Fault detection and isolation of dissipative parabolic PDEs: Finite-dimensional geometric approach

In this paper, a nonlinear geometric fault detection and isolation (FDI) method is developed for a system that is governed by a dissipative parabolic partial differential equation (PDE) and that can be approximated by a finite-dimensional ordinary differential equations (ODE). The Galerkin method is employed to derive an approximate ODE which is utilized to design a geometric FDI system. Using singular perturbation theory, it is shown that under certain conditions the designed FDI system can detect and isolate faults corresponding to the original PDE. In addition, the Approximate Inertial Manifold (AIM) concept is used to improve the performance of the designed FDI filter. It is shown that by using the AIM-based approach, one can accomplish fault detection to an arbitrary degree of accuracy, although this technique cannot improve the fault isolation problem.