Combining just‐in‐time modelling and batch‐wise unfolded PLS model for the derivative‐free batch‐to‐batch optimization

Abstract

In this work, a derivative‐free batch‐to‐batch optimization method is proposed. In order to conquer the difficulties in building a first principal model, a local batch‐wise unfolded PLS (BW‐PLS) model is used to accurately describe the concerned region, and the first principal model based dynamic optimization problem is transformed into a static one. The just‐in‐time (JIT) modelling method is employed to dynamically update the local BW‐PLS model upon request, and the nonlinearity and abrupt changes from one batch run to another can be effectively resolved. Then the proposed local BW‐PLS model with JIT modelling method is integrated into the trust‐region framework. Not only can the issue of plant‐model mismatch be dealt with, but also the computation of the experimental gradients can be avoided. In addition, taking the advantages of PLS regression, the Hotelling's T2 statistic is utilized as a hard constraint to ensure the reliability of the optimal solution. Extension to handle soft inequality constraints is also included in this work. Finally, the efficacy of the proposed batch‐to‐batch optimization method is illustrated via a toy example and a simulated cobalt oxalate synthesis process under different operating conditions, and satisfied optimization performances were obtained.