Dynamic Study and PI Control of Milk Cooling Process

Rudy Agustriyanto, Endang Srihari Mochni


The background of this research is to understand the operation process, which is the main goal of developing the process model. This model is often used for operator training, process design, safety system analysis, or control system design. The dynamic model of the milk cooling process from 36ËšC to 4ËšC using chilled water available at 2ËšC was performed. Chilled water was maintained at a constant temperature by using a refrigerant unit. The process being investigated 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-hr cooling process, the gain and time constant values are 1.00 and 42.3548 mins, respectively. Heat balance was then extended to continuous processes so that its transfer function could also be obtained. This study simulated and investigated the behavior of batch and continuous processes. Process Identification via input-output data was also introduced for continuous process. The process model obtained from the system identification toolbox was very useful in control, such as for determining tuning parameters via the Ziegler-Nichol method for Proportional-Integral control. However, a small delay was required to be introduced to the system as the first order process without time Ziegler Nichol method cannot be implemented. Further research may include other system identification methods, such as ARX, ARMAX, Output-Error, Box Jenkins etc., or implementing advanced process control for milk cooling.


Dynamic study; milk cooling; simulation; process control.

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P. D. Edwards et al., Maternal effects in mammals: Broadening our understanding of offspring programming, Frontiers in Neuroendocrinology, vol. 62, p. 100924, Jul. 2021, doi: 10.1016/J.YFRNE.2021.100924.

A. Valldecabres and N. Silva-del-Río, First-milking colostrum mineral concentrations and yields: Comparison to second milking and associations with serum mineral concentrations, parity, and yield in multiparous Jersey cows, Journal of Dairy Science, Jan. 2022, doi: 10.3168/JDS.2021-21069.

T. F. OCallaghan et al., The bovine colostrum and milk metabolome at the onset of lactation as determined by 1H-NMR, International Dairy Journal, vol. 113, p. 104881, Feb. 2021, doi: 10.1016/J.IDAIRYJ.2020.104881.

P. D. Edwards et al., Maternal effects in mammals: Broadening our understanding of offspring programming, Frontiers in Neuroendocrinology, vol. 62, p. 100924, Jul. 2021, doi: 10.1016/J.YFRNE.2021.100924.

R. Jongeneel and A. R. Gonzalez-Martinez, The role of market drivers in explaining the EU milk supply after the milk quota abolition, Economic Analysis and Policy, Dec. 2021, doi: 10.1016/J.EAP.2021.11.020.

A. O. da Camara, L. G. Rodrigues, T. da S. Ferreira, and O. M. G. de Moraes, Sodium found in processed cow milk and estimated intake by infants, Jornal de Pediatria, vol. 97, no. 6, pp. 665–669, Nov. 2021, doi: 10.1016/J.JPED.2021.02.003.

N. N. Nasralla et al., Compositional characteristics of dairy products and their potential nondairy applications after shelf-life, Current Research in Food Science, vol. 5, pp. 150–156, Jan. 2022, doi: 10.1016/J.CRFS.2021.12.017.

D. Lindsay, R. Robertson, R. Fraser, S. Engstrom, and K. Jordan, Heat induced inactivation of microorganisms in milk and dairy products, International Dairy Journal, vol. 121, p. 105096, Oct. 2021, doi: 10.1016/J.IDAIRYJ.2021.105096.

X. Yang et al., The complex community structures and seasonal variations of psychrotrophic bacteria in raw milk in Heilongjiang Province, China, LWT, vol. 134, p. 110218, Dec. 2020, doi: 10.1016/J.LWT.2020.110218.

J. B. Ndahetuye et al., MILK Symposium review: Microbiological quality and safety of milk from farm to milk collection centers in Rwanda, Journal of Dairy Science, vol. 103, no. 11, pp. 9730–9739, Nov. 2020, doi: 10.3168/JDS.2020-18302.

D. Annie Rose Nirmala, S. Ramaswamy, K. Logesh, and S. Joe Patrick Gnanaraj, Empirical study on risk mitigation for dairy supply chain management of Aavin Co-operative Milk Producers Union Ltd., Materials Today: Proceedings, vol. 49, pp. 3657–3660, Jan. 2022, doi: 10.1016/J.MATPR.2021.09.243.

