Offset-free tracking MPC: A tutorial review and comparison of different formulations

Offset-free Model Predictive Control formulations refer to a class of algorithms that are able to achieve output tracking of reference signals despite the presence of plant/model mismatch or unmeasured nonzero mean disturbances. The general approach is to augment the nominal system with disturbances, i.e. to build a disturbance model, and to estimate the state and disturbance from output measurements. Some alternatives are available, which are based on a non augmented system with state disturbance observer, or on velocity form representations of the system to be controlled. In this paper, we review the disturbance model approach and two different approaches in a coherent framework. Then, differently from what is reported in the literature, we show that the two alternative formulations are indeed particular cases of the general disturbance model approach.