Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer

Augustine Kweku Mbeah; Erwin Normanyo

doi:doi:10.11648/j.acis.20261403.11

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Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer

Augustine Kweku Mbeah^*

, Erwin Normanyo

Published in Automation, Control and Intelligent Systems (Volume 14, Issue 3)

Received: 25 August 2026 Accepted: 4 September 2026 Published: 20 September 2026

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Abstract

A mathematical model and dynamic performance study of a Supervisory Control and Data Acquisition (SCADA) system and a Programmable Logic Controller (PLC) that were previously utilized to automate the pharmaceutical batch mixer are presented in this research. While the earlier work implemented the discrete, sequential control logic for the mixer using Siemens STEP 7 and validated it with RSLogix 5000, the continuous-time hydraulic behaviour of the three interconnected process vessels (heating, mixing and storage tanks) had not been characterised. In this study, the batch mixing system is partitioned into three sections, each represented by a pump-and-tank arrangement, and first-principles mass-balance, Bernoulli energy-balance and Darcy friction-loss equations are used to derive the transfer functions relating pump flow rate and tank level to valve resistance and tank cross-sectional area. Laplace transformation of the governing equations yields an overall block-diagram model of the three-tank system, which is implemented and simulated in MATLAB/SIMULINK. The simulation results show that the flow response settles at 0.5 m3/s with a settling time of 1.32 x 10^4 seconds, an overshoot of 11.5% and a rise time of 4.03 x 10^3 seconds. The tank-level responses show a successive filling pattern consistent with the batching sequence, with Tank 1 filling within 20 minutes, Tank 2 reaching its maximum level at 65 minutes, and Tank 3 completing filling at 210 minutes from the start of the process. These results confirm that the batch mixer exhibits stable, well-damped dynamic behaviour, providing a quantitative basis for the timer presets and control logic used in the PLC-SCADA automation reported previously, and supporting the suitability of the process for closed-loop SCADA-based control.

Published in	Automation, Control and Intelligent Systems (Volume 14, Issue 3)
DOI	10.11648/j.acis.20261403.11
Page(s)	50-58
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Batch Mixer, Mathematical Modelling, Transfer Function, MATLAB/SIMULINK, Performance Analysis, Programmable Logic Controller, Supervisory Control and Data Acquisition, Pharmaceutical Process

