Increasing adoption of smart meters and phasor measurement units (PMUs) in power distribution networks are enabling the adoption of data-driven/model-less control schemes to mitigate grid issues such as over/under voltages and power-flow congestions. However, such a scheme can lead to infeasible/inaccurate control decisions due to measurement inaccuracies. In this context, the authors' previous work proposed a robust measurement-based control scheme accounting for the uncertainties of the estimated models. In this scheme, a recursive least squares (RLS)-based method estimates the grid model (in the form of voltage magnitude sensitivity coefficients). Then, a robust control problem optimizes power set-points of distributed energy resources (DERs) such that the nodal voltage limits are satisfied. The estimated voltage sensitivity coefficients are used to model the nodal voltages, and the control robustness is achieved by accounting for their uncertainties. This work presents the first experimental validation of such a robust model-less control scheme on a real power distribution grid. The scheme is applied for voltage control by regulating two photovoltaic (PV) inverters connected in a real microgrid which is a replica of the CIGRE benchmark microgrid network at the EPFL Distributed Electrical Systems Laboratory.