Abstract-Heterogeneous System Architectures (HSA) are gaining importance in the High Performance Computing (HPC) domain due to increasing computational requirements coupled with energy consumption concerns, which conventional CPU architectures fail to effectively address. Systems based on Field Programmable Gate Array (FPGA) recently emerged as an effective alternative to Graphical Processing Units (GPUs) for demanding HPC applications, although they lack the abstractions available in conventional CPU-based systems. This work tackles the problem of runtime resource management of a system using FPGA-based co-processors to accelerate multiprogrammed HPC workloads. We propose a novel resource manager able to dynamically vary the number of FPGAs allocated to each of the jobs running in a multi-accelerator system, with the goal of meeting a given Quality of Service metric for the running jobs measured in terms of deadline or throughput. We implement the proposed resource manager in a commercial HPC system, evaluating its behavior with representative workloads.