Batch-to-Batch Optimal Control of Batch Processes Based on Recursively Updated Nonlinear Partial Least Squares Models

Abstract

A batch-to-batch optimal control approach for batch processes based on batch-wise updated nonlinear partial least squares (NLPLS) models is presented in this article. To overcome the difficulty in developing mechanistic models for batch=semi-batch processes, a NLPLS model is developed to predict the final product quality from the batch control profile. Mismatch between the NLPLS model and the actual plant often exists due to low-quality training data or variations in process operating conditions. Thus, the optimal control profile calculated from a fixed NLPLS model may not be optimal when applied to the actual plant. To address this problem, a recursive nonlinear PLS (RNPLS) algorithm is proposed to update the NLPLS model using the information newly obtained after each batch run. The proposed algorithm is computationally efficient in that it updates the model using the current model parameters and data from the current batch. Then the new optimal control profile is recalculated from the updated model and implemented on the next batch. The procedure is repeated from batch to batch and, usually after several batches, the control profile will converge to the optimal one. The effectiveness of this method is demonstrated on a simulated batch polymerization process. Simulation results show that the proposed method achieves good performance, and the optimization with the proposed NLPLS model is more effective and stable than that with a batch-wise updated linear PLS model.

Integrated batch‐to‐batch and nonlinear model predictive control for polymorphic transformation in pharmaceutical crystallization

“…Each row of the matrix X consists of the input variables (i.e., temperature in this article) at sampling instances 0 to k À 1 for a particular batch, while each row of the matrix Y contains the deviation between a real process variable (i.e., solute concentration at each sampling instance k and product quality at the end of each batch) and that predicted by the firstprinciples model in the same batch. Note that the solute concentration prediction is used to handle solute concentration constraints (14) and (15). There are two common approaches to determine the number of datasets (n) kept in the database.…”

“…Xiong and Zhang 14 presented a recurrent neural network-based ILC scheme for batch processes where the filtered recurrent neural network prediction errors from previous batches are added to the model predictions for the current batch and the updated predictions used in optimization. Li et al 15 presented batch-tobatch optimal control in which a batchwise recursive nonlinear PLS algorithm updates the model after each batch.…”

“…The inequality constraint (14) aims to avoid the nucleation and growth rate of a-form crystals and the dissolution of b-form crystals during the polymorphic transformation. The end-point inequality constraint (15) ensures that the minimum yield required by economic considerations is satisfied. …”

Batch to batch optimal control based on multiinput multioutput adaptive hinging hyperplanes prediction and Kalman filter correction

“…In fact, To handle this, References 7,23 used the corrected predicted value and reoptimize the optimal control problem again, in which the corrected predicted value is obtained by adding modeling errors of previous runs. In Reference 24, the authors updated the data driven model with the data in the new batch, and then resolved the optimization problem according to the updated model 24 . Besides, References 25‐27 used the idea of iterative learning control to calculate the input updating equations.…”

A nonlinear partial least squares algorithm using quadratic fuzzy inference system

“…Originally, the PLS method was introduced as a linear regression technique. This linearity assumption between inputs X and outputs Y was recognized as a main drawback in the PLS method because the real world data often exhibit nonlinearity [2,3]. Several nonlinear PLS techniques were developed to cope with the nonlinearity.…”