Research Article
Modelling and Simulation of Flow and Level Dynamics in a Pharmaceutical Batch Mixer
Augustine Kweku Mbeah*
,
Erwin Normanyo
Issue:
Volume 14, Issue 3, September 2026
Pages:
50-58
Received:
25 August 2026
Accepted:
4 September 2026
Published:
20 September 2026
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.
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 usi...
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