Enhanced Temperature Control of Continuous Stirred Tank Reactors Using QIO-based 2-DoF PID Controller

Authors

  • Serdar Ekinci Istanbul Gedik University
  • Davut Izci Istanbul Gedik University; Bursa Uludag University; Applied Science Private University
  • Mostafa Jabari Sahand University of Technology
  • Alfian Ma'arif Universitas Ahmad Dahlan

DOI:

https://doi.org/10.18196/jrc.v6i3.26586

Keywords:

Two-Degree-of-Freedom (2-DOF) PID Controller, Quadratic Interpolation Optimization, Metaheuristics, Continuous Stirred Tank Reactor, Temperature Control

Abstract

Accurate temperature control of continuous stirred tank reactors (CSTRs) remains a major challenge due to the nonlinear dynamics and inherent time delay of the system. Conventional proportional-integral-derivative (PID) controllers often struggle to maintain optimal performance under such complexities, highlighting the need for more advanced control strategies. In this study, a two-degree-of-freedom (2-DOF) PID controller is designed and optimized using the quadratic interpolation optimization (QIO) to enhance temperature regulation in CSTRs. The proposed approach aims to minimize steady-state error, settling time, and overshoot. To implement this method, the nonlinear model of the CSTR is linearized around a stable operating point, and the controller parameters are tuned by minimizing a composite cost function consisting of normalized overshoot and instantaneous error. Simulation results demonstrate that the QIO-based 2-DOF PID controller significantly outperforms other metaheuristic approaches such as differential evolution, particle swarm optimization, slime mould algorithm, and greater cane rat algorithm. Furthermore, comparisons with recent works reveal substantial improvements in rise time, settling time, and steady-state accuracy.

References

D. Izci et al., “A new intelligent control strategy for CSTH temperature regulation based on the starfish optimization algorithm,” Sci. Rep., vol. 15, p. 12327, 2025, doi: 10.1038/s41598-025-96621-3.

A. Sinha and R. K. Mishra, “Temperature regulation in a Continuous Stirred Tank Reactor using event triggered sliding mode control,” IFAC-PapersOnLine, vol. 51, pp. 401–406, 2018, doi: 10.1016/j.ifacol.2018.05.060.

A. M. Abdel-hamed, A. Y. Abdelaziz, and A. El-Shahat, “Design of a 2DOF-PID Control Scheme for Frequency/Power Regulation in a Two-Area Power System Using Dragonfly Algorithm with Integral-Based Weighted Goal Objective,” Energies (Basel), vol. 16, p. 486, 2023, doi: 10.3390/en16010486.

M. Jabari and A. Rad, "Optimization of Speed Control and Reduction of Torque Ripple in Switched Reluctance Motors Using Metaheuristic Algorithms Based PID and FOPID Controllers at the Edge," in Tsinghua Science and Technology, vol. 30, no. 4, pp. 1526-1538, August 2025, doi: 10.26599/TST.2024.9010021.

R. K. Sahu, S. Panda, U. K. Rout, and D. K. Sahoo, “Teaching learning based optimization algorithm for automatic generation control of power system using 2-DOF PID controller,” International Journal of Electrical Power & Energy Systems, vol. 77, pp. 287–301, 2016, doi: 10.1016/j.ijepes.2015.11.082.

M. Jabari, S. Ekinci, D. Izci, M. Bajaj, and I. Zaitsev, “Efficient DC motor speed control using a novel multi-stage FOPD(1 + PI) controller optimized by the Pelican optimization algorithm,” Sci Rep., vol. 14, p. 22442, 2024, doi: 10.1038/s41598-024-73409-5.

M. Jabari, S. Ekinci, D. Izci, M. Bajaj, V. Blazek, and L. Prokop, “Efficient pressure regulation in nonlinear shell-and-tube steam condensers via a Novel TDn(1 + PIDn) controller and DCSA algorithm,” Sci Rep., vol. 15, p. 2090, 2025, doi: 10.1038/s41598-025-86107-7.

