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Modelling and Chaotic Based Parameter Optimization of Sliding Mode Controller

Year 2025, Volume: 8 Issue: 2, 42 - 55, 28.06.2025
https://doi.org/10.33187/jmsm.1617412

Abstract

This study presents a sliding mode controller design for DC motor speed control using optimization algorithms. The design of sliding mode controllers typically requires expert input during the parameter determination phase. Traditionally, these parameters are set through trial-and-error methods based on the experience of specialists. However, this approach can be both time-consuming and costly. The application of optimization methods automates the parameter-tuning process, reducing human intervention and, in turn, minimizing both design time and costs. The goal of this study is to enhance the performance of optimization methods by hybridizing them with chaotic systems. The random structures of chaotic systems allow optimization algorithms to explore a broader solution space, thereby improving their performance. The analyses conducted in this study reveal that hybrid chaotic algorithms outperform their original ones. The data indicate that the use of hybrid algorithms generally leads to a decrease in Steady-State Error. Additionally, it is observed that when all hybrid algorithms are employed, the sliding mode controller does not exhibit any overshoot. The results demonstrate that the sliding mode controller performs effectively, achieving low settling time, rise time, and steady-state error, while also preventing chattering. Among the methods examined, the sliding mode controller optimized with the Chaotic Henry Gas Solubility Optimization algorithm delivers the best performance, ensuring optimal system stability.