References

[1]	Mbeah, A. K., Normanyo, E. Automation of a Pharmaceutical Batch Mixer Using Programmable Logic Controller (PLC) and Supervisory Control and Data Acquisition System (SCADA). Automation, Control and Intelligent Systems. 2024, 12(4), 71-107. https://doi.org/10.11648/j.acis.20241204.11
[2]	Jagnade, S. A., Pandit, R. A., Bagde, A. R. Modelling, Simulation and Control of Flow Tank System. International Journal of Science and Research. 2015, 4(2), 1-13.
[3]	Fellani, M. A., Gabaj, A. M. PID Controller Design for Two Tanks Liquid Level Control System using Matlab. International Journal of Electrical and Computer Engineering. 2015, 5(3), 436-442. https://doi.org/10.11591/ijece.v5i3.pp436-442
[4]	Saraswathi K. (2022), “PLC Based Automatic Sequential Batch Process System”, International Journal of Research Publication and Reviews, Vol 3, no 6, pp 938-940. www.ijrpr.com
[5]	Li G. et al. Evaluation of Mixing Process in Batch Mixer Using CFD-DEM Simulation. Processes 2024, 12(12), 2840; https://doi.org/10.3390/pr12122840
[6]	Ramirez-Lopez A. Analysis of Mixing Efficiency in a Stirred Reactor Using Computational Fluid Dynamics. Processes, Symmetry 2024 16(2), 237, 2024. https://doi.org/10.3390/sym16020237
[7]	Karthikeyan C., Kumar V. P, Preetha V., Arakkal F. Mathematical Modeling of a Batch Reactor and a Non-Isothermal CSTR with Their Respective Simulation Using MATLAB and ASPEN PLUS, 2025. https://doi.org/10.1002/9781394372379.ch3
[8]	Ahmed, G. S., Humadi, J. I., & Aabid, A. A. (2021). Mathematical Model, Simulation and Scale up of Batch Reactor Used in Oxidative Desulfurization of Kerosene. Iraqi Journal of Chemical and Petroleum Engineering, 22(3), 11-17. https://doi.org/10.31699 /IJCPE.2021.3.2
[9]	Karthikeyan, C., et al. Mathematical Modeling of a Batch Reactor and a Non-Isothermal CSTR with Their Respective Simulation Using MATLAB and ASPEN PLUS. Chemical Engineering Essentials 2, Wiley, 18 April 2025. https://doi.org/10.1002/9781394372379.ch3
[10]	Vargas R. O. & Lopez-Serrano F. Modeling, Simulation and Scale-up of a Batch Reactor. Experimental and Computational Fluid Mechanics January 2014 https://doi.org/10.1007/978-3-319-00116-6_18
[11]	Gaur, A. S., et al. Advanced Fluid Level Control in Interconnected Tank Systems Using Fuzzy Logic and Neural Networks. Journal of Electrical Systems, 20(3), 2024: 3362-3372
[12]	Mystkowski A. & Kierdelewicz A. Fractional-Order Water Level Control Based on PLC: Hardware-In-The-Loop Simulation and Experimental Validation. Energies 2018, 11(11), 2928; https://doi.org/10.3390/en11112928
[13]	Rosman, E., Mohd S. N. Nor A. S. M., Wen H. R. Liquid Level Control Performance Study of Conventional and Advanced Model-Based Controller for a Quadruple Tank System. Journal of Engineering Research and Education, 17, 181-194, 2026. https://doi.org/10.58915/jere.v17.2025.2928
[14]	Mirza, K., & Farzi, A. Optimization of PID Controller for Three Tanks System By MATLAB/Simulink/Genetic Algorithm. Eurasian Journal of Science and Engineering, 10(3), 2024. https://doi.org/10.23918/eajse.v10i3p3
[15]	Schukwuweike J., Anang A. N. Enhancing Industrial Efficiency through Automation: Leveraging PLC, SCADA, HMI, Batch, and DCS Systems. For Downtime Mitigation In Industrial Control Systems. September 2024 IJRPR, 5(9): 1466-1478, https://doi.org/10.55248/gengpi.5.0924.2530
[16]	Mishra R. & Ojha C. S. P. Application of AI-Based techniques on Moody’s diagram for predictive friction factor in pipe flow. J (2023), 6(4), 544-563. https://doi.org/10.3390/j6040036

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APA Style

Mbeah, A. K., Normanyo, E. (2026). Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer. Automation, Control and Intelligent Systems, 14(3), 50-58. https://doi.org/10.11648/j.acis.20261403.11

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ACS Style

Mbeah, A. K.; Normanyo, E. Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer. Autom. Control Intell. Syst. 2026, 14(3), 50-58. doi: 10.11648/j.acis.20261403.11

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AMA Style

Mbeah AK, Normanyo E. Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer. Autom Control Intell Syst. 2026;14(3):50-58. doi: 10.11648/j.acis.20261403.11

