This article presents a model predictive control (MPC) approach for the management of traffic lights (TLs) at a single road intersection. The proposed controller incorporates a microscopic traffic model, capturing the position, velocity, and acceleration of every single vehicle at the intersection. This allows us to achieve a detailed modeling of the dynamics of the queues. The proposed controller can adapt to work in scenarios that go from one in which vehicles are manually controlled by the drivers, to one in which some or all of the vehicles are automatically driven. In the former scenario, the dynamics of the vehicles' variables are intended to mimic the drivers' behavior, in the latter ones (i.e., semi or fully autonomous driving), vehicles' variables are references to the automated vehicles, sent by the TL controller. Numerical simulations on a real intersection with realistic traffic characteristics are discussed and results in the scenarios from the manual one to the fully automated one are compared, evaluating the performance in terms of queue length and waiting times. It is shown how the proposed controller can significantly improve the management of the intersection, leading to less traffic.