Integrating model-based fault detection and fault-tolerant control of distributed processes

This paper presents a fault-tolerant control (FTC) architecture for spatially distributed processes described by quasi-linear parabolic partial differential equations (PDEs) with control constraints and control actuator faults. The architecture integrates model-based fault detection, spatially distributed feedback and supervisory control to orchestrate switching between different actuator configurations in the event of faults. The various components are designed on the basis of appropriate reduced-order models that capture the dominant dynamics of the distributed process. The fault detection filter replicates the dynamics of the fault-free, reduced-order model; and uses the discrepancy from the behavior of the actual system as a residual for fault detection. Owing to the inherent approximation errors in the reduced-order model, appropriate fault detection and control reconfiguration criteria are derived for the implementation of the FTC architecture on the distributed system to prevent false alarms. The criteria is expressed in terms of residual thresholds that capture the closeness of solutions between the fault-free, reduced and full-order models. A singular perturbation formulation is used to link these thresholds with the separation between the slow and fast eigenvalues of the spatial differential operator necessary for closed-loop stability