Abstract
In this paper the problem of rejecting sinusoidal disturbances is dealt with in an optimal control setting. First, the existing approaches are concisely surveyed and their deficiencies pointed out. Two main approaches are investigated: Frequency Shaping relies on a frequency-weighted LQ cost functional, while Disturbance Modelling augments the system by including a state-space description of the disturbance. The main result of the paper is that a cross term in the LQ cost functional is needed in order to achieve disturbance rejection via Disturbance Modelling. Dually, when resorting to Frequency Shaping, the LQG problem must take into account correlated state and observation noises.
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