In a solid-oxide fuel cell assembly, at least one positive displacement air supply (PDAS) pump supplies at least a portion of the air required for various functional air streams through the assembly. Mass air flow through each PDAS pump is readily controlled to a predetermined flow by controlling the rotational speed of the pump, obviating the need for an MAF sensor and control valve. Preferably, each different air stream through the assembly is controlled by its own PDAS pump, sized for the required flow, allowing each to operate at its optimal pressure and thereby minimizing the parasitic electrical cost of providing air to the SOFC assembly.