M. Jabari, D. Izci, S. Ekinci, M. Bajaj, and I. Zaitsev, “Performance analysis of DC-DC Buck converter with innovative multi-stage PIDn(1+PD) controller using GEO algorithm,” Sci Rep., vol. 14, p. 25612, 2024, doi: 10.1038/s41598-024-77395-6.

S. Das and P. N. Suganthan, "Differential Evolution: A Survey of the State-of-the-Art," in IEEE Transactions on Evolutionary Computation, vol. 15, no. 1, pp. 4-31, Feb. 2011, doi: 10.1109/TEVC.2010.2059031.

D. Wang, D. Tan, and L. Liu, “Particle swarm optimization algorithm: an overview,” Soft Comput., vol. 22, pp. 387–408, 2018, doi: 10.1007/s00500-016-2474-6.

S. Li, H. Chen, M. Wang, A.A. Heidari, and S. Mirjalili, “Slime mould algorithm: A new method for stochastic optimization,” Future Generation Computer Systems, vol. 111, pp. 300–323, 2020, doi: 10.1016/j.future.2020.03.055.

J. O. Agushaka, A. E. Ezugwu, A. K. Saha, J. Pal, L. Abualigah, and S. Mirjalili, “Greater cane rat algorithm (GCRA): A nature-inspired metaheuristic for optimization problems,” Heliyon, vol. 10, p. e31629, 2024, doi: 10.1016/j.heliyon.2024.e31629.

W. Zhao, L. Wang, Z. Zhang, S. Mirjalili, N. Khodadadi, and Q. Ge, “Quadratic Interpolation Optimization (QIO): A new optimization algorithm based on generalized quadratic interpolation and its applications to real-world engineering problems,” Comput. Methods Appl. Mech. Eng., vol. 417, p. 116446, 2023, doi: 10.1016/j.cma.2023.116446.

S. Ekinci, D. Izci, V. Gider, M. Bajaj, V. Blazek, and L. Prokop, “Quadratic interpolation optimization-based 2DoF-PID controller design for highly nonlinear continuous stirred-tank heater process,” Sci Rep., vol. 15, p. 16324, 2025, doi: 10.1038/s41598-025-01379-3.

S. Ekinci, D. Izci, V. Gider, L. Abualigah, M. Bajaj, and I. Zaitsev, Efficient control strategy for electric furnace temperature regulation using quadratic interpolation optimization,” Sci Rep., vol. 15, p. 154, 2025, doi: 10.1038/s41598-024-84085-w.

D. Izci, S. Ekinci, E. Çelik, M. Bajaj, V. Blazek, and L. Prokop, “Dynamic load frequency control in Power systems using a hybrid simulated annealing based Quadratic Interpolation Optimizer,” Sci Rep., vol. 14, p. 26011, 2024, doi: 10.1038/s41598-024-77247-3.

F. Dao, Y. Zeng, Y. Zou, and J. Qian, “Fault diagnosis method for hydropower unit via the incorporation of chaotic quadratic interpolation optimized deep learning model,” Measurement, vol. 237, p. 115199, 2024, doi: 10.1016/j.measurement.2024.115199.

A. S. A. Bayoumi, R. A. El Sehiemy, M. El-Kemary, and A. Abaza, “Advanced extraction of PV parameters’ models based on electric field impacts on semiconductor conductivity using QIO algorithm,” Sci Rep., vol. 14, p. 15397, 2024, doi: 10.1038/s41598-024-65091-4.

N. H. Khan, Y. Wang, R. Jamal, M. Ebeed, S. Kamel, G. Ali, F. Jurado, and A.-R. Youssef, “Improved quadratic interpolation optimizer for stochastic short-term hydrothermal scheduling with integration of solar PV and wind power,” Sci Rep., vol. 15, p. 11283, 2025, doi: 10.1038/s41598-025-86881-4.

