Disturbance rejection for the control of batch end-product quality using latent variable models

The control of batch end-product quality is an important issue in many high value-added manufacturing industries, particularly specialty chemicals and pharmaceuticals. An attractive approach for controlling such systems is to apply partial least squares (PLS) models, which can utilize the low-dimensional latent variable (or score) space with the corresponding control optimization performed on these few latent variables. The manipulated variable trajectories (MVTs) can then be reconstructed from the optimized scores. The existing PLS-based batch end-product quality control methodology does not incorporate the disturbance model in its formulation. As a result, it is demonstrated in this paper that these control formulations can be incapable of adequate disturbance rejection. To reject disturbances adequately, it is necessary to utilize feedback information and re-compute optimal control sequences at multiple instants during a batch run. However, this can lead to erratic control action, resulting in the deterioration of batch end-product quality. To resolve this issue, a revised PLS-based batch end-product quality controller is proposed in this paper that explicitly accounts for disturbance induced plant-model mismatch by including a simple disturbance model. Furthermore, the proposed controller formulation adds hard constraints to incremental changes of the re-computed control sequences to avoid erratic behavior in the case of multiple control decision points. The ability of the proposed control scheme to reject disturbances and obtain desirable MVTs is demonstrated using a benchmark simulation of a fed-batch fermentation process.