Optimizing Three-Tank Liquid Level Control: Insights from Prairie Dog Optimization

(1) * Davut Izci Mail (Batman University, Turkey)
(2) Serdar Ekinci Mail (Middle East University, Jordan)
*corresponding author


The management of chemical process liquid levels poses a significant challenge in industrial process control, affecting the efficiency and stability of various sectors such as food processing, nuclear power generation, and pharmaceutical industries. While Proportional-Integral-Derivative (PID) control is a widely-used technique for maintaining liquid levels in tanks, its efficacy in optimizing complex and nonlinear systems has limitations. To overcome this, researchers are exploring the potential of metaheuristic algorithms, which offer robust optimization capabilities. This study introduces a novel approach to liquid level control using the Prairie Dog Optimization (PDO) algorithm, a metaheuristic algorithm inspired by prairie dog behavior. The primary objective is to design and implement a PID-controlled three-tank liquid level system that leverages PDO to regulate liquid levels effectively, ensuring enhanced stability and performance. The performance of the proposed system is evaluated using the ZLG criterion, a time domain metric-based objective function that quantifies the system's efficiency in maintaining desired liquid levels. Several analysis techniques are employed to understand the behavior of the system. Convergence curve analysis assesses the PDO-controlled system's convergence characteristics, providing insights into its efficiency and stability. Statistical analysis determines the algorithm's reliability and robustness across multiple runs. Stability analysis from both time and frequency response perspectives further validates the system's performance. A comprehensive comparison study with state-of-the-art metaheuristic algorithms, including AOA-HHO, CMA-ES, PSO, and ALC-PSODE, is conducted to benchmark the performance of PDO. The results highlight PDO's superior convergence, stability, and optimization capabilities, establishing its efficacy in real-world industrial applications. The research findings underscore the potential of PDO in PID control applications for three-tank liquid level systems. By outperforming benchmark algorithms, PDO demonstrates its value in industrial control scenarios, contributing to the advancement of metaheuristic-based control techniques and process optimization. This study opens avenues for engineers and practitioners to harness advanced control solutions, thereby enhancing industrial processes and automation.


Prairie dog optimization; Liquid level system; PID controller; Stability




Article metrics

10.31763/ijrcs.v3i3.1116 Abstract views : 502 | PDF views : 157




Full Text



[1] T. Agitha and T. S. Sivarani, “Deep neural fuzzy based fractional order PID controller for level control applications in quadruple tank system,” J. Intell. Fuzzy Syst., vol. 45, no. 1, pp. 1847–1861, Jul. 2023, https://doi.org/10.3233/JIFS-221674.

[2] S. Mandal and A. Afza, “Liquid Level Control of Coupled Tank System Using FOPID Controller,” in International Conference on Signals, Machines, and Automation, 2023, pp. 357–363, https://doi.org/10.1007/978-981-99-0969-8_36.

[3] S. K. Vavilala, V. Thirumavalavan, and C. K, “Level control of a conical tank using the fractional order controller,” Comput. Electr. Eng., vol. 87, p. 106690, Oct. 2020, https://doi.org/10.1016/j.compeleceng.2020.106690.

[4] N. Divya, S. Manoharan, J. Arulvadivu, and P. Palpandian, “An efficient tuning of fractional order PID controller for an industrial control process,” Mater. Today Proc., vol. 57, pp. 1654–1659, 2022, https://doi.org/10.1016/j.matpr.2021.12.255.

[5] S. Ekinci, D. Izci, E. Eker, L. Abualigah, C.-L. Thanh, and S. Khatir, “Hunger games pattern search with elite opposite-based solution for solving complex engineering design problems,” Evol. Syst., Jul. 2023, https://doi.org/10.1007/s12530-023-09526-9.

[6] D. Izci, S. Ekinci, and A. G. Hussien, “Effective PID controller design using a novel hybrid algorithm for high order systems,” PLoS One, vol. 18, no. 5, p. e0286060, May 2023, https://doi.org/10.1371/journal.pone.0286060.

