A Generalized Proportional-integral Observer With Zero Assignment for Disturbance Rejection Residual Evaluation and Fault Detection
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摘要: 针对一类存在周期性扰动的系统, 提出了一种新型的基于广义PI观测器零点配置的抗扰残差评估框架, 充分利用了广义PI观测器的零点可配置性, 通过调整传递函数矩阵在阻塞零点处的相位响应并利用该频点处矩阵的零特征向量对残差信号进行滤波, 实现了残差信号与周期性扰动的解耦. 此外, 还创新性地提出了一种基于矩阵条件数的优化目标函数, 改善了残差信号对故障的敏感性. 最后, 通过两轮自平衡小车的仿真对比实验和实物测试, 验证了所提方法在残差抑扰和故障检测方面的有效性.Abstract: For a class of systems subject to periodic disturbances, a disturbance rejection residual evaluation architecture based on the generalized proportional-integral observer with zero-configuration is proposed for fault detection. It can make full use of the zero configurability of the generalized proportional-integral observer and achieve decoupling of the residual signal from the periodic disturbances by adjusting the phase response of the transfer function matrix at the blocking zero and using the zero eigenvector of the transfer function matrix at the disturbance frequency to filter the residual signal. In addition, this paper also proposes a fault-sensitive optimization objective function based on the condition number. Finally, the effectiveness of the proposed method in terms of the disturbance rejection and fault detection is verified through simulated comparative experiments and physical tests on a two-wheeled self-balancing trolley.
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图 1 基于广义PI观测器和残差评估的故障检测系统框图
Fig. 1 Block diagram of a fault detection system based on a generalized PI observer and residual evaluation section
图 2 传递函数矩阵相位调整和抗扰滤波原理示意图
Fig. 2 Concept illustration of the proposed phase adjustment of disturbance transfer function matrix for disturbance rejection
图 3 比例观测器的输出残差信号的1024-FFT频谱
Fig. 3 Spectrum of the residual from a proportional observer by 1024-FFT
图 5 无故障时残差信号的1024-FFT对比图
Fig. 5 Comparison of the 1024-FFT spectrum of the residuals in fault-free scenario
图 7 发生较小的渐变式故障时残差信号对比图
Fig. 7 Comparison of the residuals under the smaller ramp fault
表 1 残差特征和安全阈值对比
Table 1 Comparison of residual characteristics and safety thresholds
检测方法 均值$E\left(\tilde{r}_{k}\right)$ 标准差$\delta\left(\tilde{r}_{k}\right)$ 安全阈值$\pm 3\delta$ P观测器 −0.060 6.949 [−20.91, 20.79] PI观测器 −1.229 5.268 [−17.03, 14,58] 广义PI观测器 −0.694 1.510 [−5.22, 3.84] 广义PI观测器+实
系数增益向量−0.003 0.075 [−0.23, 0.22] 
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