This paper proposes a current Model Predictive Control (MPC) of an RLE load, implemented in a quasicontinuous Real-Time Simulator (RTS) on the Zynq-7000 All Programmable (AP) System-on-Chip (SoC). This device is a new platform recently introduced by Xilinx and has the benefit of integrating an FPGA fabric along with a powerful processor. The RLE load dynamical model is implemented in the FPGA fabric of the Zynq-7000 and is run at very high frequencies (50 MHz) to approximate a quasi-continuous time behavior, whereas the Model Predictive Control (MPC), which is a computationally intensive control algorithm, is implemented in the processing part. Both the RTS and MPC are challenging and allow the analysis of the hardware and software capabilities of the chosen Zynq-7000 AP SoC device. Real-time simulation results are presented and compared for validation with simulation results obtained using MATLAB.