Research Article
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Synchronization of a 4D Hyperchaotic System with Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm

Year 2024, Volume: 24 Issue: 2, 465 - 475, 29.04.2024

Erdem İlten

https://doi.org/10.35414/akufemubid.1379669

Abstract

In this paper, a synchronization study is proposed by using a 4D hyperchaotic system model to be used in secure data transfer applications. Active Disturbance Rejection Control (ADRC) method is used for synchronization process. To prove the success of ADRC method, it is compared with Proportional-Integral-Derivative (PID) control method. The coefficients of both control methods are optimized with Particle Swarm Optimization (PSO) algorithm. Synchronization system is modelled and tested in Matlab/Simulink environment. ADRC and PID methods are tested in simulation environment for the cases without disturbance and under disturbance. It can be seen from the test results that the ADRC method managed to keep the system synchronous without being affected by any disturbances. On the other hand, it is clearly seen that the PID method cannot maintain the synchronization of system under disturbance effects.

Keywords

Chaotic system Synchronization ADRC PID PSO

Supporting Institution

Balikesir University

Project Number

BAP-2023/179

Thanks

The authors would like to thank the anonymous reviewers for their valuable comments. This work was funded by Balikesir University under research grant BAP-2023/179.

References

  • Assali, E.A., 2021. Predefined-time synchronization of chaotic systems with different dimensions and applications, Chaos, Solitons & Fractals, 147, 1-11. https://doi.org/10.1016/j.chaos.2021.110988
  • Azar, A.T., Vaidyanathan, S., 2015. Chaos Modeling and Control Systems Design, Springer, 581, 3-17. https://doi.org/10.1007/978-3-319-13132-0
  • Boccaletti, S., Grebogi, C., Lai, Y.-C., Mancini, H., Maza, D., 2000. The control of chaos: theory and applications, Physics Reports, 329(3), 103–197. https://doi.org/10.1016/S0370-1573(99)00096-4
  • Çaşka, S., Uysal, A., 2021. İHA Yardımcı İniş Sisteminin Meta-Sezgisel Optimizasyon Yöntemleri ile Kontrolü, Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 21(5), 1223–1230. https://doi.org/10.35414/akufemubid.888652
  • Chong, E.K.P., Lu, W.-S., Żak, S.H., 2023. An Introduction to Optimization, John Wiley & Sons, 1-5.
  • Demirtas, M., Ilten, E., Calgan, H., 2019. Pareto-Based Multi-objective Optimization for Fractional Order PIλ Speed Control of Induction Motor by Using Elman Neural Network, Arabian Journal for Science and Engineering, 44(3), 2165–2175. https://doi.org/10.1007/s13369-018-3364-2
  • Fareh, R., Khadraoui, S., Abdallah, M.Y., Baziyad, M., Bettayeb, M., 2021. Active disturbance rejection control for robotic systems: A review, Mechatronics, 80, 1-13. https://doi.org/10.1016/j.mechatronics.2021.102671
  • Feng, H., Guo, B.-Z., 2017. Active disturbance rejection control: Old and new results, Annual Reviews in Control, 44, 238–248. https://doi.org/10.1016/j.arcontrol.2017.05.003
  • Fradkov, A., 2007. Cybernetical Physics: From Control of Chaos to Quantum Control, Springer, 2-4.
  • Fradkov, A.L., Evans, R.J., 2005. Control of chaos: Methods and applications in engineering, Annual Reviews in Control, 29(1), 33–56. https://doi.org/10.1016/j.arcontrol.2005.01.001
  • Gökçe, C.O., 2023. Intelligent Quadcopter Control Using Artificial Neural Networks, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 23(1), 138–142. https://doi.org/10.35414/akufemubid.1229424
  • Gokyildirim, A., Kocamaz, U.E., Uyaroglu, Y., Calgan, H., 2023. A novel five-term 3D chaotic system with cubic nonlinearity and its microcontroller-based secure communication implementation, AEU-International Journal of Electronics and Communications, 160, 1-14. https://doi.org/10.1016/j.aeue.2022.154497
  • Gong, L., Wu, R., Zhou, N., 2020. A new 4D chaotic system with coexisting hidden chaotic attractors, International Journal of Bifurcation and Chaos, 30(10), 1-14. https://doi.org/10.1142/S0218127420501424
  • Guegan, D., 2009. Chaos in economics and finance, Annual Reviews in Control, 33(1), 89–93. https://doi.org/10.1016/j.arcontrol.2009.01.002
  • Güven, K., 2022. Conformable Kesirli Mertebeden COVID-19 Modelinin Reel Veriye Bağlı Kaotik Davranışları ve Kaos Kontrolü, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 22(6), 1299–1306. https://doi.org/10.35414/akufemubid.1125850
