Two-time dimensional dynamic matrix control for batch processes with convergence analysis against the 2D interval uncertainty

A batch process can be treated as a 2-dimentional (2D) system with a time dimension within each batch and a batch dimension from batch to batch. This paper integrates the learning ability of iterative learning control (ILC) into the prediction model of model predictive control (MPC). Based on this integrated model, a 2D dynamic matrix control (2D-DMC) algorithm with a feedback control and an optimal feed-forward control is proposed. The sufficient conditions for exponentially asymptotic and monotonic convergence of the proposed 2D-DMC are established with proof under certain assumptions, in the presence of not only the completely repeatable uncertainties but also the non-repeatable interval uncertainties. The effectiveness of the proposed control scheme is tested through simulation and experimental implementation in the context of injection molding, a typical batch process. The results show that the batch process control performance is significantly improved. (C) 2012 Elsevier Ltd. All rights reserved.