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Auto Regressive eXogenous (ARX) System Identification of Batch Milk Cooling Process Rudy Agustriyanto; Endang Srihari Mochni; Puguh Setyopratomo
ASEAN Journal of Chemical Engineering Vol 22, No 2 (2022)
Publisher : Department of Chemical Engineering, Universitas Gadjah Mada

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22146/ajche.70546

Abstract

The dynamic model of the milk cooling process from 36°C to 4°C using chilled water available at 2°C has been carried out.  The cooling water temperature is kept constant by using a refrigeration unit. The process being studied was a Packo brand milk cooling tank belonging to KUD SAE Pujon (Malang - Indonesia). A fundamental heat balance method was used to derive the model, leading to a first-order transfer function process. For a 2 hours cooling process then, the gain and time constant values are 1.00 and 42.3548 mins respectively, or G(s)=1/(42.3548s+1) (first order process). Deriving system transfer function through a mechanistic model is considered difficult; therefore, in this paper, we explored process identification via Auto Regressive eXogenous (ARX). Transient simulations could then be performed to identify the dynamic behavior of the cooling process. The system was then identified using several orders of the Auto Regressive eXogenous (ARX) model, and then the results were re-tested on different forms of perturbations and obtained quite accurate results. The transfer function identified through the ARX111 is G(s)=1/(42.3729s+1) (first order process), while via ARX441, the 5th order process was obtained: G(s)=(0.02361s^4+0.000371s^3+0.2331s^2+9.27×10^(-7) s+0.0005826)/(s^5+0.03932s^4+9.873s^3+0.2331s^2+0.02468s+0.0005826). These models particularly useful for process control design and analysis.
System identification of batch milk cooling using output error models Rudy Agustriyanto; Aloisiyus Yuli Widianto; Edy Purwanto; Puguh Setyopratomo
TELKOMNIKA (Telecommunication Computing Electronics and Control) Vol 24, No 1: February 2026
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/telkomnika.v24i1.27469

Abstract

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.