  • Huang, Y., Xue, W., 2014. Active disturbance rejection control: Methodology and theoretical analysis, ISA Transactions, 53(4), 963–976. https://doi.org/10.1016/j.isatra.2014.03.003
  • Ilten, E., 2022a. Conformable fractional order controller design and optimization for sensorless control of induction motor, COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 41(5), 1528–1541. https://doi.org/10.1108/COMPEL-09-2021-0334
  • Ilten, E., 2022b. Conformable Fractional Order Controller Design and Implementation for Per-Phase Voltage Regulation of Three-Phase SEIG Under Unbalanced Load, Electric Power Components and Systems, 50(11–12), 636–648. https://doi.org/10.1080/15325008.2022.2139433
  • İlten, E., 2021. Conformable Fractional Order PI Controller Design and Optimization for Permanent Magnet Synchronous Motor Speed Tracking System, Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 9(3), 130–144. https://doi.org/10.29130/dubited.756999
  • Ilten, E., Demirtas, M., 2019. Fractional order super-twisting sliding mode observer for sensorless control of induction motor, COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 38(2), 878–892. https://doi.org/10.1108/COMPEL-08-2018-0306
  • Ilten, E., Demirtas, M., 2023. Fuzzy Logic Position Control of DC Motor with Raspberry Pi and Real-Time Monitoring on Simulink External Mode, 1st Bilsel International World Science and Research Congress, 1, 189–195.
  • Iskakova, K., Alam, M.M., Ahmad, S., Saifullah, S., Akgül, A., Yılmaz, G., 2023. Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis, Mathematics and Computers in Simulation, 208, 219–245. https://doi.org/10.1016/j.matcom.2023.01.024
  • Johnson, M.A., Moradi, M.H., 2005. PID Control, Springer, 29-46. https://doi.org/10.1007/1-84628-148-2
  • Kennedy, J., Eberhart, R., 1995. Particle swarm optimization, Proceedings of ICNN’95-International Conference on Neural Networks, 4, 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
  • Lakomy, K., Giernacki, W., Michalski, J., Madonski, R., 2021. Active disturbance rejection control (adrc) toolbox for matlab/simulink, ArXiv, 8-10. https://doi.org/10.48550/arXiv.2112.01614
  • Mirzaei, M.J., Aslmostafa, E., Asadollahi, M., Padar, N., 2023. Fast fixed-time sliding mode control for synchronization of chaotic systems with unmodeled dynamics and disturbance; applied to memristor-based oscillator, Journal of Vibration and Control, 29(9–10), 2129–2143. https://doi.org/10.1177/10775463221075116
  • Oestreicher, C., 2022. A history of chaos theory, Dialogues in Clinical Neuroscience, 9(3), 279-289. https://doi.org/10.31887/DCNS.2007.9.3/coestreicher
  • Pecora, L.M., Carroll, T.L., 2015. Synchronization of chaotic systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(9), 1-12. https://doi.org/10.1063/1.4917383
  • Poli, R., Kennedy, J., Blackwell, T., 2007. Particle swarm optimization: An overview, Swarm Intelligence, Springer, 1, 33–57. https://doi.org/10.1007/s11721-007-0002-0
  • Qi, G., Chen, G., 2006. Analysis and circuit implementation of a new 4D chaotic system, Physics Letters A, 352(4–5), 386–397. https://doi.org/10.1016/j.physleta.2005.12.030
  • Sarangapani, J., 2018. Neural Network Control of Nonlinear Discrete-Time Systems, CRC press, 145-168.
  • Schöll, E., Schuster, H.G., 2008. Handbook of Chaos Control, Wiley Online Library, 3-28. https://doi.org/10.1002/9783527622313
  • Wibowo, W.K., Jeong, S., 2013. Genetic algorithm tuned PI controller on PMSM simplified vector control, Journal of Central South University, 20(11), 3042–3048. https://doi.org/10.1007/s11771-013-1827-x
  • Zaqueros-Martinez, J., Rodriguez-Gomez, G., Tlelo-Cuautle, E., Orihuela-Espina, F., 2023. Fuzzy Synchronization of Chaotic Systems with Hidden Attractors, Entropy, 25(3), 1-23. https://doi.org/10.3390/e25030495
  • Zheng, Y., Huang, Z., Tao, J., Sun, H., Sun, Q., Sun, M., Dehmer, M., Chen, Z., 2021. A novel chaotic fractional-order beetle swarm optimization algorithm and its application for load-frequency active disturbance rejection control, IEEE Transactions on Circuits and Systems II: Express Briefs, 69(3), 1267–1271. https://doi.org/10.1109/TCSII.2021.3100853
  • MathWorks, 2023. MATLAB documentation, The MathWorks. https://www.mathworks.com/help/ (20.12.2023)

