Aggregate drying is a crucial step in asphalt mixture production. Enhancing the model accuracy and controller performance of aggregate dryer burners is essential for consistent flame characteristics, reducing NOx emissions, and minimizing fuel consumption. This paper introduces a second-order nonlinear parametric model for coal powder burners that includes delay and noise. Model parameters were determined through experimental data using the Salp Swarm Algorithm, showing higher accuracy than models based on the least square method. A dual-layer model predictive control (MPC) based on this mathematical model was developed to improve the economic efficiency of the aggregate drying process. Simulation results showed that the dual-layer MPC saves 1.08 tons of coal every 10 h compared to a standard MPC. A full-scale prototype demonstrated average flame length, flame temperature, and NOx emissions of 4242.6 mm, 1729.4 °C, and 460.2 mg/m³, respectively, validating the accuracy of the proposed mathematical model and controller.