The controller placement problem (CPP) is one of the key challenges of software defined networks to increase performance. Given the locations of switches, CPP consists of choosing the controller locations that minimize the latency between switches and controllers. In its current form, however, CPP assumes a fixed traffic and no existing solutions adapt the placement to the load. In this paper, we introduce the dynamic controller placement problem that consists of (i) determining the locations of controller modules to bound communication latencies, and of (ii) determining the number of controllers per module to support the load. We propose, LiDy, a solution that combines a controller placement algorithm with a dynamic flow management algorithm. We evaluate the latency and the controller utilization of LiDy on sparse and dense regions. Our results show that, in all settings, LiDy achieves a higher utilization than the most recent controller placement solution.