In this paper, we propose and experimentally validate a scheduling and control framework for distributed energy resources (DERs) that achieves to track a day-ahead dispatch plan of a distribution network hosting controllable and stochastic heterogeneous resources while respecting the local grid constraints on nodal voltages and lines ampacities. The framework consists of two algorithmic layers. In the first one (day-ahead scheduling), we determine an aggregated dispatch plan. In the second layer (real-time control), a distributed model predictive control (MPC) determines the active and reactive power setpoints of the DERs so that their aggregated contribution tracks the dispatch plan while obeying to DERs operational constraints as well as the grid's ones. The proposed framework is experimentally validated on a real-scale microgrid that reproduces the network specifications of the CIGRE microgrid benchmark system.