Case Study Fault Diagnosis

The effectiveness of the proposed approach has been tested in simulation by considering a jacketed batch reactor in which the phenol-formaldehyde reaction presented in Chap. 2 takes place. The complete system of differential equations given by the 13 mass balances presented in Sect. 2.4 has been simulated in the MATLAB/SIMULINK environment. 

The same assumptions in Chap. 5 on the experimental setup have been done. The reactor parameters and the initial conditions for the reactant concentrations and the temperatures of the vessel and the jacket are reported in Table 5.1. The model-based temperature controller proposed in Chap. 5 is adopted. Finally, both in the reactor vessel and in the jacket, duplicated temperature sensors have been considered. 

In order to design the bank of observers and the controller, the reduced model (3.57) identified in Chap. 3 with first-order kinetics has been considered. Moreover, a 5% estimation error on the parameter 0 has been assumed, i.e., 9 = 0.95 0. 

It is worth remarking that the above reduced model has been adopted so as to emulate the presence of modeling errors with a twofold nature, namely  

The gain matrices of all the diagnostic observers have been set as follows  

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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. 

The proposed method will be illustrated with the case study of a heat exchanger and a CSTR. This process is originally used by Kramer (1987) and is simulated by the model of Sorsa (1991). The sampling interval is 5 s, and total diagnosis time is 2000 s. The first or single fault occurs at 100 s, and the second fault occurs at 100 or 200 s. Diagnosis result of this study will be compared with the one of the qualitative method... 

In the next section, we present a brief overview of our SDG-related work. In section 3, we discuss the unified SDG model for control loops. Various fault scenarios are also analyzed. In section 4, two case studies are presented to show the diagnostic efficiency of the proposed framework for fault diagnosis of systems with control loops. The article is concluded with discussion on future work. 

Case study 1 deals with fault diagnosis in a tank level-control system. Case study 2 deals with fault diagnosis of a CSTR system. 

The importance of this case study is three-fold (1) to explain simple concepts, (2) comparison with the results discussed in the literature and, (3) to emphasize the ability to perform multiple fault diagnosis. The controlled tank and its SDG under the perfect control scenario are given in Figure 2 (a) and (b), respectively. fi and / are the inlet and outlet flowrates, respectively. L is the level of the liquid in the tank, kc is negative. The measurements are f , and CS. Diagnosis for two fault scenarios is discussed below. Positive sensor bias The observed pattern is [/<, Xm G5] = [0 0 +). Any fault in /< or set point is ruled out. The candidate faults are VPuas = (= X= 0 ) or Xm,bias = + (= X = - ). Further resolution cannot be achieved. 

A brief discussion on our SDG-related work followed by a detailed discussion on the SDG-based modeling and analysis of control loops has been provided. Two case studies have been presented to elucidate the use of the framework for fault diagnosis. In future, the framework would be used for control loop monitoring and distributed fault diagnosis in large-scale systems. 

In any case, fault detection and isolation is a prerequisite for real-time system supervision. In order to ensure reliability and safety it is important to take into account detection and diagnosis of possible abnormal system behaviour and means for automatic correction already during an integrated, concurrent design of complex intelligent mechationic system by deliberately injecting faults into a system model and to study their effects on the system s dynamic behaviour. 

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