References

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  • [7] S. Ekinci, B. Hekimoğlu, D. Izci, Opposition based Henry gas solubility optimization as a novel algorithm for PID control of DC motor, Eng. Sci. Technol., Int. J., 24(2) (2021), 331-342. https://doi.org/10.1016/j.jestch.2020.08.011
  • [8] S. Ravikumar, D. Kavitha, CNN-OHGS: CNN-oppositional-based Henry gas solubility optimization model for autonomous vehicle control system, J. Field Robot., 38(7) (2021), 967-979.https://doi.org/10.1002/rob.22020
  • [9] B.M. Alshammari, A. Farah, K. Alqunun, et al., Robust design of dual-input power system stabilizer using chaotic Jaya algorithm, Energies, 14(17) (2021), Article ID 5294. https://doi.org/10.3390/en14175294
  • [10] E. Emary, H.M. Zawbaa, Impact of chaos functions on modern swarm optimizers, PLoS ONE, 11(7) (2016), Article ID e0158738. https://doi.org/10.1371/journal.pone.0158738
  • [11] D. Yan, Y. Lu, M. Zhou, et al., Empirically characteristic analysis of chaotic PID controlling particle swarm optimization, PLoS ONE, 12(5) (2017), Article ID e0176359. https://doi.org/10.1371/journal.pone.0176359
  • [12] D. Tian, Particle swarm optimization with chaotic maps and Gaussian mutation for function optimization, Int. J. Grid Distrib. Comput., 8(4) (2015), 123-134. http://dx.doi.org/10.14257/ijgdc.2015.8.4.12
  • [13] M.L. Huang, Hybridization of chaotic quantum particle swarm optimization with SVR in electric demand forecasting, Energies, 9(6) (2016), Article ID 426. https://doi.org/10.3390/en9060426
  • [14] Y. Du, F. Xu, A hybrid multi-step probability selection particle swarm optimization with dynamic chaotic inertial weight and acceleration coefficients for numerical function optimization, Symmetry, 12(6) (2020), Article ID 922. https://doi.org/10.3390/sym12060922
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  • [18] M. Verma, M. Sreejeth, M. Singh, et al., Chaotic mapping based advanced Aquila Optimizer with single stage evolutionary algorithm, IEEE Access, 10 (2022), 89153-89169. https://doi.org/10.1109/ACCESS.2022.3200386
  • [19] H. Lu, L. Yin, X. Wang, et al., Chaotic multiobjective evolutionary algorithm based on decomposition for test task scheduling problem, Math. Probl. Eng., 2014(1) (2014), Article ID 640764.https://doi.org/10.1155/2014/640764
  • [20] H. Lu, X. Wang, Z. Fei, et al., The effects of using chaotic map on improving the performance of multiobjective evolutionary algorithms, Math. Probl. Eng., 2014(1) (2014), Article ID 924652. http://dx.doi.org/10.1155/2014/924652
  • [21] L. Wang, S. Li, F. Tian, et al., A noisy chaotic neural network for solving combinatorial optimization problems: Stochastic chaotic simulated annealing, IEEE Trans. Syst. Man Cybern. Part B: Cybern., 34(5) (2004), 2119-2125. https://doi.org/10.1109/TSMCB.2004.829778
  • [22] Y. Jiang, Y. Lei, Z. Zhong, et al., A wavelet chaotic simulated annealing neural network and its application to optimization problems, In 2011 International Conference on Network Computing and Information Security (NCIS), (2011), 347-351. https://doi.org/10.1109/NCIS.2011.166
  • [23] K. Ferens, D. Cook, W. Kinsner, Chaotic simulated annealing for task allocation in a multiprocessing system, In 12th IEEE International Conference on Cognitive Informatics and Cognitive Computing (ICCI*CC), (2013), 26-35. https://doi.org/10.1109/ICCI-CC.2013.6622222
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  • [25] H. Ding, Z. Wu, L. Zhao, Whale optimization algorithm based on nonlinear convergence factor and chaotic inertial weight, Concurr. Comput.: Pract. Exper., 32(24) (2020), Article ID e5949. https://doi.org/10.1002/cpe.5949
  • [26] Y. Mousavi, A. Alfi, I.B. Kucukdemiral, Enhanced fractional chaotic whale optimization algorithm for parameter identification of isolated wind-diesel power systems, IEEE Access, 8 (2020), 140862-140875. https://doi.org/10.1109/ACCESS.2020.3012686
  • [27] M.S. Sarıkaya, Y. Hamida El Naser, S. Kaçar, et al., Chaotic-Based Improved Henry Gas Solubility Optimization Algorithm: Application to Electric Motor Control, Symmetry, 16(11) (2024), Article ID 1435. https://doi.org/10.3390/sym16111435
  • [28] F.A. Hashim, E.H. Houssein, M.S. Mabrouk, et al., Henry gas solubility optimization: A novel physics-based algorithm, Future Gener. Comput Syst., 101 (2019), 646-667. https://doi.org/10.1016/j.future.2019.07.015
  • [29] Y. Hamida El Naser, D. Karayel, Modeling the effects of external oscillations on mucus clearance in obstructed airways, Biomech. Model. Mechanobiol. 23(1), (2024), 335-348. https://doi.org/10.1007/s10237-023-01778-3
  • [30] M. Rafikov, J.M. Balthazar, On an optimal control design for Rössler system, Phys. Lett. A, 333(3-4), (2004), 241-245. https://doi.org/10.1016/j.physleta.2004.10.032
  • [31] J.Y. Hung, W. Gao, J.C. Hung, Variable structure control: A survey, IEEE Trans. Ind. Electron., 40(1) (1993), 2-22. https://doi.org/10.1109/41.184817
  • [32] Y. Shi, R.C. Eberhart, A modified particle swarm optimizer, In Proceedings of the IEEE International Conference on Evolutionary Computation, (1998), 69–73. https://doi.org/10.1109/ICEC.1998.699146
  • [33] S. Mirjalili, A. Lewis, The whale optimization algorithm, Adv. Eng. Softw., 95 (2016), 51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008
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  • [36] L. Xie, T. Han, H. Zhou, et al., Tuna swarm optimization: A novel swarm-based metaheuristic algorithm for global optimization, Comput. Intell. Neurosci., 2021(1) (2021), Article ID 9210050. https://doi.org/10.1155/2021/9210050
Year 2025, Volume: 8 Issue: 2, 42 - 55, 28.06.2025
https://doi.org/10.33187/jmsm.1617412

