The power synchronization control strategy for grid-connected voltage-source converters (VSCs) provides an operation similar to synchronous machines. It is able to avoid the instability caused by a standard phase-locked loop in integration into weak grids. However, the non-minimum phase phenomenon in the developed dynamics places a fundamental limitation on the ac system's stability. This paper proposes a one-degree-of-freedom internal-model-based control methodology. It introduces a control approach to incorporate the dynamics of the system's nominal model in the control structure. It also rectifies the unwanted effects of the right-half plane zeros. The explicit incorporation of the model enhances the tracking capabilities of the controller in a PV-based VSC. Besides, this article shows that a single-loop of control will suffice to regulate active and reactive power. Validating results are generated via a hardware-in-the-loop system based on a Xilinx Zynq-7000 SoC field-programmable gate array (FPGA). Furthermore, experimental results are conducted for low-power prototyping to examine the satisfactory performance of the proposed control architecture.