Open Access

ARTICLE

Dynamic Modeling and Control of Phosphate-Pebble Drying Systems—A Comprehensive Approach

José M. Campos-Salazar^1,*, Felipe Santander², Eduardo Keim³

1 Electronic Engineering Department, Universitat Politècnica de Catalunya, Barcelona, Spain
2 Process Department, Celulosa Arauco y Constitución SA, Concepción, Chile
3 Process Research Department, Celulosa Bioforest SA, Concepción, Chile

* Corresponding Author: José M. Campos-Salazar. Email:

Energy Engineering 2026, 123(6), 14 https://doi.org/10.32604/ee.2026.075407

Received 31 October 2025; Accepted 20 March 2026; Issue published 27 May 2026

Abstract

A nonlinear dynamic framework is developed to represent the coupled mass- and energy-transfer phenomena governing an industrial phosphate-pebble dryer. The formulation integrates combustion, gas–solid heat exchange, moisture evaporation, and exhaust-draft dynamics into a unified set of nonlinear differential equations suitable for transient analysis and control design. Steady-state operating conditions are first established, followed by local linearization to enable the synthesis of decentralized proportional–integral (PI) controllers using direct-synthesis principles. The resulting control architecture regulates key process variables, including vacuum pressure, outlet moisture content, and furnace temperature. The proposed model is implemented in MATLAB/Simulink using a modular structure that preserves the physical interpretation of each subsystem while enabling efficient numerical simulation. Closed-loop performance is evaluated under multiple disturbance scenarios, including variations in pressure, feed moisture, temperature, and flow conditions representative of industrial operation. Simulation results demonstrate that the designed controllers satisfy operational constraints, achieving overshoot values below 20% and steady-state errors under 5% across all regulated variables. The responses exhibit stable and well-damped behavior, confirming the suitability of the control-oriented modeling approach for capturing dominant process dynamics. The resulting framework provides a physically grounded and computationally efficient representation that supports dynamic performance assessment, disturbance rejection analysis, and future extensions toward advanced control strategies and energy-efficiency optimization.

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