In this paper, we employ formal feedback control theory to achieve desired communication throughput across a network-on-chip (NoC) based multicore. When the output of the system needs to follow a certain reference input over time, our controller regulates the system to obtain the desired effect on the output. In this work, targeting a multicore that executes multiple applications simultaneously, we demonstrate how to design and employ a PID (Proportional Integral Derivative) controller to obtain the desired throughput for communications by tuning the weights of the virtual channels of the routers in the NoC. We also propose a global controller architecture that implements policies to handle situations in which the network cannot provide the overlapping communications with sufficient resources or the throughputs of the communications can be enhanced (beyond their specified values) due to the availability of excess resources. Finally, we discuss how our novel control architecture works under different scenarios by presenting experimental results obtained using four embedded applications. These results show how the global controller adjusts the virtual channels weights to achieve the desired throughputs of different communications across the NoC, and as a result, the system output successfully tracks the specified input.