Abstract

References

  • [1] W. Cao, X. Liu, J. Ni, Parameter optimization of support vector regression using Henry gas solubility optimization algorithm, IEEE Access, 8 (2020), 88633-88642. https://doi.org/10.1109/ACCESS.2020.2993267
  • [2] M. Liu, T. Liu, M. Zhu, et al., A PI control method with HGSO parameter regulator for trajectory planning of 9-DOF redundant manipulator, Sensors, 22(18) (2022), Article ID 6860. https://doi.org/10.3390/s22186860
  • [3] H. Abdel-Mawgoud, S. Kamel, M. Khasanov, et al., Khurshaid, A strategy for PV and BESS allocation considering uncertainty based on a modified Henry gas solubility optimizer, Electr. Power. Syst. Res., 191 (2021), Article ID 106886. https://doi.org/10.1016/j.epsr.2020.106886
  • [4] D.T. Mosa, A. Mahmoud, J. Zaki, et al., Henry gas solubility optimization double machine learning classifier for neurosurgical patients, PLoS One, 18(5) (2023), Article ID e0285455. https://doi.org/10.1371/journal.pone.0285455
  • [5] W. Xie, C. Xing, J. Wang, et al., Hybrid henry gas solubility optimization algorithm based on the harris hawk optimization, IEEE Access, 8 (2020), 144665-144692. https://doi.org/10.1109/ACCESS.2020.3014309
  • [6] M. Abd Elaziz, D. Yousri, Automatic selection of heavy-tailed distributions-based synergy Henry gas solubility and Harris hawk optimizer for feature selection: Case study drug design and discovery, Artif. Intell. Rev., 54(6) (2021), 4685-4730. https://doi.org/10.1007/s10462-021-10009-z
  • [7] S. Ekinci, B. Hekimoğlu, D. Izci, Opposition based Henry gas solubility optimization as a novel algorithm for PID control of DC motor, Eng. Sci. Technol., Int. J., 24(2) (2021), 331-342. https://doi.org/10.1016/j.jestch.2020.08.011
  • [8] S. Ravikumar, D. Kavitha, CNN-OHGS: CNN-oppositional-based Henry gas solubility optimization model for autonomous vehicle control system, J. Field Robot., 38(7) (2021), 967-979.https://doi.org/10.1002/rob.22020
  • [9] B.M. Alshammari, A. Farah, K. Alqunun, et al., Robust design of dual-input power system stabilizer using chaotic Jaya algorithm, Energies, 14(17) (2021), Article ID 5294. https://doi.org/10.3390/en14175294
  • [10] E. Emary, H.M. Zawbaa, Impact of chaos functions on modern swarm optimizers, PLoS ONE, 11(7) (2016), Article ID e0158738. https://doi.org/10.1371/journal.pone.0158738
  • [11] D. Yan, Y. Lu, M. Zhou, et al., Empirically characteristic analysis of chaotic PID controlling particle swarm optimization, PLoS ONE, 12(5) (2017), Article ID e0176359. https://doi.org/10.1371/journal.pone.0176359
  • [12] D. Tian, Particle swarm optimization with chaotic maps and Gaussian mutation for function optimization, Int. J. Grid Distrib. Comput., 8(4) (2015), 123-134. http://dx.doi.org/10.14257/ijgdc.2015.8.4.12
  • [13] M.L. Huang, Hybridization of chaotic quantum particle swarm optimization with SVR in electric demand forecasting, Energies, 9(6) (2016), Article ID 426. https://doi.org/10.3390/en9060426
  • [14] Y. Du, F. Xu, A hybrid multi-step probability selection particle swarm optimization with dynamic chaotic inertial weight and acceleration coefficients for numerical function optimization, Symmetry, 12(6) (2020), Article ID 922. https://doi.org/10.3390/sym12060922
  • [15] I.A. Hodashinsky, M.B. Bardamova, Tuning fuzzy systems parameters with chaotic particle swarm optimization, J. Phys. Conf. Ser., 803 (2017), Article ID 012053. https://doi.org/10.1088/1742-6596/803/1/012053
  • [16] P. Qu, F. Du, Improved particle swarm optimization for laser cutting path planning, IEEE Access, 11 (2023), 4574-4588. https://doi.org/10.1109/ACCESS.2023.3236006
  • [17] C. Yanguang, M. Zhang, C. Hao, A hybrid chaotic quantum evolutionary algorithm, In 2010 IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS), (2010), pp. 771–776. https://doi.org/10.1109/ICICISYS.2010.5658622
  • [18] M. Verma, M. Sreejeth, M. Singh, et al., Chaotic mapping based advanced Aquila Optimizer with single stage evolutionary algorithm, IEEE Access, 10 (2022), 89153-89169. https://doi.org/10.1109/ACCESS.2022.3200386
