  Nonlinear model predictive control (NMPC) requires accurate and
computationally efficient plant models. Our previous work has shown that the
classical compartmentalization model reduction approach for distillation
columns can be enhanced by replacing parts of the system of equations by
artificial neural networks (ANNs) trained on offline solved solutions to
improve computational performance. In real-life applications, the absence of a
high-fidelity model for data generation can, however, prevent the deployment of
this approach. Therefore, we propose a method that utilizes solely plant
measurement data, starting from a small initial data set and then continuously
adapting to newly measured data. The efficacy of the proposed approach is
examined in silico for a distillation column from literature. To this end, we
first adjust our reduced hybrid mechanistic/data-driven modeling approach that
originally builds on compartmentalization to a stage-aggregation procedure,
tailoring it for the application within the adaptive learning framework.
Second, we apply an adaptive learning algorithm that trains the ANNs replacing
the stationary stage-to-stage calculations on newly available data. We apply
the adaptive learning of the hybrid model within a regulatory NMPC framework
and conduct closed-loop simulations. We demonstrate that by using the proposed
method, the control performance can be steadily improved over time compared to
a non-adaptive approach while being real-time applicable. Moreover, we show
that the performance when using either a model trained on excessive amounts of
offline generated data or the original high-fidelity model can be approached in
the limit.
