Residuals Generation and Fault Isolation

Detection of sensor faults can be achieved on the basis of the following residuals  

For isolation purposes (i.e., determination of the faulty sensor), two other residuals must be defined, 

In sum, a fault can be declared and, eventually, isolated, provided that simultaneous faults on different sensors do not occur during the same batch operation, according to the logic summarized in Table 6.1. 

When a sensor fault (occurring at t = tf) affects one of the sensors in the couple Sr , Sjj] (i = 1, 2), the following equality holds  

Therefore, a sufficient condition ensuring isolation of a fault affecting sensor S j ( =r, j) is 

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