  • [19] H. Lu, L. Yin, X. Wang, et al., Chaotic multiobjective evolutionary algorithm based on decomposition for test task scheduling problem, Math. Probl. Eng., 2014(1) (2014), Article ID 640764.https://doi.org/10.1155/2014/640764
  • [20] H. Lu, X. Wang, Z. Fei, et al., The effects of using chaotic map on improving the performance of multiobjective evolutionary algorithms, Math. Probl. Eng., 2014(1) (2014), Article ID 924652. http://dx.doi.org/10.1155/2014/924652
  • [21] L. Wang, S. Li, F. Tian, et al., A noisy chaotic neural network for solving combinatorial optimization problems: Stochastic chaotic simulated annealing, IEEE Trans. Syst. Man Cybern. Part B: Cybern., 34(5) (2004), 2119-2125. https://doi.org/10.1109/TSMCB.2004.829778
  • [22] Y. Jiang, Y. Lei, Z. Zhong, et al., A wavelet chaotic simulated annealing neural network and its application to optimization problems, In 2011 International Conference on Network Computing and Information Security (NCIS), (2011), 347-351. https://doi.org/10.1109/NCIS.2011.166
  • [23] K. Ferens, D. Cook, W. Kinsner, Chaotic simulated annealing for task allocation in a multiprocessing system, In 12th IEEE International Conference on Cognitive Informatics and Cognitive Computing (ICCI*CC), (2013), 26-35. https://doi.org/10.1109/ICCI-CC.2013.6622222
  • [24] J. Li, L. Guo, Y. Li, et al., Enhancing whale optimization algorithm with chaotic theory for permutation flow shop scheduling problem, Int. J. Comput. Intell. Syst., 14(1) (2021), 651–675. https://doi.org/10.2991/ijcis.d.210112.002
  • [25] H. Ding, Z. Wu, L. Zhao, Whale optimization algorithm based on nonlinear convergence factor and chaotic inertial weight, Concurr. Comput.: Pract. Exper., 32(24) (2020), Article ID e5949. https://doi.org/10.1002/cpe.5949
  • [26] Y. Mousavi, A. Alfi, I.B. Kucukdemiral, Enhanced fractional chaotic whale optimization algorithm for parameter identification of isolated wind-diesel power systems, IEEE Access, 8 (2020), 140862-140875. https://doi.org/10.1109/ACCESS.2020.3012686
  • [27] M.S. Sarıkaya, Y. Hamida El Naser, S. Kaçar, et al., Chaotic-Based Improved Henry Gas Solubility Optimization Algorithm: Application to Electric Motor Control, Symmetry, 16(11) (2024), Article ID 1435. https://doi.org/10.3390/sym16111435
  • [28] F.A. Hashim, E.H. Houssein, M.S. Mabrouk, et al., Henry gas solubility optimization: A novel physics-based algorithm, Future Gener. Comput Syst., 101 (2019), 646-667. https://doi.org/10.1016/j.future.2019.07.015
  • [29] Y. Hamida El Naser, D. Karayel, Modeling the effects of external oscillations on mucus clearance in obstructed airways, Biomech. Model. Mechanobiol. 23(1), (2024), 335-348. https://doi.org/10.1007/s10237-023-01778-3
  • [30] M. Rafikov, J.M. Balthazar, On an optimal control design for Rössler system, Phys. Lett. A, 333(3-4), (2004), 241-245. https://doi.org/10.1016/j.physleta.2004.10.032
  • [31] J.Y. Hung, W. Gao, J.C. Hung, Variable structure control: A survey, IEEE Trans. Ind. Electron., 40(1) (1993), 2-22. https://doi.org/10.1109/41.184817
  • [32] Y. Shi, R.C. Eberhart, A modified particle swarm optimizer, In Proceedings of the IEEE International Conference on Evolutionary Computation, (1998), 69–73. https://doi.org/10.1109/ICEC.1998.699146
  • [33] S. Mirjalili, A. Lewis, The whale optimization algorithm, Adv. Eng. Softw., 95 (2016), 51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008
  • [34] P.J. Van Laarhoven, E.H. Aarts, Simulated Annealing, Springer, Berlin, 1987. https://doi.org/10.1007/978-94-015-7744-1 2
  • [35] H.G. Beyer, H.P. Schwefel, Evolution strategies–a comprehensive introduction, Nat. Comput., 1 (2002), 3–52. https://doi.org/10.1023/A:1015059928466
  • [36] L. Xie, T. Han, H. Zhou, et al., Tuna swarm optimization: A novel swarm-based metaheuristic algorithm for global optimization, Comput. Intell. Neurosci., 2021(1) (2021), Article ID 9210050. https://doi.org/10.1155/2021/9210050
There are 36 citations in total.