[7] D. Izci, S. Ekinci, E. Eker, and A. Demirören, “Biomedical Application of a Random Learning and Elite Opposition-Based Weighted Mean of Vectors Algorithm with Pattern Search Mechanism,” J. Control. Autom. Electr. Syst., vol. 34, no. 2, pp. 333–343, Apr. 2023, https://doi.org/10.1007/s40313-022-00959-2.

[8] T. Dlabač, S. Antić, M. Ćalasan, A. Milovanović, and N. Marvučić, “Nonlinear Tank-Level Control Using Dahlin Algorithm Design and PID Control,” Appl. Sci., vol. 13, no. 9, p. 5414, Apr. 2023, https://doi.org/10.3390/app13095414.

[9] Y. Yang, “Comparison of Various PID Control Algorithms on Coupled-Tank Liquid Level Control System,” J. Phys. Conf. Ser., vol. 1622, no. 1, p. 012129, Sep. 2020, https://doi.org/10.1088/1742-6596/1622/1/012129.

[10] P. Choudhari, N. R. Kulkarni, and M. Bakshi, “A System Theoretic-Based Optimum Controller for Single-Tank System and Its Performance Comparison with PID Controller,” J. Inst. Eng. Ser. B, vol. 104, no. 3, pp. 551–561, Jun. 2023, https://doi.org/10.1007/s40031-023-00878-z.

[11] H. R. Patel and V. A. Shah, “Application of metaheuristic algorithms in interval type-2 fractional order fuzzy TID controller for nonlinear level control process under actuator and system component faults*,” Int. J. Intell. Comput. Cybern., vol. 14, no. 1, pp. 33–53, Feb. 2021, https://doi.org/10.1108/IJICC-08-2020-0104.

[12] V. Snášel, R. M. Rizk-Allah, D. Izci, and S. Ekinci, “Weighted mean of vectors optimization algorithm and its application in designing the power system stabilizer,” Appl. Soft Comput., vol. 136, p. 110085, Mar. 2023, https://doi.org/10.1016/j.asoc.2023.110085.

[13] D. Izci, S. Ekinci, and H. L. Zeynelgil, “Controlling an automatic voltage regulator using a novel Harris hawks and simulated annealing optimization technique,” Adv. Control Appl., Mar. 2023, https://doi.org/10.1002/adc2.121.

[14] D. Izci and S. Ekinci, “The promise of metaheuristic algorithms for efficient operation of a highly complex power system,” in Comprehensive Metaheuristics, 2023, pp. 325–346, https://doi.org/10.1016/B978-0-323-91781-0.00017-X.

[15] A. K. Vincent and R. Nersisson, “Particle swarm optimization based PID controller tuning for level control of two tank system,” IOP Conf. Ser. Mater. Sci. Eng., vol. 263, p. 052001, Nov. 2017, https://doi.org/10.1088/1757-899X/263/5/052001.

[16] J. Bhookya, M. Vijaya Kumar, J. Ravi Kumar, and A. Seshagiri Rao, “Implementation of PID controller for liquid level system using mGWO and integration of IoT application,” J. Ind. Inf. Integr., vol. 28, p. 100368, Jul. 2022, https://doi.org/10.1016/j.jii.2022.100368.

[17] T. Jitwang and D. Puangdownreong, “Application of cuckoo search to robust PIDA controller design for liquid-level system,” Int. J. Innov. Comput. Inf. Control, vol. 16, no. 1, pp. 189–205, 2020, https://doi.org/10.24507/ijicic.16.01.189.

[18] S. Balochian and E. Ebrahimi, “Parameter Optimization via Cuckoo Optimization Algorithm of Fuzzy Controller for Liquid Level Control,” J. Eng., vol. 2013, pp. 1–7, 2013, https://doi.org/10.1155/2013/982354.

