Chromatographic processes for performing difficult separations such as enantiomers separation with high purity are an expanding technology. An interesting alternative to the expensive conventional batch chromatography is the true moving bed, a counter-current continuous process. However, for feasibility reasons, the TMB cannot be realized. The simulated moving bed (SMB) is realized in practice by connecting several single chromatographic columns in series and simulating the movement of solid by cyclic switching of the inlet and outlet ports. The complex dynamics, important non linearity, and multivariable character of the SMB make its control a challenging task. At this stage of the study, model predictive control (MPC) under the form of quadratic dynamic matrix control (QDMC) is applied on the TMB and the SMB. The numerical simulations of reference trajectory tracking performed show that the QDMC is well adapted for TMB control while the control of the SMB remains improvable.