Modeling and implementation of Linear Time-Varying Model Predictive Control (LTV-MPC) for a distillation system

Abstract

The primary challenge in batch distillation control is severe temperature fluctuations caused by time-varying system dynamics, which can significantly reduce the purity of the distillation product. Previous studies have commonly employed conventional PI/PID controllers or Linear Time-Invariant Model Predictive Control (LTI-MPC) approaches. However, PI/PID controllers are limited by their inability to explicitly incorporate process constraints, while LTI-MPC relies on invariant linear models that are insufficient to represent the inherently non-steady-state behavior of batch distillation processes. These limitations reveal a clear research gap, namely the absence of an adaptive multivariable predictive control strategy capable of accommodating system constraints while simultaneously capturing time-varying dynamics in real time. Therefore, this study proposes a multivariable Linear Time-Varying Model Predictive Control (LTV-MPC) strategy based on a modified physics-based nonlinear model. The proposed control strategy integrates two control inputs simultaneously, namely the solenoid-valve duty cycle of the heat rate and the feed flow rate, while updating the linearization matrices at every sampling instant, enabling the predictive model to adaptively track the evolving time-varying dynamics throughout the batch distillation process. Simulation results show that, at the 75th minute after the mixture begins to boil, the uncontrolled system experiences a temperature increase up to 96°C, causing the product purity to decrease to 25%. In contrast, the proposed LTV-MPC suppresses the temperature to 92°C and maintains the product purity at 38%. These findings demonstrate that the LTV-MPC framework is effective in controlling temperature and maintaining the quality of the distillation product.