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This paper presents the simulation and construction of a 9-level Flying Capacitor Multilevel Inverter (FCMI), with a control based on the Fundamental Frequency Switching Method (FFSM) and redundant switching states. The system was built and the hardware implementation process is documented. A Particle Swarm Optimization (PSO) algorithm was developed to determine the MOSFETs firing angles to reduce the resulting Total Harmonic Distortion (THD). MATLAB/Simulink was used to simulate the FCMI and implement the PSO algorithm. A microcontroller was used to generate the sixteen different signals to control the firing angles for the hardware implementation. Simulation and experimental results confirmed the proper function of the FFSM control and capacitor balancing.