This paper deals with the control of a grinding circuit by means of a constrained model predictive control. Under this formulation the sump box is used to attenuate, in a natural way, the effects of the inlet flow disturbances over the battery of hydrocyclones, achieving a smoother operation. An efficient linear programming algorithm solves the optimization problem posed by this approach. The proposed constrained MPC controller is compared to a control strategy based on locals GPC controllers using a tight level control around the sump box.