  Harmonic model predictive control (HMPC) is a recent model predictive control
(MPC) formulation for tracking piece-wise constant references that includes a
parameterized artificial harmonic reference as a decision variable, resulting
in an increased performance and domain of attraction with respect to other MPC
formulations. This article presents an extension of the HMPC formulation to
track periodic harmonic references and discusses its use to track arbitrary
references. The proposed formulation inherits the benefits of its predecessor,
namely its good performance and large domain of attraction when using small
prediction horizons, and that the complexity of its optimization problem does
not depend on the period of the periodic reference. We show closed-loop results
discussing its performance and comparing it to other MPC formulations.