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@article{10.11648/j.acis.20261403.11,
  author = {Augustine Kweku Mbeah and Erwin Normanyo},
  title = {Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer},
  journal = {Automation, Control and Intelligent Systems},
  volume = {14},
  number = {3},
  pages = {50-58},
  doi = {10.11648/j.acis.20261403.11},
  url = {https://doi.org/10.11648/j.acis.20261403.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20261403.11},
  abstract = {A mathematical model and dynamic performance study of a Supervisory Control and Data Acquisition (SCADA) system and a Programmable Logic Controller (PLC) that were previously utilized to automate the pharmaceutical batch mixer are presented in this research. While the earlier work implemented the discrete, sequential control logic for the mixer using Siemens STEP 7 and validated it with RSLogix 5000, the continuous-time hydraulic behaviour of the three interconnected process vessels (heating, mixing and storage tanks) had not been characterised. In this study, the batch mixing system is partitioned into three sections, each represented by a pump-and-tank arrangement, and first-principles mass-balance, Bernoulli energy-balance and Darcy friction-loss equations are used to derive the transfer functions relating pump flow rate and tank level to valve resistance and tank cross-sectional area. Laplace transformation of the governing equations yields an overall block-diagram model of the three-tank system, which is implemented and simulated in MATLAB/SIMULINK. The simulation results show that the flow response settles at 0.5 m3/s with a settling time of 1.32 x 10^4 seconds, an overshoot of 11.5% and a rise time of 4.03 x 10^3 seconds. The tank-level responses show a successive filling pattern consistent with the batching sequence, with Tank 1 filling within 20 minutes, Tank 2 reaching its maximum level at 65 minutes, and Tank 3 completing filling at 210 minutes from the start of the process. These results confirm that the batch mixer exhibits stable, well-damped dynamic behaviour, providing a quantitative basis for the timer presets and control logic used in the PLC-SCADA automation reported previously, and supporting the suitability of the process for closed-loop SCADA-based control.},
 year = {2026}
}

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TY  - JOUR
T1  - Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer
AU  - Augustine Kweku Mbeah
AU  - Erwin Normanyo
Y1  - 2026/09/20
PY  - 2026
N1  - https://doi.org/10.11648/j.acis.20261403.11
DO  - 10.11648/j.acis.20261403.11
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 50
EP  - 58
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20261403.11
AB  - A mathematical model and dynamic performance study of a Supervisory Control and Data Acquisition (SCADA) system and a Programmable Logic Controller (PLC) that were previously utilized to automate the pharmaceutical batch mixer are presented in this research. While the earlier work implemented the discrete, sequential control logic for the mixer using Siemens STEP 7 and validated it with RSLogix 5000, the continuous-time hydraulic behaviour of the three interconnected process vessels (heating, mixing and storage tanks) had not been characterised. In this study, the batch mixing system is partitioned into three sections, each represented by a pump-and-tank arrangement, and first-principles mass-balance, Bernoulli energy-balance and Darcy friction-loss equations are used to derive the transfer functions relating pump flow rate and tank level to valve resistance and tank cross-sectional area. Laplace transformation of the governing equations yields an overall block-diagram model of the three-tank system, which is implemented and simulated in MATLAB/SIMULINK. The simulation results show that the flow response settles at 0.5 m3/s with a settling time of 1.32 x 10^4 seconds, an overshoot of 11.5% and a rise time of 4.03 x 10^3 seconds. The tank-level responses show a successive filling pattern consistent with the batching sequence, with Tank 1 filling within 20 minutes, Tank 2 reaching its maximum level at 65 minutes, and Tank 3 completing filling at 210 minutes from the start of the process. These results confirm that the batch mixer exhibits stable, well-damped dynamic behaviour, providing a quantitative basis for the timer presets and control logic used in the PLC-SCADA automation reported previously, and supporting the suitability of the process for closed-loop SCADA-based control.
VL  - 14
IS  - 3
ER  -

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Author Information

Augustine Kweku Mbeah

Marine Electrical and Electronic Engineering Department, Regional Maritime University, Accra, Ghana

Contact Email

http://orcid.org/0009-0003-6276-0507
Erwin Normanyo

Electrical Electronics Engineering Department, University of Mines and Technology, Tarkwa, Ghana

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APA Style

Mbeah, A. K., Normanyo, E. (2026). Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer. Automation, Control and Intelligent Systems, 14(3), 50-58. https://doi.org/10.11648/j.acis.20261403.11

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ACS Style

Mbeah, A. K.; Normanyo, E. Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer. Autom. Control Intell. Syst. 2026, 14(3), 50-58. doi: 10.11648/j.acis.20261403.11

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AMA Style

Mbeah AK, Normanyo E. Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer. Autom Control Intell Syst. 2026;14(3):50-58. doi: 10.11648/j.acis.20261403.11

