Actuator fault detection and reconfiguration in distributed processes with measurement sampling constraints

This work develops a model-based approach for the detection and compensation of actuator faults in distributed processes described by parabolic PDEs with a limited number of measurements that are sampled at discrete time instances. Using an approximate finite-dimensional system that captures the dominant dynamics of the PDE, an observer based output feedback controller that stabilizes the closed-loop system in the absence of faults is initially designed. The observer estimates are also used for fault detection by comparing the output of the observer with that of the process, and using the discrepancy as a residual. To compensate for measurement unavailability, a model of the approximate finite-dimensional system is embedded within the controller to provide the observer with estimates of the output measurements between sampling instances. The state of the model is then updated using the actual measurements whenever they become available from the sensors. By formulating the closed-loop system as a combined discrete-continuous system, an explicit characterization of the minimum allowable sampling rate that guarantees both closed-loop stability and residual convergence in the absence of faults is obtained in terms of the model accuracy, the controller design parameters and the spatial placement of the control actuators. This characterization is used as the basis for deriving (1) a time-varying threshold on the residual which can be used to detect faults for a given sampling period, and (2) an actuator reconfiguration law that determines the set of feasible fall-back actuators that preserve closed-loop stability under a given measurement sampling rate. Finally, the implementation of the fault detection and fault-tolerant control architecture on the infinite-dimensional system is analyzed using singular perturbations, and the results are demonstrated using a diffusion-reaction process example.