Fault Isolation and Identification

Once a process/actuator fault has been detected, isolation and identification can be achieved via N-p nonlinear adaptive observers. Each observer is designed in such a way to be insensitive to a particular type of fault. In fact, the ith observer (hereafter i =, . Np) has the form 

Theorem 6.2 In the presence of the ith fault i.e., /a = fa i) and in the absence of uncertainties and sensor noise i.e., rj = 0 and n = 0), if the rate constants are bounded as in (2.32) and (2.33), there exists a set of observer gains such that the state estimation error x of the observer (6.29) is globally uniformly convergent to 0 ast oo, and the parameter estimation error 0 j is uniformly bounded for every t. 

The proof is based on the arguments in [5] and is reported in Appendix A.6. Remarkably, in the presence of bounded uncertainties and sensors noise, the boundedness of 0 is no longer guaranteed. A sufficient condition to achieve the boundedness is given by the persistency of excitation [2, 27] (see Remark 5.1). If 

To achieve fault isolation, the following residuals are computed  

It is worth remarking that, when a fault occurs which is not included in the NF types considered in the design of the bank of observers, it can be only detected but not isolated and identified. 

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Then, the healthy signal is used to feed a bank of /Vp + 1 nonlinear adaptive observers (where /Vp is the number of the possible process/actuator faults). The first observer is in charge of detecting the occurrence of process/actuator faults. The other /Vp observers, each corresponding to a particular type of process/actuator fault, achieve fault isolation and identification by adopting a suitable adaption mechanism. Figure 6.3 shows a block diagram representation of the overall architecture. 

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