Reachability-based fault detection method for uncertain chemical flow reactors

We consider the problem of computing reachable sets for continuous-time nonlinear continuous-stirred tank reactors (CSTRs) using differential inequalities method. Existing comparison-based methods yield a conservative enclosure for the reachable set due to the non-quasi-monotonic property for CSTR systems. The method proposed in Scott and Barton [2013] is effective; however, it requires a nontrivial a priori enclosure for the reachable set, which is difficult to construct for CSTR reaction systems. We propose a linear transformation to map the dynamics of the CSTR system onto a sparse state-space. Exploiting the sparsity, we construct a priori enclosure for CSTR systems. The application of the proposed method in designing a fault detection procedure is discussed, and its efficacy illustrated on an example problem.