[19] L. Xiao, “Parameter Tuning of PID Controller for Beer Filling Machine Liquid Level Control Based on Improved Genetic Algorithm,” Comput. Intell. Neurosci., vol. 2021, pp. 1–10, Jul. 2021, https://doi.org/10.1155/2021/7287796.

[20] A. R. Laware, D. B. Talange, and V. S. Bandal, “Evolutionary optimization of sliding mode controller for level control system,” ISA Trans., vol. 83, pp. 199–213, Dec. 2018, https://doi.org/10.1016/j.isatra.2018.08.011.

[21] A. E. Ezugwu, J. O. Agushaka, L. Abualigah, S. Mirjalili, and A. H. Gandomi, “Prairie Dog Optimization Algorithm,” Neural Comput. Appl., vol. 34, no. 22, pp. 20017–20065, Nov. 2022, https://doi.org/10.1007/s00521-022-07530-9.

[22] D. Izci and S. Ekinci, “Comparative Performance Analysis of Slime Mould Algorithm For Efficient Design of Proportional–Integral–Derivative Controller,” Electrica, vol. 21, no. 1, pp. 151–159, Jan. 2021, https://doi.org/10.5152/electrica.2021.20077.

[23] D. Izci, S. Ekinci, E. Eker, and M. Kayri, “Augmented hunger games search algorithm using logarithmic spiral opposition-based learning for function optimization and controller design,” J. King Saud Univ. - Eng. Sci., Mar. 2022, https://doi.org/10.1016/j.jksues.2022.03.001.

[24] D. Izci, S. Ekinci, E. Eker, and M. Kayri, “A novel modified opposition‐based hunger games search algorithm to design fractional order proportional‐integral‐derivative controller for magnetic ball suspension system,” Adv. Control Appl., vol. 4, no. 1, p. e96, Mar. 2022, https://doi.org/10.1002/adc2.96.

[25] A. R. V, P. D, and T. M, “A Novel Optimization of Fractional Order PID Controller Using Chaotic Maps Based Atomic Search Optimization for pH Control in Continuous Stirred Tank Reactor,” J. Vib. Eng. Technol., vol. 10, no. 8, pp. 3059–3087, Nov. 2022, https://doi.org/10.1007/s42417-022-00538-4.

[26] M. Issa, “Enhanced Arithmetic Optimization Algorithm for Parameter Estimation of PID Controller,” Arab. J. Sci. Eng., vol. 48, no. 2, pp. 2191–2205, Feb. 2023, https://doi.org/10.1007/s13369-022-07136-2.

[27] A. Moharam, M. A. El-Hosseini, and H. A. Ali, “Design of optimal PID controller using hybrid differential evolution and particle swarm optimization with an aging leader and challengers,” Appl. Soft Comput., vol. 38, pp. 727–737, Jan. 2016, https://doi.org/10.1016/j.asoc.2015.10.041.

[28] D. Gürses, P. Mehta, S. M. Sait, S. Kumar, and A. R. Yildiz, “A multi-strategy boosted prairie dog optimization algorithm for global optimization of heat exchangers,” Mater. Test., Jul. 2023, https://doi.org/10.1515/mt-2023-0082.

[29] L. Abualigah, A. Diabat, C.-L. Thanh, and S. Khatir, “Opposition-based Laplacian distribution with Prairie Dog Optimization method for industrial engineering design problems,” Comput. Methods Appl. Mech. Eng., vol. 414, p. 116097, Sep. 2023, https://doi.org/10.1016/j.cma.2023.116097.

[30] J. Liu, S. Zhang, and Z. Druzhinin, “Performance prediction of the PEMFCs based on gate recurrent unit network optimized by improved version of prairie dog optimization algorithm,” Int. J. Hydrogen Energy, vol. 48, no. 69, pp. 26951–26963, Aug. 2023, https://doi.org/10.1016/j.ijhydene.2023.03.349.

