Robust fault detection and reconfiguration in sampled-data uncertain distributed processes

This paper focuses on robust model-based fault detection and fault-tolerant control of spatially distributed processes described by parabolic partial differential equations (PDEs) subject to time-varying external disturbances, control actuator faults and measurement sampling rate constraints. Using an approximate finite-dimensional system that captures the dominant dynamics of the PDE, an observer-based output feedback controller is initially designed to enforce robust stability with an arbitrarily small ultimate bound on the closed-loop state in the absence of faults. A finite-dimensional inter-sample model predictor is then embedded within the controller to provide the observer with estimates of the measured output between the sampling times, and the state of the model is updated using the measured output at each sampling time. By formulating the sampled-data finite-dimensional closed-loop system as a combined discrete-continuous system, a necessary and sufficient condition for robust closed-loop stability is obtained and used to explicitly characterize the tradeoffs between the sampling rate, the degree of model uncertainty, the disturbance size, the size of the achievable ultimate bound on the closed-loop state, and the choice of actuator/sensor locations. Based on this analysis, a time-varying alarm threshold on the fault detection residual is obtained, together with an actuator reconfiguration law that determines the set of feasible fall-back actuators that preserve robust closed-loop stability. Finally, the result is illustrated through an application to a representative diffusion-reaction process.