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

F. Moffat, S. Khanal, A. Bennet, T. B. Thapa, and S. M. George, Technical and Investment Guidelines for Milk Cooling Centers. Rome: Food and Agriculture Organization of the United Nations, 2016.

R. Al-Shannaq, A. Auckaili, and M. Farid, 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, pp. 207–228, Jan. 2022, doi: 10.1016/B978-0-12-821292-9.00006-6.

M. D. Murphy, J. Upton, and M. J. OMahony, Rapid milk cooling control with varying water and energy consumption, Biosystems Engineering, vol. 116, pp. 15–22, 2013.

P. Shine, J. Upton, P. Sefeedpari, and M. D. Murphy, Energy consumption on dairy farms: A review of monitoring, prediction modelling, and analyses, Energies, vol. 13, no. 5. MDPI AG, Mar. 01, 2020. doi: 10.3390/en13051288.

P. Shine, T. Scully, J. Upton, L. Shalloo, and M. D. Murphy, Electricity & direct water consumption on Irish pasture based dairy farms: A statistical analysis, Applied Energy, vol. 210, pp. 529–537, Jan. 2018, doi: 10.1016/j.apenergy.2017.07.029.

J. Upton, M. Murphy, P. French, and P. Dillon, Dairy farm energy consumption, 2010.

D. R. Coughanowr and S. E. LeBlanc, Process Systems Analysis and Control, 3rd ed. McGraw-Hill, 2009.

S. N. Sapali, S. M. Pise, A. T. Pise, and D. V. Ghewade, Investigations of waste heat recovery from bulk milk cooler, Case Studies in Thermal Engineering, vol. 4, pp. 136–143, 2014.

R. A. Jordan, L. A. B. Cortez, V. Silveira Jr, M. E. R. M. Cavalcantimata, and F. D. de Oliveira, Modeling and testing of an ice bank for milk cooling after milking, Journal of the Brazilian Association of Agricultural Engineering, vol. 38, no. 4, pp. 510–517, 2018.

R. Agustriyanto, A. Febriyanto, and P. S. Widiawati, “Perbandingan kinerja penyetelan Hagglund-Astorm dan Tyreus Luyben pada sistem kendali pendinginan susu,†Jurnal Rekayasa Proses, vol. 12, no. 2, pp. 10–18, 2018.

R. Agustriyanto, Regulatory performance of two different tuning methods for milk cooling control system, IOP Conf. Series: Materials Science and Engineering, vol. 703, 2019.

X. Dong, Y. Yu, Z. Zhang, and X. Huang, Mathematical analysis of heat balance model for the bubble growth in the subcooled boiling flow, Case Studies in Thermal Engineering, vol. 28, p. 101630, Dec. 2021, doi: 10.1016/J.CSITE.2021.101630.

D. Vinoth Kumar, S. Vijayaraghavan, and P. Thakur, Analytical and experimental investigation on heat transfer and flow parameters of Multichannel louvered fin cross flow heat exchanger using iterative LMTD and ∊-NTU method, Materials Today: Proceedings, Nov. 2021, doi: 10.1016/J.MATPR.2021.11.045.

X. Cui, K. J. Chua, M. R. Islam, and W. M. Yang, Fundamental formulation of a modified LMTD method to study indirect evaporative heat exchangers, Energy Conversion and Management, vol. 88, pp. 372–381, Dec. 2014, doi: 10.1016/J.ENCONMAN.2014.08.056.

K. L. Wong, M. T. Ke, and S. S. Ku, The log mean heat transfer rate method of heat exchanger considering the influence of heat radiation, Energy Conversion and Management, vol. 50, no. 11, pp. 2693–2698, Nov. 2009, doi: 10.1016/J.ENCONMAN.2009.05.024.

M. Mistry and R. Misener, Optimising heat exchanger network synthesis using convexity properties of the logarithmic mean temperature difference, Computers & Chemical Engineering, vol. 94, pp. 1–17, Nov. 2016, doi: 10.1016/J.COMPCHEMENG.2016.07.001.

H. Fatoorehchi and R. Rach, A method for inverting the Laplace transforms of two classes of rational transfer functions in control engineering, Alexandria Engineering Journal, vol. 59, no. 6, pp. 4879–4887, Dec. 2020, doi: 10.1016/J.AEJ.2020.08.052.

