Production high-performance computing systems continue to grow in complexity and size. As applications struggle to make use of increasingly heterogeneous compute nodes, maintaining high efficiency (performance per watt) for the whole platform becomes a challenge. Alongside the growing complexity of scientific workloads, this extreme heterogeneity is also an opportunity: as applications dynamically undergo variations in workload, due to phases or data/compute movement between devices, one can dynamically adjust power across compute elements to save energy without impacting performance. With an aim toward an autonomous and dynamic power management strategy for current and future HPC architectures, this paper explores the use of control theory for the design of a dynamic power regulation method. Structured as a feedback loop, our approach-which is novel in computing resource management-consists of periodically monitoring application progress and choosing at runtime a suitable power cap for processors. Thanks to a preliminary offline identification process, we derive a model of the dynamics of the system and a proportional-integral (PI) controller. We evaluate our approach on top of an existing resource management framework, the Argo Node Resource Manager, deployed on several clusters of Grid'5000, using a standard memory-bound HPC benchmark.