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

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 T-2 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.