Data-driven model predictive control of a seeded batch crystallization process

Particulates production has undergone phenomenal growth in the past few decades. They are used for manufacturing of numerous high-value industrial products such crystals, polymers etc. The products are often manufactured using batch processes to provide the flexibility of achieving different products by changing recipes.  The physio-chemical and mechanical properties of the end product are known to be linked to the particle size distribution (PSD). For instance, in case of emulsion polymerization, PSD strongly impacts the polymer’s rheology (viscosity), adhesion, drying characteristics etc. [1] Traditional approach for control of batch processes (particulates or otherwise) have been to use open loop, recipe based policy. In this approach, a predefined input trajectory is applied to each batch [2]. The approach assumes that the desired product quality can be obtained by repeating historically successful input profiles. Although these approaches are easy to implement and do not require a model for the process, they are incapable of rejecting disturbances that affect the process. This has motivated the use of feedback control strategies. A classical closed loop control approach in batch process is trajectory tracking. In this approach, a predefined set-point trajectory for a measured process variable, often obtained from past successful batches, is tracked. PI controllers are often used for implementing trajectory tracking control. When implementing trajectory tracking approaches (with PI or otherwise) even with perfect tracking, the desired quality may not be obtained, as the relationship between the measured/tracked variable and final quality may change significantly with changes in the process conditions. These challenges are addressed by control strategies that are cognizant of the causal relationship not only between the manipulated and the (online) measured variables, but also between the manipulated and the final quality variable. A popular model based control approach, model predictive control (MPC), has increasingly been studied for the control of batch processes [3-6]. The reasons for popularity of these control schemes are twofold: first, the feedback controller can counter the model uncertainties that are associated with model simplifications and measurement errors, the other being their ability to handle the ever present input/output constraints. In implementing these formulations, where possible, good first principles models are preferred due to the ability to predict process behavior beyond the data set used to estimate the model parameters. However, first principles models are difficult to develop as it is often impractical to estimate the parameters through experiments, particularly because of the associated cost. Further, these first principles models, particularly in case of distributed parameter systems such as batch particulate processes, pose computational challenges for direct use in predictive control formulation. These issues have motivated the use of simpler, often linear, models derived from past batches database. A variety of approaches for development of data-driven models have been proposed. One of the most celebrated and widely used approach is partial least squares (PLS), which models the process in a projected latent space [7]. These models are essentially time-varying linear models, linearized around mean past trajectories, and therefore require the batches to be of same length, or to recognize an appropriate alignment variable. To account for these limitations, a multi-model approach was proposed in [6]. These models were based on the 'current measurements' of the process instead of the 'time'. These developments were followed by contributions in the area of integration of these data-driven models with the advanced control formulations [5-6]. More recently a subspace identification based batch control approach was proposed in [8] where a LTI state-space model of the batch process is estimated. The existing formulations have, however, dealt generally with lumped parameter systems and the applications of data-driven approaches for PBE systems have been limited. Some variation of PLS approach have been proposed for distributed parameter processes. In one approach [9] a PLS model is used in conjunction with the predictions obtained from PBEs for batch to batch optimization. A similar strategy is presented in [10] where only a PLS model is used for predicting the final PSD. As with other latent variable approaches, a limitation with the use of PLS models for batch processes is the need to align the batch lengths. Motivated by these considerations, this work presents a subspace identification based state-space modeling and control approach for a seeded batch crystallization process. The proposed control design is compared with an open loop policy as well as a traditional trajectory tracking policy using classical control. The proposed MPC is shown to achieve 27.22% and 29.90% improvements in the desired product quality, and the ability to respect tighter product quality constraints compared to existing approaches.