Auto Regressive eXogenous (ARX) System Identification of Batch Milk Cooling Process

https://doi.org/10.22146/ajche.70546

Rudy Agustriyanto(1*), Endang Srihari Mochni(2), Puguh Setyopratomo(3)

(1) University of Surabaya
(2) University of Surabaya
(3) University of Surabaya
(*) Corresponding Author

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.


Keywords


Dynamic Study, Milk Cooling, Simulation, Process Identification

Full Text:

PDF


References

Agustriyanto, R., 2019. “Regulatory performance of two different tuning methods for milk cooling control system.” IOP Conf. Series: Materials Science and Engineering, 703. https://doi.org/10.1088/1757-899X/703/1/012004

Agustriyanto, R., Setyopratomo, P., and Srihari, E., 2022. “Dynamic study of batch milk cooling process at KUD SAE Pujon.” AIP Conference Proceedings, 2470, p. 030001. https://doi.org/10.1063/5.0080176

Al-Shannaq, R., Auckaili, A., and Farid, M., 2022. “Cooling of milk on dairy farms: an application of a novel ice encapsulated storage system in New Zealand.” Food Engineering Innovations Across the Food Supply Chain, 207–228. https://doi.org/10.1016/B978-0-12-821292-9.00006-6

Bajarangbali, R., Majhi, S., and Pandey, S. 2014. “Identification of FOPDT and SOPDT process dynamics using closed loop test.” ISA Transactions, 53, 1223–1231. https://doi.org/10.1016/J.ISATRA.2014.05.014

Behnam, P., Shafieian, A., Zargar, M., and Khiadani, M., 2022. “Development of machine learning and stepwise mechanistic models for performance prediction of direct contact membrane distillation module- A comparative study.” Chemical Engineering and Processing - Process Intensification, 173, 108857. https://doi.org/10.1016/J.CEP.2022.108857

Bequette, B.W., 2019. “Process control practice and education: Past, present and future.” Computers & Chemical Engineering, 128, 538–556. https://doi.org/10.1016/J.COMPCHEMENG.2019.06.011

Chakraborty, R., Jain, H., and Seo, G.-S., 2022. “A review of active probing-based system identification techniques with applications in power systems.” International Journal of Electrical Power & Energy Systems, 140, 108008. https://doi.org/10.1016/J.IJEPES.2022.108008

Ee, C. T., Khaw, Y. J., Hii, C. L., Chiang, C. L., and Djaeni, M., 2021. “Drying kinetics and modelling of convective drying of kedondong fruit.” ASEAN Journal of Chemical Engineering, 21, 93–103.

Cheng, L., Cigada, A., Lang, Z., Zappa, E., and Zhu, Y., 2021. “An output-only ARX model-based sensor fusion framework on structural dynamic measurements using distributed optical fiber sensors and fiber Bragg grating sensors.” Mechanical Systems and Signal Processing, 152, 107439. https://doi.org/10.1016/J.YMSSP.2020.107439

Coughanowr, D.R., and LeBlanc, S.E., 2009. Process systems analysis and control, 3rd ed. McGraw-Hill.

Dhanya Ram, V., and Chidambaram, M., 2014. “Closed loop Reaction Curve method for Identification of TITO systems.” IFAC Proceedings, 47, 989–996. https://doi.org/10.3182/20140313-3-IN-3024.00135

Fung, P.L., Zaidan, M.A., Timonen, H., Niemi, J. v., Kousa, A., Kuula, J., Luoma, K., Tarkoma, S., Petäjä, T., Kulmala, M., and Hussein, T., 2021. “Evaluation of white-box versus black-box machine learning models in estimating ambient black carbon concentration.” Journal of Aerosol Science, 152, 105694. https://doi.org/10.1016/J.JAEROSCI.2020.105694

