System identification of batch milk cooling using output error models

Rudy Agustriyanto (University of Surabaya)
Aloisiyus Yuli Widianto (University of Surabaya)
Edy Purwanto (University of Surabaya)
Puguh Setyopratomo (University of Surabaya)

TELKOMNIKA (Telecommunication Computing Electronics and Control)
Vol 24, No 1: February 2026

Accurate modelling of milk cooling dynamics is essential to maintain product quality and improve energy efficiency in small-scale dairy operations. This study aims to develop a dynamic model for a batch milk-cooling system used at Koperasi Unit Desa Sinau Andandani Ekonomi (KUD SAE) Pujon. Synthetic temperature data were generated under controlled perturbations reflecting actual process conditions, and the data were analysed using the output error (OE) identification method implemented in the MATLAB System Identification Toolbox. Several OE model structures were compared using statistical indicators, including the coefficient of determination (R²) and root mean square error (RMSE). The OE (2,2,1) model achieved the best performance with R² = 0.9923 and RMSE = 0.0600, accurately representing the first-order dynamics of the cooling process. The identified model provides a reliable foundation for process optimisation, controller design, and operator training in dairy systems. Although the validation is limited to simulated data, the proposed approach offers substantial potential for real-time implementation and can be extended to other temperature-sensitive food processes.