An Interval Observer Approach for the Online Temperature Estimation in Solid Oxide Fuel Cell Stacks

Interval observers that are based on the structural property of cooperativity allow for the computation of guaranteed lower and upper bounds for all state trajectories of dynamic systems by defining two sets of bounding systems for the dynamic behavior. In such a way, they remove the disadvantage of predictor-corrector interval estimation schemes which often suffer from the fact that the dynamic system model has to be evaluated over finitely large domains of state variables and parameters (often interval boxes or zonotopes). This evaluation typically results in overestimation that includes unphysical parts of the state-space in the computed results. To counteract this so-called wrapping effect, computationally expensive, problem-specific algorithms need to be implemented. However, this drawback can be removed for systems that have certain monotonicity and stability properties. In this paper, it is shown that appropriately defined system models for the thermal behavior of high-temperature fuel cells belong to this class of systems. The corresponding interval observer design is presented methodologically and demonstrated with the help of measured data from a test rig available at the Chair of Mechatronics at the University of Rostock.