Actuator and sensor fault isolation of nonlinear systems subject to uncertainty
Automatic control techniques have been widely employed in industry to increase efficiency and profitability of the processes. However, this comes at a price of increased impact of abnormalities in major control equipment such as actuators and sensors. This realization has motivated design of frameworks for fault detection and isolation (FDI) and fault tolerant control (FTC). Important issues such as system nonlinearities and existence of uncertainties must be considered in FDI and FTC design to be able to successfully decrease or tackle the severity of the fault effects.
The FDI problem for nonlinear systems has been considered widely in the literature during the past decade (see, e.g., , ,  and ). Most of the existing results, however, focused on isolation of single actuator or single sensor faults. Recently, results have enabled distinguishing between simultaneous sensor and actuator faults, where the results are derived assuming no uncertainty (see e.g., ).
In , the problem of isolation of complex actuator faults (occurrence of several actuator faults in same order of differentiation) in the presence of uncertainty is handled by explicitly characterizing the way the faults affect the nonlinear process system, and driving the system to a point that enables fault isolation. The problem of FDI in the presence of uncertainty has also been studied (see e.g.,  and ) using adaptive estimation techniques. First a fault detection scheme is designed which simply uses output estimation error as residual. Then, a bank of fault isolation estimators is designed using adaptive estimation techniques. The existing results, however, consider only single fault scenarios. In summary, there is a lack of results for nonlinear systems subject to uncertainty where the problem of fault detection and isolation for simultaneous actuator and sensor faults is addressed.
Motivated by the above considerations, this work considers the problem of actuator and sensor fault isolation for simultaneous faults in the presence of uncertainty. This is achieved by building a bank of residuals, each using an appropriate subset of the available measurements (and associated state estimators), to determine the expected behavior of the system and compare with the observed evolution. To this end, at first we establish boundedness of estimation error for discretized fashion high gain observer presented in  in the presence of uncertainty. Next, we propose the fault detection and isolation design, which comprises a bank of fault detection and isolation filters that trigger an alarm based on appropriately defined residuals breaching their thresholds. Thresholds are defined in a way that they account for the impact of the uncertainty on the estimation error and the prediction of the expected system behavior. In this way, the fault isolation mechanism explicitly accounts for effect of the uncertainty. Then we present the detectability conditions for single and simultaneous faults. The efficacy of proposed FDI framework in presence of uncertainty and measurement noise is illustrated using a chemical reactor example.
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