Order reduction via balancing and suboptimal control of a fuel cell - Reformer system

In this paper we first perform system balancing of an eighth-order mathematical model of a polymer electrolyte membrane fuel cell (PEMFC) dynamic coupled with a tenth-order mathematical model of a hydrogen gas reformer. Based on that information we determine reduced-order mathematical models of the original eighteen-order model by eliminating state variables that have negligible contribution to the model dynamics. Having obtained the reduced-order models, we study their step and impulse responses, and compare them to those of the original full-order model. In addition, we design corresponding suboptimal feedback controllers based on the reduced-order models. Comparing the obtained suboptimal controllers (that require a reduced number (only six or even five) of feedback loops making them easy for implementation) we find that their suboptimal performances are very close to the optimal performance of the full-state optimal feedback controller. It is important to emphasize that the full-order state feedback controller requires the same number of the feedback loops as the dimension of the original full-order state space model (in this case eighteen), which makes it complex and sometimes impractical to implement.