Copy | Download

@article{10.11648/j.acis.20261403.11,
  author = {Augustine Kweku Mbeah and Erwin Normanyo},
  title = {Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer},
  journal = {Automation, Control and Intelligent Systems},
  volume = {14},
  number = {3},
  pages = {50-58},
  doi = {10.11648/j.acis.20261403.11},
  url = {https://doi.org/10.11648/j.acis.20261403.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acis.20261403.11},
  abstract = {A mathematical model and dynamic performance study of a Supervisory Control and Data Acquisition (SCADA) system and a Programmable Logic Controller (PLC) that were previously utilized to automate the pharmaceutical batch mixer are presented in this research. While the earlier work implemented the discrete, sequential control logic for the mixer using Siemens STEP 7 and validated it with RSLogix 5000, the continuous-time hydraulic behaviour of the three interconnected process vessels (heating, mixing and storage tanks) had not been characterised. In this study, the batch mixing system is partitioned into three sections, each represented by a pump-and-tank arrangement, and first-principles mass-balance, Bernoulli energy-balance and Darcy friction-loss equations are used to derive the transfer functions relating pump flow rate and tank level to valve resistance and tank cross-sectional area. Laplace transformation of the governing equations yields an overall block-diagram model of the three-tank system, which is implemented and simulated in MATLAB/SIMULINK. The simulation results show that the flow response settles at 0.5 m3/s with a settling time of 1.32 x 10^4 seconds, an overshoot of 11.5% and a rise time of 4.03 x 10^3 seconds. The tank-level responses show a successive filling pattern consistent with the batching sequence, with Tank 1 filling within 20 minutes, Tank 2 reaching its maximum level at 65 minutes, and Tank 3 completing filling at 210 minutes from the start of the process. These results confirm that the batch mixer exhibits stable, well-damped dynamic behaviour, providing a quantitative basis for the timer presets and control logic used in the PLC-SCADA automation reported previously, and supporting the suitability of the process for closed-loop SCADA-based control.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer
AU  - Augustine Kweku Mbeah
AU  - Erwin Normanyo
Y1  - 2026/09/20
PY  - 2026
N1  - https://doi.org/10.11648/j.acis.20261403.11
DO  - 10.11648/j.acis.20261403.11
T2  - Automation, Control and Intelligent Systems
JF  - Automation, Control and Intelligent Systems
JO  - Automation, Control and Intelligent Systems
SP  - 50
EP  - 58
PB  - Science Publishing Group
SN  - 2328-5591
UR  - https://doi.org/10.11648/j.acis.20261403.11
AB  - A mathematical model and dynamic performance study of a Supervisory Control and Data Acquisition (SCADA) system and a Programmable Logic Controller (PLC) that were previously utilized to automate the pharmaceutical batch mixer are presented in this research. While the earlier work implemented the discrete, sequential control logic for the mixer using Siemens STEP 7 and validated it with RSLogix 5000, the continuous-time hydraulic behaviour of the three interconnected process vessels (heating, mixing and storage tanks) had not been characterised. In this study, the batch mixing system is partitioned into three sections, each represented by a pump-and-tank arrangement, and first-principles mass-balance, Bernoulli energy-balance and Darcy friction-loss equations are used to derive the transfer functions relating pump flow rate and tank level to valve resistance and tank cross-sectional area. Laplace transformation of the governing equations yields an overall block-diagram model of the three-tank system, which is implemented and simulated in MATLAB/SIMULINK. The simulation results show that the flow response settles at 0.5 m3/s with a settling time of 1.32 x 10^4 seconds, an overshoot of 11.5% and a rise time of 4.03 x 10^3 seconds. The tank-level responses show a successive filling pattern consistent with the batching sequence, with Tank 1 filling within 20 minutes, Tank 2 reaching its maximum level at 65 minutes, and Tank 3 completing filling at 210 minutes from the start of the process. These results confirm that the batch mixer exhibits stable, well-damped dynamic behaviour, providing a quantitative basis for the timer presets and control logic used in the PLC-SCADA automation reported previously, and supporting the suitability of the process for closed-loop SCADA-based control.
VL  - 14
IS  - 3
ER  -

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