An adaptive data-based modeling approach for predictive control of batch systems

In this work, we generalize a previously developed data-based modeling methodology for batch processes to account for time-varying dynamics by incorporating online learning ability into the model, making it adaptive. First, the standard recursive least squares (RLS) algorithm with a forgetting factor is applied to update the model parameters. However, applying the standard RLS algorithm leads to a global update of all the models, which may be unnecessary depending on the operating conditions of the process. We address this issue by developing a probabilistic RLS (PRLS) estimator (also with a forgetting factor) for each model that takes the probability of the model being representative of the current plant dynamics into account in the update. The main advantage of adopting this localized update approach is adaptation tuning flexibility. Specifically, the model adaptations can be made more aggressive while maintaining better parameter precision compared to the standard RLS algorithm. The benefits from incorporating both RLS algorithms are demonstrated via simulations of a nylon-6,6 batch polymerization reactor. Closed-loop simulation results illustrate the improvement in tracking performance (over the non-adaptive model based design). The model adaptation is also shown to be crucial for achieving acceptable control performance when encountering large disturbances in the initial conditions.