Constrained latent variable model predictive control for trajectory tracking and economic optimization in batch processes

• A constrained LV-MPC technique is proposed for trajectory tracking in batch processes.
• This technique is based on a time-varying dynamic model derived from MPCA.
• Nonlinear processes can efficiently be handled algebraically by MPCA models.
• An economic LV-MPC with model and trajectory updating batch-to-batch is also proposed.
• Both proposed techniques are successfully applied onto a benchmark batch process.

A constrained latent variable model predictive control (LV-MPC) technique is proposed for trajectory tracking and economic optimization in batch processes. The controller allows the incorporation of constraints on the process variables and is designed on the basis of multi-way principal component analysis (MPCA) of a batch data array rearranged by means of a regularized batch-wise unfolding. The main advantages of LV-MPC over other MPC techniques are: (i) requirements for the dataset are rather modest (only around 10–20 batch runs are necessary), (ii) nonlinear processes can efficiently be handled algebraically through MPCA models, and (iii) the tuning procedure is simple. The LV-MPC for tracking is tested through a benchmark process used in previous LV-MPC formulations. The extension to economic LV-MPC includes an economic cost and it is based on model and trajectory updating from batch to batch to drive the process to the economic optimal region. A data-driven model validity indicator is used to ensure the prediction’s validity while the economic cost drives the process to regions with higher profit. This technique is validated through simulations in a case study.