In this paper, we consider the problem of designing a robust controller for an unknown, infinite-dimensional, exponentially stable, linear time-invariant plant. The controller should be able to asymptotically track and reject reference and disturbance signals which are finite linear combinations of constants and sinusoids of known frequencies, in such a way that the plant and controller states remain bounded. A self-tuning controller is proposed, which generalizes to infinite-dimensional systems and sinusoidal reference and disturbance signals the controller given by Miller and Davison in 1989 for finite-dimensional systems and constant reference and disturbance signals. The only information needed of the plant is the values of its transfer function P (i omega(k)) at the reference and disturbance frequencies. Since the values P (i omega(k)) can be measured from the open loop plant with frequency response measurements, no plant model is needed. As far as the authors know, the results given in this paper are new even for finite-dimensional systems.