Regionless explicit MPC of a distillation column

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 avoided altogether and is instead replaced by a two-step procedure. In the first step, all optimal active sets are enumerated off-line and the 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 advantage of such an approach is that it allows to construct explicit MPC solutions even for complex systems. The feasibility of the approach is demonstrated on a laboratory distillation column described by a dynamical model with 10 state variables. We show that the control algorithm requires only modest computational resources on-line. The performance of the proposed regionless explicit MPC strategy is validated using experimentally collected data. The paper also covers identification of the dynamical behavior of the distillation column and the design of a suitable state observer.