A system includes a control system configured to control one or more parameters of an exhaust gas recirculation (EGR) gas turbine system to control a portion of electrical power for export from a generator driven by the turbine to an electrical grid. The control system includes a closed-loop controller configured to control parameters of the EGR gas turbine system and an open-loop controller configured to temporarily control the parameters of the EGR gas turbine system to increase the portion of the electrical power exported to the electrical grid to provide a Primary Frequency Response (PFR) in response to a transient event associated with the electrical power. The open-loop controller is configured to provide control signals to increase a concentration of an oxidant in a combustor to provide the PFR in response to the transient event when the EGR gas turbine system is operating in an emissions compliant mode.