4D Hiperkaotik Sistemin Aktif Bozucu Reddetme Kontrolü ile Senkronizasyonu ve Parçacık Sürü Algoritması ile Optimizasyonu

Year 2024, Volume: 24 Issue: 2, 465 - 475, 29.04.2024

Erdem İlten

https://doi.org/10.35414/akufemubid.1379669

Abstract

Bu çalışmada, güvenli veri aktarım uygulamalarında kullanılmak üzere 4 boyutlu hiperkaotik sistem modeli kullanılarak bir senkronizasyon çalışması önerilmektedir. Senkronizasyon işlemi için Aktif Bozucu Reddetme Kontrolü (Active Disturbance Rejection Control (ADRC)) yöntemi kullanılmaktadır. ADRC yönteminin başarısının kanıtlanması için Oransal-İntegral-Türev (Proportional-Integral-Derivative (PID)) kontrol yöntemiyle karşılaştırması yapılmıştır. Her iki kontrol yönteminin katsayıları Parçacık Sürü Optimizasyonu (Particle Swarm Optimization (PSO)) algoritması ile optimize edilmiştir. Senkronizasyon sistemi Matlab/Simulink ortamında modellenip test edilmiştir. ADRC ve PID yöntemleri, bozucunun olmadığı ve bozucunun olduğu durumlar için simülasyon ortamında test edilmektedir. ADRC yönteminin, sistemi herhangi bir bozulmadan etkilenmeden senkron tutmayı başardığı test sonuçlarında görülmektedir. Öte yandan PID yönteminin, bozucu etkiler altında sistemin senkronizasyonunu sağlayamadığı açıkça görülmektedir.

