Enhanced control of continuous stirred tank reactor with two-degree-of-freedom PID driven by Kirchhoff’s law algorithm

Gökhan Yüksek; Serdar Ekinci; Musa Yılmaz

doi:10.1038/s41598-026-44778-w

journal article Open Access Mar 27, 2026

Enhanced control of continuous stirred tank reactor with two-degree-of-freedom PID driven by Kirchhoff’s law algorithm

Gökhan Yüksek

Serdar Ekinci

Musa Yılmaz

Scientific Reports Vol. 16 No. 1 · Springer Science and Business Media LLC

View at Publisher Save 10.1038/s41598-026-44778-w

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References

32

[1]

Cherkasov, N., Adams, S. J., Bainbridge, E. G. A. & Thornton, J. A. M. Continuous stirred tank reactors in fine chemical synthesis for efficient mixing, solids-handling, and rapid scale-up. React. Chem. Eng. 8(2), 266–277. https://doi.org/10.1039/D2RE00232A (2023). 10.1039/d2re00232a

[2]

Gkogkos, G., Kahil, E. E., Storozhuk, L., Thanh, N. T. K. & Gavriilidis, A. Scaling study of miniaturised continuous stirred tank reactors via residence time distribution analysis and application in the production of iron oxide nanoparticles. Chem. Eng. Process. - Process Intensif. 203, 109880. https://doi.org/10.1016/j.cep.2024.109880 (2024). 10.1016/j.cep.2024.109880

[3]

Ouyang, M., Wang, Y., Wu, F. & Lin, Y. Continuous reactor temperature control with optimized PID parameters based on improved sparrow algorithm. Processes 11(5), 1302. https://doi.org/10.3390/pr11051302 (2023). 10.3390/pr11051302

[4]

Siddiqui, M. A., Anwar, Md. N. & Laskar, S. H. Control of non-linear jacketed continuous stirred tank reactor using different control structures. J. Process Control 108, 112–124. https://doi.org/10.1016/j.jprocont.2021.11.005 (2021). 10.1016/j.jprocont.2021.11.005

[5]

Deifalla, M. & Gasmelseed, G. optimal temperature control for non-linear jacketed continuous stirred tank reactors using genetic algorithm. J. Karary Univ. Eng. Sci. https://doi.org/10.54388/jkues.v4i1.329 (2025). 10.54388/jkues.v4i1.329

[6]

Ekinci, S., Izci, D., Jabari, M. & Ma’arif, A. Enhanced temperature control of continuous stirred tank reactors using QIO-based 2-DoF PID controller. J. Robotics Control (JRC) 6(3), 1340–1346. https://doi.org/10.18196/jrc.v6i3.26586 (2025). 10.18196/jrc.v6i3.26586

[7]

Sharma, A., Kar, M. K. & Goud, H. A novel modified grey wolf optimization tuned PID controller with fractional filter for the CSTR system. Heat Mass Transf. 61(4), 36. https://doi.org/10.1007/s00231-025-03553-9 (2025). 10.1007/s00231-025-03553-9

[8]

Ben Abdelwahed, I., Guerfel, M., El Anes, A. & Bouzrara, K. An enhanced non-linear PID controller design for the CSTR system utilizing NARX-Laguerre model. Trans. Inst. Meas. Control https://doi.org/10.1177/01423312251360838 (2025). 10.1177/01423312251360838

[9]

Ajlouni, N. et al. Enhancing PID control robustness in CSTRs: A hybrid approach to tuning under external disturbances with GA, PSO, and machine learning. Neural Comput. Appl. 37(18), 12153–12177. https://doi.org/10.1007/s00521-025-11170-0 (2025). 10.1007/s00521-025-11170-0

[10]

Chaturvedi, S., Kumar, N. & Kumar, R. A PSO-optimized novel PID neural network model for temperature control of jacketed CSTR: design, simulation, and a comparative study. Soft Comput. 28(6), 4759–4773. https://doi.org/10.1007/s00500-023-09138-0 (2024). 10.1007/s00500-023-09138-0

[11]

Jabari, M. & Rad, A. Optimization of speed control and reduction of torque ripple in switched reluctance motors using metaheuristic algorithms based PID and FOPID controllers at the edge. Tsinghua Sci. Technol. 30(4), 1526–1538. https://doi.org/10.26599/TST.2024.9010021 (2025). 10.26599/tst.2024.9010021

[12]

Turkeri, C., Ekinci, S., Yüksek, G. & Li, D. A modified enzyme action optimizer-based FOPID controller for temperature regulation of a non-linear continuous stirred tank reactor. Fractal Fract. 9(12), 811. https://doi.org/10.3390/fractalfract9120811 (2025). 10.3390/fractalfract9120811

[13]

Yüksek, G. A novel delay-affected two degree of freedom PID controller using physics-inspired optimization for robust control applications. Sci. Rep. https://doi.org/10.1038/s41598-025-33481-x (2025). 10.1038/s41598-025-33481-x

[14]

Guras, R., Strambersky, R. & Mahdal, M. The PID and 2DOF control of the integral system - Influence of the 2DOF parameters and practical implementation. Meas. Control 55(1–2), 94–101. https://doi.org/10.1177/00202940221076961 (2022). 10.1177/00202940221076961

[15]

Bingi, K., Ibrahim, R., Karsiti, M. N., Hassan, S. M. & Harindran, V. R. A comparative study of 2DOF PID and 2DOF fractional order PID controllers on a class of unstable systems. Arch. Control Sci. https://doi.org/10.24425/acs.2018.125487 (2023). 10.24425/acs.2018.125487

