Distributed embedded systems are pervasive components jointly operating in a wide range of applications. Moving toward energy harvesting powered systems enables their long-term, sustainable, scalable, and maintenance-free operation. When these systems are used as components of an automatic control system to sense a control plant, energy availability limits when and how often sensed data are obtainable and therefore when and how often control updates can be performed. The time-varying and non-deterministic availability of harvested energy and the necessity to plan the energy usage of the energy harvesting sensor nodes ahead of time, on the one hand, have to be balanced with the dynamically changing and complex demand for control updates from the automatic control plant and thus energy usage, on the other hand. We propose a hierarchical approach with which the resources of the energy harvesting sensor nodes are managed on a long time horizon and on a faster timescale, self-triggered model predictive control controls the plant. The controller of the harvesting-based nodes' resources schedules the future energy usage ahead of time and the self-triggered model predictive control incorporates these time-varying energy constraints. For this novel combination of energy harvesting and automatic control systems, we derive provable properties in terms of correctness, feasibility, and performance. We evaluate the approach on a double integrator and demonstrate its usability and performance in a room temperature and air quality control case study.