Solid oxide fuel cell (SOFC) power plants have been demonstrated to produce power efficiently in theory and in practice. However, popular control methods have not accounted for controlling the SOFC and the connecting power inverter in tandem. In addition, the literature often used an elegant but erroneous model to test SOFC control methods. Inspired by classical control of conventional power plants, this paper develops coordinated controls for a corrected simple model and a separate detailed model. Testing these models with these controls results in satisfactory performance comparable to the original tests with the original model.