We consider a demand aggregator handling a large number of deferrable loads through a simple interface, who must align their overall consumption with an operator-provided reference. A macroscopic model of the load aggregate is developed as a two-state stochastic differential equation, with a scalar input controlling deferred service, and where deadlines are enforced. Through linearization the feedback control design is cast within the framework of H₂ control, with an objective that embeds frequency domain characteristics of the tracked reference. The solution yields a distributed implementation with mild communication requirements. We tested it in a simulation environment using real-world grid frequency regulation signals, achieving high performance with the relevant industry metric.