Simultaneous Fault Detection and Control of Two-dimensional Fornasini-Marchesini Systems
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摘要: 本文研究二维Fornasini-Marchesini (FM)系统的同时故障检测与控制问题.针对故障和干扰的有限频特性, 设计满足有限频性能指标的故障检测滤波器/控制器, 在实现故障检测目标的同时兼顾控制性能.借助于二维广义KYP引理, 将有限频性能指标转化为矩阵不等式条件.在此基础上, 采用构造切平面的方法以及两步算法解决设计过程中出现的非凸问题.最后, 将所提出的方法应用于带钢轧制过程以验证其有效性.Abstract: The paper addresses the problem of integrated fault detection and control of two-dimensional (2-D) Fornasini-Marchesini (FM) systems. A fault detection filter/controller is designed simultaneously to detect faults in finite frequency domain and satisfy some control specifications. By means of the generalized KYP lemma, the finite frequency performance indices are transformed into matrix inequality conditions. Based on these conditions, a method of constructing a tangent plane and a two-step algorithm are proposed to solve the obtained non-convex problem. The effectiveness of the proposed method is illustrated by an example about metal rolling process.
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Key words:
- 2-D system /
- FM model /
- fault detection /
- integrated design
1) 本文责任编委 邓方 -
图 4 三维空间中的残差评价函数$ {J_r}(i, j)$和阈值$ {J_{th}}$
Fig. 4 Residual evalution function $ {J_r}(i, j)$ and threshold $ {J_{th}}$ in three-dimensional space
图 5 二维空间中的残差评价函数$ {J_r}(i, j)$和阈值$ {J_{th}}$
Fig. 5 Residual evalution function $ {J_r}(i, j)$ and threshold $ {J_{th}}$ in two-dimensional space
图 6 故障到残差传递函数${G_{\tilde yf}}({\omega _1}, {\omega _2})$的奇异值比较
Fig. 6 Singular value comparison of transfer functions ${G_{\tilde yf}}({\omega _1}, {\omega _2})$ from fault to residual signal
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