This paper presents different formulations of Model Predictive Control (MPC) to handle static friction in control valves for industrial processes. A fully unaware formulation, a stiction embedding structure, and a stiction inversion controller are considered. These controllers are applied to multivariable systems, with linear and nonlinear process dynamics. A semiphysical model is used for valve stiction dynamics and the corresponding inverse model is derived and used within the stiction inversion controller. The two-move stiction compensation method is revised and used as warm-start to build a feasible trajectory for the MPC optimal control problem. Some appropriate choices of objective functions and constraints are used with the aim of improving performance in set-points tracking. The different MPC formulations are reviewed, compared, and tested on several simulation examples. Stiction embedding MPC proves to guarantee good performance in set-points tracking and also stiction compensation, at the expense of a lower robustness with respect to other two formulations. (C) 2018 Elsevier Ltd. All rights reserved.