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This work describes an efficient implementation in terms of computation time and resource usage in a Field-Programmable System-On-Chip (FPSoC) of a Finite Control Set Model Predictive Control (FCS-MPC) algorithm. As an example, the FCS-MPC implementation is used for the current reference tracking of a two-level three-phase power converter. The proposed solution is an enabler for using both complex control algorithms and digital controllers for high switching frequency semiconductor technologies. An original HW/SW (hardware and software) system architecture for an FPSoC is designed to take advantage of a modern operating system, while removing time uncertainty in real-time software tasks, and exploiting dedicated FPGA fabric for the most complex computations. In addition, two different architectures for the FPGA-implemented functionality are proposed and compared in order to study the area-speed trade-off. Experimental results show the feasibility of the proposed implementation, which achieves a speed hundreds of times faster than the conventional Digital Signal Processor (DSP)-based control platform. [ABSTRACT FROM AUTHOR]