Model-Based Fault Isolation and Reconfigurable Control of Transport-Reaction Processes with Actuator Faults

This paper presents a methodology for the design and implementation of integrated fault detection and isolation (FDI) and fault-tolerant control (FTC) systems for transport- reaction processes modeled by nonlinear parabolic partial differential equations (PDEs) with control constraints and actuator faults. Using a finite-dimensional system that captures the PDE´s dominant dynamic modes, a family of nonlinear feedback controllers with well-characterized constrained stability regions are initially designed. Then, following a coordinate transformation that diagonalizes the input operator of the finite-dimensional system, a set of dedicated FDI filters - each replicating the fault-free behavior of a given state of the transformed system - are constructed. The choice of actuator locations ensures that each filter´s residual is sensitive to faults in only one actuator and decoupled from the rest. Following FDI, a set of actuator reconfiguration laws are derived to preserve closed-loop stability and minimize performance deterioration. Finally, the FDI-FTC architecture is implemented on the infinite-dimensional system, and appropriate FDI thresholds and actuator reconfiguration criteria are established to provide the necessary robustness against model reduction errors. Using singular perturbation techniques, these criteria are tied to the two time-scale separation between the slow and fast eigenvalues of the differential operator.