The Supercritical Carbon Dioxide (S-CO2) Brayton Cycle is a promising alternative to Rankine steam cycle and recuperated gas Brayton cycle energy converters for use with Sodium-Cooled Fast Reactors (SFRs), Lead-Cooled Fast Reactors (LFRs), as well as other advanced reactor concepts. The S-CO2 Brayton Cycle offers higher plant efficiencies than Rankine or recuperated gas Brayton cycles operating at the same liquid metal reactor core outlet temperatures as well as reduced costs or size of key components especially the turbomachinery. A new Plant Dynamics Computer Code has been developed at Argonne National Laboratory for simulation of a S-CO2 Brayton Cycle energy converter coupled to an autonomous load following liquid metal-cooled fast reactor. The Plant Dynamics code has been applied to investigate the effectiveness of a control strategy for the S-CO2 Brayton Cycle for the STAR-LM 181 MWe (400 MWt) Lead-Cooled Fast Reactor. The strategy, which involves a combination of control mechanisms, is found to be effective for controlling the S-CO2 Brayton Cycle over the complete operating range from 0 to 100% load for a representative set of transient load changes. While the system dynamic analysis of control strategy performance for STARLM is carried out for a S-CO2 Brayton Cycle energy converter incorporating an axial flow turbine and compressors, investigations of the S-CO2 Brayton Cycle have identified benefits from the use of centrifugal compressors which offer a wider operating range, greater stability near the critical point, and potentially further cost reductions due to fewer stages than axial flow compressors.