Asymptotic rejection of sinusoidal disturbances with recovered nominal transient performance for uncertain linear systems

This paper presents a disturbance observer (DOB) for a class of linear systems which has the following features: 1) it recovers the nominal pre-designed time trajectory (approximately but arbitrarily closely) under plant uncertainties and disturbances, not only in the steady-state but also in the transient period; and moreover 2) it eliminates sinusoidal disturbances asymptotically (rather than approximately) by embedding the generating model of the disturbances into the DOB structure. In particular, we implement the embedding with reduced order compared to other DOB schemes, at the expense of complexity on the stability condition. Furthermore, a new design guideline is provided to cope with this condition under arbitrarily large (but bounded) plant uncertainties.