Keywords

Kaotik sistem Senkronizasyon ADRC PID PSO

Project Number

BAP-2023/179

References

  • Assali, E.A., 2021. Predefined-time synchronization of chaotic systems with different dimensions and applications, Chaos, Solitons & Fractals, 147, 1-11. https://doi.org/10.1016/j.chaos.2021.110988
  • Azar, A.T., Vaidyanathan, S., 2015. Chaos Modeling and Control Systems Design, Springer, 581, 3-17. https://doi.org/10.1007/978-3-319-13132-0
  • Boccaletti, S., Grebogi, C., Lai, Y.-C., Mancini, H., Maza, D., 2000. The control of chaos: theory and applications, Physics Reports, 329(3), 103–197. https://doi.org/10.1016/S0370-1573(99)00096-4
  • Çaşka, S., Uysal, A., 2021. İHA Yardımcı İniş Sisteminin Meta-Sezgisel Optimizasyon Yöntemleri ile Kontrolü, Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 21(5), 1223–1230. https://doi.org/10.35414/akufemubid.888652
  • Chong, E.K.P., Lu, W.-S., Żak, S.H., 2023. An Introduction to Optimization, John Wiley & Sons, 1-5.
  • Demirtas, M., Ilten, E., Calgan, H., 2019. Pareto-Based Multi-objective Optimization for Fractional Order PIλ Speed Control of Induction Motor by Using Elman Neural Network, Arabian Journal for Science and Engineering, 44(3), 2165–2175. https://doi.org/10.1007/s13369-018-3364-2
  • Fareh, R., Khadraoui, S., Abdallah, M.Y., Baziyad, M., Bettayeb, M., 2021. Active disturbance rejection control for robotic systems: A review, Mechatronics, 80, 1-13. https://doi.org/10.1016/j.mechatronics.2021.102671
  • Feng, H., Guo, B.-Z., 2017. Active disturbance rejection control: Old and new results, Annual Reviews in Control, 44, 238–248. https://doi.org/10.1016/j.arcontrol.2017.05.003
  • Fradkov, A., 2007. Cybernetical Physics: From Control of Chaos to Quantum Control, Springer, 2-4.
  • Fradkov, A.L., Evans, R.J., 2005. Control of chaos: Methods and applications in engineering, Annual Reviews in Control, 29(1), 33–56. https://doi.org/10.1016/j.arcontrol.2005.01.001
  • Gökçe, C.O., 2023. Intelligent Quadcopter Control Using Artificial Neural Networks, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 23(1), 138–142. https://doi.org/10.35414/akufemubid.1229424
  • Gokyildirim, A., Kocamaz, U.E., Uyaroglu, Y., Calgan, H., 2023. A novel five-term 3D chaotic system with cubic nonlinearity and its microcontroller-based secure communication implementation, AEU-International Journal of Electronics and Communications, 160, 1-14. https://doi.org/10.1016/j.aeue.2022.154497
  • Gong, L., Wu, R., Zhou, N., 2020. A new 4D chaotic system with coexisting hidden chaotic attractors, International Journal of Bifurcation and Chaos, 30(10), 1-14. https://doi.org/10.1142/S0218127420501424
  • Guegan, D., 2009. Chaos in economics and finance, Annual Reviews in Control, 33(1), 89–93. https://doi.org/10.1016/j.arcontrol.2009.01.002
  • Güven, K., 2022. Conformable Kesirli Mertebeden COVID-19 Modelinin Reel Veriye Bağlı Kaotik Davranışları ve Kaos Kontrolü, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 22(6), 1299–1306. https://doi.org/10.35414/akufemubid.1125850
  • Huang, Y., Xue, W., 2014. Active disturbance rejection control: Methodology and theoretical analysis, ISA Transactions, 53(4), 963–976. https://doi.org/10.1016/j.isatra.2014.03.003
  • Ilten, E., 2022a. Conformable fractional order controller design and optimization for sensorless control of induction motor, COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 41(5), 1528–1541. https://doi.org/10.1108/COMPEL-09-2021-0334
  • Ilten, E., 2022b. Conformable Fractional Order Controller Design and Implementation for Per-Phase Voltage Regulation of Three-Phase SEIG Under Unbalanced Load, Electric Power Components and Systems, 50(11–12), 636–648. https://doi.org/10.1080/15325008.2022.2139433
  • İlten, E., 2021. Conformable Fractional Order PI Controller Design and Optimization for Permanent Magnet Synchronous Motor Speed Tracking System, Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 9(3), 130–144. https://doi.org/10.29130/dubited.756999
  • Ilten, E., Demirtas, M., 2019. Fractional order super-twisting sliding mode observer for sensorless control of induction motor, COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 38(2), 878–892. https://doi.org/10.1108/COMPEL-08-2018-0306
  • Ilten, E., Demirtas, M., 2023. Fuzzy Logic Position Control of DC Motor with Raspberry Pi and Real-Time Monitoring on Simulink External Mode, 1st Bilsel International World Science and Research Congress, 1, 189–195.
  • Iskakova, K., Alam, M.M., Ahmad, S., Saifullah, S., Akgül, A., Yılmaz, G., 2023. Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis, Mathematics and Computers in Simulation, 208, 219–245. https://doi.org/10.1016/j.matcom.2023.01.024
  • Johnson, M.A., Moradi, M.H., 2005. PID Control, Springer, 29-46. https://doi.org/10.1007/1-84628-148-2
  • Kennedy, J., Eberhart, R., 1995. Particle swarm optimization, Proceedings of ICNN’95-International Conference on Neural Networks, 4, 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
  • Lakomy, K., Giernacki, W., Michalski, J., Madonski, R., 2021. Active disturbance rejection control (adrc) toolbox for matlab/simulink, ArXiv, 8-10. https://doi.org/10.48550/arXiv.2112.01614
  • Mirzaei, M.J., Aslmostafa, E., Asadollahi, M., Padar, N., 2023. Fast fixed-time sliding mode control for synchronization of chaotic systems with unmodeled dynamics and disturbance; applied to memristor-based oscillator, Journal of Vibration and Control, 29(9–10), 2129–2143. https://doi.org/10.1177/10775463221075116
  • Oestreicher, C., 2022. A history of chaos theory, Dialogues in Clinical Neuroscience, 9(3), 279-289. https://doi.org/10.31887/DCNS.2007.9.3/coestreicher
  • Pecora, L.M., Carroll, T.L., 2015. Synchronization of chaotic systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(9), 1-12. https://doi.org/10.1063/1.4917383
  • Poli, R., Kennedy, J., Blackwell, T., 2007. Particle swarm optimization: An overview, Swarm Intelligence, Springer, 1, 33–57. https://doi.org/10.1007/s11721-007-0002-0
  • Qi, G., Chen, G., 2006. Analysis and circuit implementation of a new 4D chaotic system, Physics Letters A, 352(4–5), 386–397. https://doi.org/10.1016/j.physleta.2005.12.030
  • Sarangapani, J., 2018. Neural Network Control of Nonlinear Discrete-Time Systems, CRC press, 145-168.
  • Schöll, E., Schuster, H.G., 2008. Handbook of Chaos Control, Wiley Online Library, 3-28. https://doi.org/10.1002/9783527622313
  • Wibowo, W.K., Jeong, S., 2013. Genetic algorithm tuned PI controller on PMSM simplified vector control, Journal of Central South University, 20(11), 3042–3048. https://doi.org/10.1007/s11771-013-1827-x
  • Zaqueros-Martinez, J., Rodriguez-Gomez, G., Tlelo-Cuautle, E., Orihuela-Espina, F., 2023. Fuzzy Synchronization of Chaotic Systems with Hidden Attractors, Entropy, 25(3), 1-23. https://doi.org/10.3390/e25030495
  • Zheng, Y., Huang, Z., Tao, J., Sun, H., Sun, Q., Sun, M., Dehmer, M., Chen, Z., 2021. A novel chaotic fractional-order beetle swarm optimization algorithm and its application for load-frequency active disturbance rejection control, IEEE Transactions on Circuits and Systems II: Express Briefs, 69(3), 1267–1271. https://doi.org/10.1109/TCSII.2021.3100853
  • MathWorks, 2023. MATLAB documentation, The MathWorks. https://www.mathworks.com/help/ (20.12.2023)
There are 36 citations in total.

