Industrial Automatic Control Systems and Controllers Annotation << Back A Hybrid Kinetic Flotation Model Accounting for Particle Size Distribution and Reagent Regime Chadin D.A., Mokrova N.V. This paper presents a hybrid kinetic flotation model combining fundamental physicochemical principles with machine learning-based parametric identification. The objective is to develop a predictive tool balancing physical interpretability with data-driven flexibility, addressing limitations of purely classical or purely machine learning approaches. The classical Beloglazov model is extended by introducing influence functions relating particle size distribution and reagent dosage to the kinetic parameters. Both ultimate recovery and fl otation rate constant are shown to depend on these factors. To approximate these dependencies, a hierarchical parametric structure is proposed: the infl uence functions adopt physically meaningful forms – a logistic curve for recovery and an exponential saturation function for the rate constant – while their coeffi cients are themselves represented as parametric functions of particle size. This multi-level structure ensures interpretability and minimizes training data requirements. The model was validated using experimental galena fl otation data for four size fractions (−38+23, −23+18, −18+9, −9+0 μm) with potassium butyl xanthate concentrations ranging from 0.2 to 10.0 mg/L. Results confirm accurate capture of flotation kinetics, yielding R2 = 0.9835 and mean absolute error of 2.21 %. Analysis reveals correct reproduction of key physical phenomena, including maximum reagent sensitivity for intermediate-sized particles (−18+9 μm) and minimal flotation rate for the finest fraction (−9+0 μm). Verification under limiting conditions – zero reagent concentration and infinite flotation time – confirms physical consistency. The proposed framework demonstrates strong potential for digital twins in flotation processes and adaptive control systems in mineral processing plants, combining predictive accuracy with mechanistic insight. Keywords: flotation; kinetic model; hybrid modeling; machine learning; particle size distribution; reagent regime; influence functions; model validation. DOI: 10.25791/asu.9.2026.1684 Pp. 27-37.