A. Ghosh, T. Rakesh Krishnan, P. Tejaswy, A. Mandal, J. K. Pradhan, and S. Ranasingh, “Design and implementation of a 2-DOF PID compensation for magnetic levitation systems,” ISA Trans., vol. 53, pp. 1216–1222, 2014, doi: 10.1016/j.isatra.2014.05.015.

D. Sain, “Real-Time implementation and performance analysis of robust 2-DOF PID controller for Maglev system using pole search technique,” J Ind Inf Integr., vol. 15, pp. 183–190, 2019, doi: 10.1016/j.jii.2018.11.003.

D. S. Acharya, S. K. Swain, and S. K. Mishra, “Real-Time Implementation of a Stable 2 DOF PID Controller for Unstable Second-Order Magnetic Levitation System with Time Delay,” Arab J Sci Eng., vol. 45, pp. 6311–6329, 2020, doi: 10.1007/s13369-020-04425-6.

P. E. Kamalakkannan, B. Vinoth Kumar, and M. Kalamani, “Optimal nonlinear Fractional-Order Proportional-Integral-Derivative controller design using a novel hybrid atom search optimization for nonlinear Continuously stirred Tank reactor,” Thermal Science and Engineering Progress, vol. 54, p. 102862, 2024, doi: 10.1016/j.tsep.2024.102862.

A. Rani, D. Prabhakaran, and M. Thirumarimurugan, “A Novel Optimization of Fractional Order PID Controller Using Chaotic Maps Based Atomic Search Optimization for pH Control in Continuous Stirred Tank Reactor,” Journal of Vibration Engineering & Technologies, vol. 10, pp. 3059–3087, 2022, doi: 10.1007/s42417-022-00538-4.

K. R. Sundaresan and P. R. Krishnaswamy, “Estimation of time delay time constant parameters in time, frequency, and laplace domains, The Canadian Journal of Chemical Engineering, vol. 56, no. 2, pp. 257–262, 1978, doi: 10.1002/cjce.5450560215.

K. G. Begum, “Coot bird optimization algorithm for the temperature control of continuous stirred tank reactor process,” Asia-Pacific Journal of Chemical Engineering, vol. 18, 2023, doi: 10.1002/apj.2787.

M. Qaraad, S. Amjad, N. K. Hussein, M. A. Farag, S. Mirjalili, and M. A. Elhosseini, “Quadratic interpolation and a new local search approach to improve particle swarm optimization: Solar photovoltaic parameter estimation,” Expert Syst Appl., vol. 236, p. 121417, 2024, doi: 10.1016/j.eswa.2023.121417.

S.-L. Cheng and C. Hwang, “Designing PID controllers with a minimum IAE criterion by a differential evolution algorithm,” Chem Eng Commun., vol. 170, pp. 83–115, 1998, doi: 10.1080/00986449808912737.

D. Izci, “A novel modified arithmetic optimization algorithm for power system stabilizer design,” Sigma Journal of Engineering and Natural Sciences, vol. 40, pp. 529–541, 2022, doi: 10.14744/sigma.2022.00056.

K. Jagatheesan, B. Anand, K. N. Dey, A. S. Ashour, and S. C. Satapathy, “Performance evaluation of objective functions in automatic generation control of thermal power system using ant colony optimization technique-designed proportional–integral–derivative controller,” Electrical Engineering, vol. 100, pp. 895–911, 2018, doi: 10.1007/s00202-017-0555-x.

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Published

2025-05-25

How to Cite

[1]
S. Ekinci, D. Izci, M. Jabari, and A. Ma’arif, “Enhanced Temperature Control of Continuous Stirred Tank Reactors Using QIO-based 2-DoF PID Controller”, J Robot Control (JRC), vol. 6, no. 3, pp. 1340–1346, May 2025.

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