This paper proposes a sensor fault detection approach for linear discrete-time system with unknown disturbances and measurement noises. A new linear dynamic system, which is equivalent to the original system, is obtained by considering the fault as an auxiliary state. To make the generated residual robust to disturbances and noises, and sensitive to fault, a fault detection observer is constructed based on the robust observer design and pole assignment techniques. Moreover, a residual evaluation method via ellipsoidal analysis is proposed, which can detect fault by checking whether the residual is included by the fault-free residual ellipsoid. Finally, numerical simulation of a second-order RC circuit model is given to illustrate the effectiveness and superiority of the proposed approach.
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Key words:
- Fault detection /
- observer design /
- pole assignment /
- ellipsoidal analysis
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图 3 突变故障的残差${\boldsymbol{r}}_k$与残差椭球${\cal{E}}(0,R_k)$ ($k = 95\sim105$)
Fig. 3 Residual ${\boldsymbol{r}}_k$ and residual ellipsoid ${\cal{E}}(0,R_k)$ of abrupt fault ($k = 95\sim105$)
图 5 时变故障的残差${\boldsymbol{r}}_k$与残差椭球${\cal{E}}(0,R_k)$ ($k = 95\sim105$)
Fig. 5 Residual ${\boldsymbol{r}}_k$ and residual ellipsoid ${\cal{E}}(0,R_k)$ of time-varying fault ($k = 95\sim105$)
图 6 微小突变故障检测指示值对比结果
Fig. 6 Comparison result of small abrupt fault detection indication values
图 7 本文方法的残差${\boldsymbol{r}}_k$与残差椭球${\cal{E}}(0,R_k)$ ($k = 95\sim105$)
Fig. 7 Residual ${\boldsymbol{r}}_k$ and residual ellipsoid ${\cal{E}}(0,R_k)$ by the proposed approach ($k = 95\sim105$)
图 8 $H_-/H_{\infty}$方法的残差${\boldsymbol{\varrho}}_k$与残差椭球${\cal{E}}(0,H_k)$ ($k = 95\sim105$)
Fig. 8 Residual ${\boldsymbol{\varrho}}_k$ and residual ellipsoid ${\cal{E}}(0,H_k)$ by the $H_-/H_{\infty}$ method ($k = 95\sim105$)
图 9 $H_-/L_{\infty}$方法的残差${\boldsymbol{\varsigma}}_k$与残差椭球${\cal{E}}(0,L_k)$ ($k = 95\sim105$)
Fig. 9 Residual ${\boldsymbol{\varsigma}}_k$ and residual ellipsoid ${\cal{E}}(0,L_k)$ by the $H_-/L_{\infty}$ method ($k = 95\sim105$)
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