Interval-Based Modeling of High-Temperature Fuel Cells for a Real-Time Control Implementation Under State Constraints

Interval-based state estimation techniques represent promising approaches for the quantification of worst-case bounds of those sets of state variables that are reachable over a finitely long time horizon under the consideration of bounded uncertainty. In previous work, it has been shown that such estimation techniques cannot only be employed for the class of linear uncertain systems but also for nonlinear ones if they are reformulated in terms of quasi-linear state-space representations. However, naive polytopic uncertainty models may lead to quite conservative enclosures of the reachable states. Those, in turn, lead to conservative control strategies if the aforementioned interval enclosures are combined with strategies for the design of robust feedforward and feedback controllers. Therefore, this paper aims at the reduction of pessimism during interval-based state estimation by means of novel uncertainty models, relying on a parameter bounding approach that is implemented by means of a correlation analysis as well as a suitable principle axes transformation of the parameter space. The practical applicability of the proposed procedure is visualized for an experimentally validated thermal model of a solid oxide fuel cell stack, for which the computed interval bounds of reachable states represent a fundamental requirement for the design of a combined feedforward and feedback control allowing for preventing the violation of upper temperature limits in a guaranteed way. Copyright (C) 2020 The Authors.