Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control

In this contribution, we present interval methods for mathematical modeling, for parameter identification, and for control design of dynamical systems. The corresponding approaches are applied to the thermal subsystem of a high-temperature solid oxide fuel cell (SOFC) which is available as a test rig at the Chair of Mechatronics at the University of Rostock. In practice, most internal parameters of SOFC stack modules cannot be measured directly. Therefore, system characteristics such as heat capacities or internal thermal resistances cannot be identified exactly, but only bounded. For this reason, intervals represent a good first approach to dealing with parameter uncertainty. In the first part of the paper, we present interval methods for the parameter identification aiming at the computation of globally optimal parameterizations. In comparison with classical local optimization procedures, the approximation quality is improved by the presented identification approach. The corresponding bounds for admissible domains are used to design a robust sliding mode control law for arbitrary operating points compensating the impact of disturbances and parameter uncertainties in a reliable way. In the second part of the paper, we show a simple approach to handling non-smoothness appearing in SOFC models based on ordinary differential equations in a verified way. We use a generalized derivative definition for a certain type of non-smooth functions inside the algorithm of the verified solver ValEncIA-IVP to be able to compute solutions to non-smooth initial value problems. The applicability of our method is demonstrated using the designed sliding mode controller.