[31] S. Ekinci and D. Izci, “Enhanced reptile search algorithm with Lévy flight for vehicle cruise control system design,” Evol. Intell., vol. 16, no. 4, pp. 1339–1351, Aug. 2023, https://doi.org/10.1007/s12065-022-00745-8.

[32] E. Eker, M. Kayri, S. Ekinci, and M. A. Kacmaz, “Performance Evaluation of PDO Algorithm through Benchmark Functions and MLP Training,” Electrica, vol. 23, no. 3, pp. 597-606, Jun. 2023, https://doi.org/10.5152/electr.2023.22179.

[33] D. Izci, “Design and application of an optimally tuned PID controller for DC motor speed regulation via a novel hybrid Lévy flight distribution and Nelder–Mead algorithm,” Trans. Inst. Meas. Control, vol. 43, no. 14, pp. 3195–3211, Oct. 2021, https://doi.org/10.1177/01423312211019633.

[34] D. Izci, S. Ekinci, C. Budak, and V. Gider, “PID Controller Design for DFIG-based Wind Turbine via Reptile Search Algorithm,” in 2022 Global Energy Conference (GEC), Oct. 2022, pp. 154–158, https://doi.org/10.1109/GEC55014.2022.9986617.

[35] D. Izci, S. Ekinci, A. Demiroren, and J. Hedley, “HHO Algorithm based PID Controller Design for Aircraft Pitch Angle Control System,” in 2020 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA), Jun. 2020, pp. 1–6, https://doi.org/10.1109/HORA49412.2020.9152897.

[36] S. Ekinci, B. Hekimoğlu, and D. Izci, “Opposition based Henry gas solubility optimization as a novel algorithm for PID control of DC motor,” Eng. Sci. Technol. an Int. J., vol. 24, no. 2, pp. 331–342, Apr. 2021, https://doi.org/10.1016/j.jestch.2020.08.011.

[37] Z.-L. Gaing, “A Particle Swarm Optimization Approach for Optimum Design of PID Controller in AVR System,” IEEE Trans. Energy Convers., vol. 19, no. 2, pp. 384–391, Jun. 2004, https://doi.org/10.1109/TEC.2003.821821.

[38] M. S. Ali, L. Wang, H. Alquhayz, O. U. Rehman, and G. Chen, “Performance Improvement of Three-Phase Boost Power Factor Correction Rectifier Through Combined Parameters Optimization of Proportional-Integral and Repetitive Controller,” IEEE Access, vol. 9, pp. 58893–58909, 2021, https://doi.org/10.1109/ACCESS.2021.3073004.

[39] V. K. Munagala and R. K. Jatoth, “Improved fractional PIλDμ controller for AVR system using Chaotic Black Widow algorithm,” Comput. Electr. Eng., vol. 97, p. 107600, 2022, https://doi.org/10.1016/j.compeleceng.2021.107600.

[40] Ö. Can, C. Andiç, S. Ekinci, and D. Izci, “Enhancing transient response performance of automatic voltage regulator system by using a novel control design strategy,” Electr. Eng., vol. 105, no. 4, pp. 1993–2005, Aug. 2023, https://doi.org/10.1007/s00202-023-01777-8.


  • There are currently no refbacks.

Copyright (c) 2023 Davut Izci

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.


About the JournalJournal PoliciesAuthor Information

International Journal of Robotics and Control Systems
e-ISSN: 2775-2658
Website: https://pubs2.ascee.org/index.php/IJRCS
Email: ijrcs@ascee.org
Organized by: Association for Scientific Computing Electronics and Engineering (ASCEE)Peneliti Teknologi Teknik IndonesiaDepartment of Electrical Engineering, Universitas Ahmad Dahlan and Kuliah Teknik Elektro
Published by: Association for Scientific Computing Electronics and Engineering (ASCEE)
Office: Jalan Janti, Karangjambe 130B, Banguntapan, Bantul, Daerah Istimewa Yogyakarta, Indonesia