Industrial rotary dryers with combustion chambers are among the most energy-intensive unit operations in nickel laterite processing, often operating below 50% thermal efficiency. This study develops low-order linear models for the air–fuel dynamics of an industrial rotary dryer at the Nickel and Cobalt Producing Company “Comandante Ernesto Che Guevara” (Cuba) using one month of passive operational data. The methodology integrates signal preprocessing, prediction-error minimization, statistical diagnostics, and AIC/BIC-based model selection to identify parsimonious transfer functions compatible with PLC-level control. The best models—ARX(1,1,0) for both the fuel and the primary-air loops—achieved FIT indices of 86.1% and 87.4%, respectively. Residual whiteness and input–residual independence remained within 95% bounds, confirming statistical adequacy and appropriate model order. Compared with high-fidelity CFD or ANN-based approaches, the identified low-order models emphasize deployability and interpretability for PLC-level, control-oriented use in brownfield environments, without claiming a quantitative performance benchmark against those methods. The identified models provide a control-oriented representation of the air–fuel dynamics, enabling systematic controller tuning aimed at supporting energy-efficient operation in industrial drying processes.