Simulation Results Sensor and Actuator Faults

Finally, a simulation has been carried out in which both a sensor and an actuator fault occur during the same batch run. First, the output of sensor 5 2 suddenly switches 

It is worth noticing that, in this case, the fault affecting the thermal insulation of the jacket (fault type 2) is correctly isolated. This can be explained by noticing that the fault rate is much larger than in the previous case (i.e., ij is ten times smaller) hence, the estimate computed by the third observer is not able to track accurately the 

The approach is able to detect, isolate, and identify a wide class of failures of sensors, actuators, and process. Sufficient conditions for residuals convergence, detectability, and isolability of faults have been derived. In detail, detection is guaranteed under mild assumptions on the magnitude of model uncertainties and disturbances, whereas correct isolation may not be achieved if multiple faults of the same nature (i.e., sensor faults and process/actuator faults) occur during the same batch operation. 

In the case study, the adaptive model-based approach is designed on the basis of a reduced model of the phenol-formaldehyde reaction introduced in Chap. 2. Noticeably, the results show that the fault diagnosis scheme achieves very good performance even when a strongly simplified mathematical model of the reactive system is adopted for the design. 

Astrom and B. Wittenmark. Adaptive Control, 2nd Edition. Addison-Wesley, Reading, 1995. 

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