Uncertain Gain and Time-Delay Control of 300-kW SOFC-GT

This paper presents a Proportional Integral Derivative (PID) controller design with the presence of an uncertain internal gain and additional time delay in the forward path of a 300 kW Solid Oxide Fuel Cell-Gas Turbine (SOFC-GT). The outputs of the system are turbine speed and the fuel cell mass flow rate. A fixed set of proportional controller coefficients are determined to graphically develop an area of selection for the integral and derivative coefficients of the PID controller. The inputs to the power plant are the electric load and cold air valve. The decentralized controllers are applied to four sub-systems as a Single Input Single Output (SISO). The PID controller coefficients are selected from a singular matrix solution that stabilizes the system and satisfies the internal gain and time delay uncertainties. Two sub-systems are the transfer functions of the turbine speed over the electric load and the cold air valve. The other two sub-systems are the transfer functions of the fuel cell mass flow rate over the electric load and the cold air bypass valve. Multiple options for selecting PID controller coefficients are beneficial to the SOFC-GT plant due to the wide range of operations and internal uncertainty interactions. The specific internal time delay and gain margins increase the reliability and robustness of the SOFC-GT with multiple uncertain parameters.