| Abstrakt: |
This work focuses on the design of a fault detection and fault-tolerant control framework for spatially distributed processes modeled by highly-dissipative partial differential equations (PDEs) subject to external disturbances and sensor faults. The main objective is to devise a suitable sensor reconfiguration strategy to reduce the performance degradation due to the errors resulting from the sensor faults. Initially, a finite-dimensional system that captures the slow dynamics of the PDE is derived and used to design a obverse-based output feedback controller. Using Lyapunov techniques, the fault-free and faulty behavior of the closed-loop system are characterized in terms of the sensor spatial placement, the size of the disturbances, the magnitude of the sensor faults as well as the controller and observer design parameters. Based on the fault-free closed-loop dynamics, the Lyapunov stability bound is used as an alarm threshold to declare the presence of sensor faults. To suppress the performance deterioration, a performance-based sensor reconfiguration policy is developed whereby the supervisor determines either to continue using the current faulty sensors or to switch to suitable backup sensors based on a comparison between the sizes of the achievable terminal sets. A singular perturbation formulation is used to analyze the implementation of the sensor fault-tolerant control structure on the infinite-dimensional system. Finally, the results are illustrated through an application to a representative diffusion-reaction process example. |
