A simple scheme for internal model based control

We propose a very simple method for tracking and disturbance rejection, when the reference and disturbance signals are superpositions of finitely many sinusoids (including constants). The internal model is a convex combination of partial internal models for the individual frequencies of interest. The stabilizing compensator is designed by solving a weighted sensitivity H^∞ problem, which is independent of the frequencies involved, or of their number. The results remain valid for infinite-dimensional plants. We comment also on the robustness properties of such control systems