Resource control in heterogeneous computers builtwith subsystems from different vendors is challenging. There is a tension between the need to quickly generate local decisions in each subsystem and the desire to coordinate the different subsystems for global optimization. In practice, global coordination among subsystems is considered hard, and current commercial systems use centralized controllers. The result is high response time and high design cost due to lack of modularity. To control emerging heterogeneous computers effectively, we propose a new control framework called Tangram that is fast, globally coordinated, and modular. Tangram introduces a new formal controller that combines multiple engines for optimization and safety, and has a standard interface. Building the controller for a subsystem requires knowing only about that subsystem. As a heterogeneous computer is assembled, the controllers in the different subsystems are connected hierarchically, exchanging standard coordination signals. To demonstrate Tangram, we prototype it in a heterogeneous server that we assemble using components from multiple vendors. Compared to state-of-the-art control, Tangram reduces, on average, the execution time of heterogeneous applications by 31% and their energy-delay product by 39%.