Dynamic real-time optimization of batch processes using Pontryagin’s minimum principle and set-membership adaptation

Abstract

This paper studies a dynamic real-time optimization in the context of modelbased time-optimal operation of batch processes under parametric model mismatch. In order to tackle the model-mismatch issue, a receding-horizon policy is usually followed with frequent re-optimization. The main problem addressed in this study is the high computational burden that is usually required by such schemes. We propose an approach that uses parameterized conditions of optimality in the adaptive predictive-control fashion. The uncertainty in the model predictions is treated explicitly using reachable sets that are projected into the optimality conditions. Adaptation of model parameters is performed online using set-membership estimation. A class of batch membrane separation processes is in the scope of the presented applications, where the benefits of the presented approach are outlined.

Optimal control and the Pontryagin's principle in chemical engineering: History, theory, and challenges

“…Later, the same authors improved upon their previous results by applying a parsimonious parameterization to the control. 34 Paulen and Fikar 163 applied the theory to identify the solution structure for the dynamic real-time optimization of batch processes. Rhein et al 164,165 presented a numerical treatment for the solution of dynamic optimization problems that result from an early lumping MPC and moving horizon estimation (MHE) design for a catalytic fixed-bed reactor model.…”

A Dynamic Real-Time Optimization Strategy for the Tennessee Eastman Benchmark

“…DRTO has been widely studied in the recent literature, with numerous papers demonstrating its benefits in various industrial applications. Some of the recent research has focused on developing new algorithms and approaches for implementing DRTO [20][21][22][23][24], while others have explored the use of DRTO in specific industrial settings, such as chemical processing [18,19,25] or energy systems [26][27][28]. Paulen and Fikar [20] proposed an approach to optimizing batch processes considering parametric model mismatch, where reachable sets were used to treat prediction uncertainty in the adaptive prediction of the DRTO.…”

“…Some of the recent research has focused on developing new algorithms and approaches for implementing DRTO [20][21][22][23][24], while others have explored the use of DRTO in specific industrial settings, such as chemical processing [18,19,25] or energy systems [26][27][28]. Paulen and Fikar [20] proposed an approach to optimizing batch processes considering parametric model mismatch, where reachable sets were used to treat prediction uncertainty in the adaptive prediction of the DRTO. Li and Swartz [21] utilized a DRTO formulation with closed-loop prediction to coordinate distributed model predictive controllers (MPCs) by predicting interactions between the MPCs and full plant response.…”