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摘要: 针对具有执行器故障和未知扰动的线性广义系统，提出一种新的故障估计器设计方法.所设计的故障估计器具有非奇异结构，便于实现.在故障频域范围有限的条件下，为了抑制未知扰动和有限频域故障对故障估计误差的影响，基于广义Kalman-Yakubovich-Popov（KYP）引理给出了故障估计器的鲁棒性设计条件，并将其转化为方便求解的线性矩阵不等式形式.最后，通过一个电路系统的仿真算例验证了所提出方法的有效性.
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关键词:
- 广义系统 /
- 故障估计器 /
- 广义Kalman-Yakubovich-Popov (KYP)引理 /
- 有限频域
Abstract: This paper proposes a novel fault estimator design method for linear descriptor systems with actuator fault and unknown disturbance. The proposed fault estimator has a nonsingular structure and hence is easy to implement. Under the condition that faults belong to a finite frequency domain, the generalized Kalman-Yakubovich-Popov (KYP) lemma is used to propose robust design conditions to attenuate the effect of unknown disturbance and faults on the fault estimation error. Moreover, the design conditions are converted to linear matrix inequalities, which can be solved easily. Finally, an electrical circuit is simulated to verify the effectiveness of the proposed method. -
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图 2 实际故障在设计频域范围内时的故障估计结果
Fig. 2 Fault estimation results when the fault is actually in the designed frequency range
图 3 实际故障频率超出设计频域范围时的故障估计结果
Fig. 3 Fault estimation results when the fault is not actually in the designed frequency range
表 1 不同频率范围的$\Omega$和$\Xi$
Table 1 $\Omega$ and $\Xi$ corresponding to different frequency ranges
低频范围 中频范围 高频范围 $\Omega$ $\vert \omega \vert \leq \varpi _l$ $\varpi_1\leq \omega \leq \varpi_2 $ $\vert \omega \vert \geq \varpi _h$ $\Xi$ $\left[ \begin{matrix} -\mathcal{Q} & \mathcal{P} \\ \mathcal{P} & \varpi^2_l \mathcal{Q} \end{matrix} \right] $ $\left[ \begin{matrix} -\mathcal{Q} & \mathcal{P}+j\varpi _c \mathcal{Q} \\ \mathcal{P} -j\varpi _c \mathcal{Q} & -\varpi_1\varpi_2 \mathcal{Q} \end{matrix} \right] $ $\left[ \begin{matrix} \mathcal{Q} & \mathcal{P} \\ \mathcal{P} & -\varpi^2_h \mathcal{Q} \end{matrix} \right] $ 
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