Details

Primary Language English
Subjects Modelling and Simulation
Journal Section Articles
Authors

Muhammed Salih Sarıkaya 0000-0002-2809-9896

Onur Demirel 0000-0002-4221-3739

Sezgin Kaçar 0000-0002-5171-237X

Adnan Derdiyok 0000-0001-8838-4018

Early Pub Date May 27, 2025
Publication Date June 28, 2025
Submission Date January 12, 2025
Acceptance Date April 15, 2025
Published in Issue Year 2025 Volume: 8 Issue: 2

Cite

APA Sarıkaya, M. S., Demirel, O., Kaçar, S., Derdiyok, A. (2025). Modelling and Chaotic Based Parameter Optimization of Sliding Mode Controller. Journal of Mathematical Sciences and Modelling, 8(2), 42-55. https://doi.org/10.33187/jmsm.1617412
AMA Sarıkaya MS, Demirel O, Kaçar S, Derdiyok A. Modelling and Chaotic Based Parameter Optimization of Sliding Mode Controller. Journal of Mathematical Sciences and Modelling. June 2025;8(2):42-55. doi:10.33187/jmsm.1617412
Chicago Sarıkaya, Muhammed Salih, Onur Demirel, Sezgin Kaçar, and Adnan Derdiyok. “Modelling and Chaotic Based Parameter Optimization of Sliding Mode Controller”. Journal of Mathematical Sciences and Modelling 8, no. 2 (June 2025): 42-55. https://doi.org/10.33187/jmsm.1617412.
EndNote Sarıkaya MS, Demirel O, Kaçar S, Derdiyok A (June 1, 2025) Modelling and Chaotic Based Parameter Optimization of Sliding Mode Controller. Journal of Mathematical Sciences and Modelling 8 2 42–55.
IEEE M. S. Sarıkaya, O. Demirel, S. Kaçar, and A. Derdiyok, “Modelling and Chaotic Based Parameter Optimization of Sliding Mode Controller”, Journal of Mathematical Sciences and Modelling, vol. 8, no. 2, pp. 42–55, 2025, doi: 10.33187/jmsm.1617412.
ISNAD Sarıkaya, Muhammed Salih et al. “Modelling and Chaotic Based Parameter Optimization of Sliding Mode Controller”. Journal of Mathematical Sciences and Modelling 8/2 (June 2025), 42-55. https://doi.org/10.33187/jmsm.1617412.
JAMA Sarıkaya MS, Demirel O, Kaçar S, Derdiyok A. Modelling and Chaotic Based Parameter Optimization of Sliding Mode Controller. Journal of Mathematical Sciences and Modelling. 2025;8:42–55.
MLA Sarıkaya, Muhammed Salih et al. “Modelling and Chaotic Based Parameter Optimization of Sliding Mode Controller”. Journal of Mathematical Sciences and Modelling, vol. 8, no. 2, 2025, pp. 42-55, doi:10.33187/jmsm.1617412.
Vancouver Sarıkaya MS, Demirel O, Kaçar S, Derdiyok A. Modelling and Chaotic Based Parameter Optimization of Sliding Mode Controller. Journal of Mathematical Sciences and Modelling. 2025;8(2):42-55.

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