This paper shows how to construct and implement explicit MPC feedback laws for systems with a large number of states. Specifically, the construction of critical regions of the explicit MPC solution is replaced by a two-step procedure. First, all optimal active sets are enumerated off-line and corresponding KKT matrices are pre-factored. Then, in the on-line step, the optimal control inputs are identified by checking primal and dual feasibility conditions using the pre-factored data. The feasibility and performance of the proposed approach are experimentally demonstrated on the control of the laboratory binary distillation column, described by a dynamical model with 10 state variables. We show that the control algorithm requires only modest computational resources on-line. A comparison of the memory and computational demands of the proposed method with the on-line solution of the corresponding quadratic program via the state-of-the-art solver as well as the approximated solution via the first-order method is made. (C) 2016 Elsevier Ltd. All rights reserved.