DAE-EKF-Based Nonlinear Predictive Control of Reactive Distillation Systems Exhibiting Input and Output Multiplicities

Abstract

Reactive distillation (RD) has become one of the most important hybrid separation processes in recent times because of its economic and operational advantages. Reactive distillation systems, however, can exhibit complex input and output multiplicity behavior simultaneously in the desired operating region. Moreover, such a system is generally stiff and is typically modeled as a set of differential-algebraic equations. These two factors render the control of RD systems a challenging problem, particularly when the desirable operating point is unstable. In this work, an observer error feedback-based NMPC scheme has been developed for achieving offset-free control of RD systems modeled as DAEs. A recently developed version of the EKF for DAE systems (Mandela et al. Chem. Eng. Sci. 2010, 65, 4548−4556) was used to carry out state estimation. Because direct use of a DAE solver in the NMPC formulation can prove to be prohibitively computationally intensive and unsuitable for online implementation, a successive-linearization-based NMPC scheme (SLNMPC) was also developed. The effectiveness of the proposed control schemes is demonstrated by simulating servo and regulatory control problems associated with a hypothetical ideal RD column that exhibits input and output multiplicity behavior simultaneously at an unstable but economically desirable operating point. The servo and regulatory performances of the proposed SLNMPC scheme were also studied by simulating an industrial RD system involving MTBE synthesis. Analysis of the simulation results indicates that the proposed SLNMPC formulation provides an effective approach for handling control problems involving moderately large-magnitude servo and regulatory changes in the operation of RD systems. Moreover, the average computation time for the SLNMPC formulation was found to be quite small when compared with the sampling interval, which establishes the feasibility of implementing the SLNMPC scheme in real time.