J. Fišer and P. Zítek, PID Controller Tuning via Dominant Pole Placement in Comparison with Ziegler-Nichols Tuning, IFAC-PapersOnLine, vol. 52, no. 18, pp. 43–48, Jan. 2019, doi: 10.1016/J.IFACOL.2019.12.204.

K. H. Tseng, M. Y. Chung, C. Y. Chang, C. L. Hsieh, and Y. K. Tseng, Parameter optimization of nanosilver colloid prepared by electrical spark discharge method using Ziegler-Nichols method, Journal of Physics and Chemistry of Solids, vol. 148, p. 109650, Jan. 2021, doi: 10.1016/J.JPCS.2020.109650.

M. Nikolaou, Ziegler and Nichols meet Kermack and McKendrick: Parsimony in dynamic models for epidemiology, Computers & Chemical Engineering, vol. 157, p. 107615, Jan. 2022, doi: 10.1016/J.COMPCHEMENG.2021.107615.

Y. Chen, H. Yan, Y. Luo, and H. Yang, A proportional–integral (PI) law based variable speed technology for temperature control in indirect evaporative cooling system, Applied Energy, vol. 251, p. 113390, Oct. 2019, doi: 10.1016/J.APENERGY.2019.113390.

B. Şenol, U. Demiroğlu, and R. Matušů, Fractional order proportional derivative control for time delay plant of the second order: The frequency frame, Journal of the Franklin Institute, vol. 357, no. 12, pp. 7944–7961, Aug. 2020, doi: 10.1016/J.JFRANKLIN.2020.06.016.

A. Atangana and A. Akgül, Can transfer function and Bode diagram be obtained from Sumudu transform, Alexandria Engineering Journal, vol. 59, no. 4, pp. 1971–1984, Aug. 2020, doi: 10.1016/J.AEJ.2019.12.028.

P. P. Arya and S. Chakrabarty, A Modified IMC Structure to Independently Select Phase Margin and Gain Cross-over Frequency Criteria, IFAC-PapersOnLine, vol. 51, no. 1, pp. 267–272, Jan. 2018, doi: 10.1016/J.IFACOL.2018.05.066.

P. Neyezhmakov and I. Zakharov, Determination of the time constant of measuring transducers, Measurement: Sensors, vol. 18, p. 100278, Dec. 2021, doi: 10.1016/J.MEASEN.2021.100278.

G. Picci, W. Cao, and A. Lindquist, Modeling and Identification of Low Rank Vector Processes, IFAC-PapersOnLine, vol. 54, no. 7, pp. 631–636, Jan. 2021, doi: 10.1016/J.IFACOL.2021.08.431.

B. Roffel and B. Betlem, Process Dynamics and Control: Modeling for Control and Prediction. West Sussex: John Wiley & Sons Ltd, 2006.

L. Cheng, A. Cigada, Z. Lang, E. Zappa, and Y. Zhu, 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, vol. 152, p. 107439, May 2021, doi: 10.1016/J.YMSSP.2020.107439.

L. Li, H. Zhang, X. Ren, and J. Zhang, A novel recursive learning identification scheme for Box–Jenkins model based on error data, Applied Mathematical Modelling, vol. 90, pp. 200–216, Feb. 2021, doi: 10.1016/J.APM.2020.08.076.

Y. Cao, Z. Wang, S. Hu, and W. Wang, Modeling of weld penetration control system in GMAW-P using NARMAX methods, Journal of Manufacturing Processes, vol. 65, pp. 512–524, May 2021, doi: 10.1016/J.JMAPRO.2021.03.039.

Shahrokhi, Mohammad, Zomorrodi, and Alireza, Comparison of PID controller tuning methods, Tehran, 2018.

T. Anitha and G. Gopu, Controlled mechanical ventilation for enhanced measurement in pressure and flow sensors, Measurement: Sensors, vol. 16, p. 100054, Aug. 2021, doi: 10.1016/J.MEASEN.2021.100054.

A. Basu, S. Mohanty, and R. Sharma, Introduction of fractional elements for improvising the performance of PID controller for heating furnace using AMIGO tuning technique, Perspectives in Science, vol. 8, pp. 323–326, Sep. 2016, doi: 10.1016/J.PISC.2016.04.065.

DOI: http://dx.doi.org/10.18517/ijaseit.12.5.16332


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