Jouhara, H., Almahmoud, S., Brough, D., Guichet, V., Delpech, B., Chauhan, A., Ahmad, L., and Serey, N., 2021. “Experimental and theoretical investigation of the performance of an air to water multi-pass heat pipe-based heat exchanger.” Energy, 219, 119624. https://doi.org/10.1016/J.ENERGY.2020.119624

Kaufhold, E., Meyer, J., and Schegner, P. 2021. “Black-box identification of grid-side filter circuit for improved modelling of single-phase power electronic devices for harmonic studies.” Electric Power Systems Research, 199, 107421. https://doi.org/10.1016/J.EPSR.2021.107421

Lee, A.P., Barbano, D.M., and Drake, M.A., 2016. “Short communication: The effect of raw milk cooling on sensory perception and shelf life of high-temperature, short-time (HTST)–pasteurized skim milk.” Journal of Dairy Science, 99, 9659–9667. https://doi.org/10.3168/JDS.2016-11771

Li, H., Huang, H., Xu, G., Wen, J., and Wu, H., 2017. “Performance analysis of a novel compact air-air heat exchanger for aircraft gas turbine engine using LMTD method.” Applied Thermal Engineering 116, 445–455. https://doi.org/10.1016/J.APPLTHERMALENG.2017.01.003

Li, X., Zhao, Z., and Liu, F., 2020. “Latent variable iterative learning model predictive control for multivariable control of batch processes.” Journal of Process Control, 94, 1–11. https://doi.org/10.1016/J.JPROCONT.2020.08.001

Ochsenbein, D.R., Billups, M., Hong, B., Schäfer, E., Marchut, A.J., and Lyngberg, O.K., 2019. “Industrial application of heat- and mass balance model for fluid-bed granulation for technology transfer and design space exploration.” International Journal of Pharmaceutics: X 1, 100028.

https://doi.org/10.1016/J.IJPX.2019.100028

Pauli, V., Elbaz, F., Kleinebudde, P., and Krumme, M., 2019. “Orthogonal Redundant Monitoring of a New Continuous Fluid-Bed Dryer for Pharmaceutical Processing by Means of Mass and Energy Balance Calculations and Spectroscopic Techniques.” Journal of Pharmaceutical Sciences, 108, 2041–2055. https://doi.org/10.1016/J.XPHS.2018.12.028

Prasad, P., Gaffel, J., and Price, N., 2019. Eco-efficiency for the Dairy Processing Industry, 2019th ed. Dairy Australia 2019, Sydney.

R2022a, n.d. System Identification Toolbox [WWW Document]. URL https://www.mathworks.com/help/ident/ (accessed 3.17.22).

Roffel, B., and Betlem, B., 2006. Process dynamics and control: Modeling for control and prediction. John Wiley & Sons Ltd, West Sussex.

Torres-Toledo, V., Hack, A., Mrabet, F., Salvatierra-Rojas, A., and Müller, J., 2018. “On-farm milk cooling solution based on insulated cans with integrated ice compartment.” International Journal of Refrigeration, 90, 22–31. https://doi.org/10.1016/J.IJREFRIG.2018.04.001

Yin, H., Wei, Y., Zhang, Y., Jing, P., Cai, D., and Liu, X., 2022. “Identification of control parameters of the permanent magnetic synchronous generator using least square method.” Energy Reports, 8, 1538–1545. https://doi.org/10.1016/J.EGYR.2022.02.034

Zacharski, K.A., Burke, N., Adley, C.C., Hogan, P., Ryan, A., and Southern, M., 2021. “Milk reception in a time-efficient manner: A case from the dairy processing plant.” Food Control, 124, 107939. https://doi.org/10.1016/J.FOODCONT.2021.107939



DOI: https://doi.org/10.22146/ajche.70546

Article Metrics

Abstract views : 1211 | views : 937

Refbacks

  • There are currently no refbacks.


ASEAN Journal of Chemical Engineering  (print ISSN 1655-4418; online ISSN 2655-5409) is published by Chemical Engineering Department, Faculty of Engineering, Universitas Gadjah Mada.