[16]

Ekinci, S., Izci, D., Jabari, M., Bajaj, M. & Rubanenko, O. Design of a novel and robust 2-DOF PIDA controller based on enzyme action optimizer for ball position regulation in magnetic levitation systems. Sci. Rep. 15(1), 29360. https://doi.org/10.1038/s41598-025-13967-4 (2025). 10.1038/s41598-025-13967-4

[17]

Ekinci, S. et al. Quadratic interpolation optimization-based 2DoF-PID controller design for highly non-linear continuous stirred-tank heater process. Sci. Rep. 15(1), 16324. https://doi.org/10.1038/s41598-025-01379-3 (2025). 10.1038/s41598-025-01379-3

[18]

Ghasemi, M. et al. Kirchhoff’s law algorithm (KLA): A novel physics-inspired non-parametric metaheuristic algorithm for optimization problems. Artif. Intell. Rev. 58(10), 325. https://doi.org/10.1007/s10462-025-11289-5 (2025). 10.1007/s10462-025-11289-5

[19]

Hassan, M., Deifalla, H. & Abdalla, K. Performance evaluation of PID tuning techniques for CSTR temperature control: classical and evolutionary approaches. J. Karary Univ. Eng. Sci. https://doi.org/10.54388/jkues.v4i3.360 (2025). 10.54388/jkues.v4i3.360

[20]

Wang, R. et al. CSTR parameter identification and PID control optimization based on improved swarm intelligence algorithm. Eng. Res. Express. https://doi.org/10.1088/2631-8695/ada0a7 (2025). 10.1088/2631-8695/ada0a7

[21]

Kumavat, M. & Thale, S. Analysis of CSTR temperature control with PID, MPC & Hybrid MPC-PID controller. ITM Web Conferences 44, 01001. https://doi.org/10.1051/itmconf/20224401001 (2022). 10.1051/itmconf/20224401001

[22]

Achu Govind, K. R., Mahapatra, S. & Mahapatro, S. R. Non-linear constraint optimization based robust decentralized PID controller for a benchmark CSTR system using Kharitonov–Hurwitz stability analysis. Arab. J. Sci. Eng. 48(11), 15377–15402. https://doi.org/10.1007/s13369-023-08076-1 (2023). 10.1007/s13369-023-08076-1

[23]

Ajlouni, N. et al. Enhancing PID control robustness in CSTRs: A hybrid approach to tuning under external disturbances with GA, PSO, and machine learning. Neural Comput. Appl. 37(18), 12153–12177. https://doi.org/10.1007/s00521-025-11170-0 (2025). 10.1007/s00521-025-11170-0

[24]

Wang, R.-B. et al. The animated oat optimization algorithm: A nature-inspired metaheuristic for engineering optimization and a case study on wireless sensor networks. Knowl. Based. Syst. 318, 113589. https://doi.org/10.1016/j.knosys.2025.113589 (2025). 10.1016/j.knosys.2025.113589

[25]

Lian, J. et al. Parrot optimizer: Algorithm and applications to medical problems. Comput. Biol. Med. 172, 108064. https://doi.org/10.1016/j.compbiomed.2024.108064 (2024). 10.1016/j.compbiomed.2024.108064

[26]

Dehghani, M., Montazeri, Z., Trojovská, E. & Trojovský, P. Coati optimization algorithm: A new bio-inspired metaheuristic algorithm for solving optimization problems. Knowl. Based. Syst. 259, 110011. https://doi.org/10.1016/j.knosys.2022.110011 (2023). 10.1016/j.knosys.2022.110011

[27]

Agushaka, J. O., Ezugwu, A. E. & Abualigah, L. Dwarf Mongoose optimization algorithm. Comput. Methods Appl. Mech. Eng. 391, 114570. https://doi.org/10.1016/j.cma.2022.114570 (2022). 10.1016/j.cma.2022.114570

[28]

M. A. Henson and D. E. Seborg. Non-linear process control. (1997).

[29]

W. B. Bequette. Dynamics Process: Modeling, Analysis, and Simulation. (1998).

[30]

Begum, K. G. Coot bird optimization algorithm for the temperature control of continuous stirred tank reactor process. Asia-Pac. J. Chem. Eng. https://doi.org/10.1002/apj.2787 (2023). 10.1002/apj.2787

[31]

Gaing, Z.-L. A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE Trans. Energy Convers. 19(2), 384–391. https://doi.org/10.1109/TEC.2003.821821 (2004). 10.1109/tec.2003.821821

[32]

Eker, E., Kayri, M., Ekinci, S. & Izci, D. A new fusion of ASO with SA algorithm and its applications to MLP training and DC motor speed control. Arab. J. Sci. Eng. 46(4), 3889–3911. https://doi.org/10.1007/s13369-020-05228-5 (2021). 10.1007/s13369-020-05228-5

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Published: Mar 27, 2026
Vol/Issue: 16(1)
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Batman Üniversitesi

Cite This Article

Gökhan Yüksek, Serdar Ekinci, Musa Yılmaz (2026). Enhanced control of continuous stirred tank reactor with two-degree-of-freedom PID driven by Kirchhoff’s law algorithm. Scientific Reports, 16(1). https://doi.org/10.1038/s41598-026-44778-w

Enhanced control of continuous stirred tank reactor with two-degree-of-freedom PID driven by Kirchhoff’s law algorithm

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