Integrating population balance modeling and machine learning for real-time control and optimization of granulation processes

Wet granulation processes play a critical role in industries like pharmaceuticals, where achieving desired granule properties is essential for product quality. The complex dynamics of granulation, driven by phenomena like aggregation and breakage, pose significant challenges for traditional control strategies. While Population Balance Models (PBMs) accurately capture the mechanistic evolution of particle size distribution (PSD), their high computational demands have hindered their use in real-time control. This research presents a novel hybrid modeling framework that integrates a PBM with a Machine Learning (ML) surrogate model to enable a computationally efficient Model Predictive Control (MPC) system. The PBM provides a mechanistic foundation, while a Random Forest-based ML model serves as a rapid surrogate, trained on PBM-generated data. The surrogate model was rigorously validated and demonstrated high fidelity, explaining over 95% of the variance in six key quality attributes (diam43, dwidth, f1dmass, d10, d50, and d90) with an average error of less than 5% validated on extensive unseen runs. When embedded in an MPC, this hybrid model delivered reliable setpoint tracking with less than a 2% overshoot and operated with a runtime suitable for real-time applications. This work demonstrates that combining physics-based modeling and data-driven learning within MPC offers a scalable, generalizable strategy for intelligent process control. This approach not only enhances control performance but also accelerates the transition from simulation to real-time implementation in industrial granulation systems, representing a significant step toward smart manufacturing. • Hybrid PBM–ML framework for wet granulation process modeling • Random Forest surrogate predicts PSD metrics with high accuracy • Surrogate explains >95% variance with <5% prediction error • MPC achieves reliable setpoint tracking with <2% overshoot • Enables real-time, scalable control of granulation processes