Details

Primary Language English
Subjects Control Engineering, Mechatronics and Robotics (Other)
Journal Section Articles
Authors

Erdem İlten 0000-0002-9608-2148

Project Number BAP-2023/179
Early Pub Date April 14, 2024
Publication Date April 29, 2024
Submission Date October 22, 2023
Acceptance Date March 10, 2024
Published in Issue Year 2024 Volume: 24 Issue: 2

Cite

APA İlten, E. (2024). Synchronization of a 4D Hyperchaotic System with Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 24(2), 465-475. https://doi.org/10.35414/akufemubid.1379669
AMA İlten E. Synchronization of a 4D Hyperchaotic System with Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. April 2024;24(2):465-475. doi:10.35414/akufemubid.1379669
Chicago İlten, Erdem. “Synchronization of a 4D Hyperchaotic System With Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 24, no. 2 (April 2024): 465-75. https://doi.org/10.35414/akufemubid.1379669.
EndNote İlten E (April 1, 2024) Synchronization of a 4D Hyperchaotic System with Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 24 2 465–475.
IEEE E. İlten, “Synchronization of a 4D Hyperchaotic System with Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 24, no. 2, pp. 465–475, 2024, doi: 10.35414/akufemubid.1379669.
ISNAD İlten, Erdem. “Synchronization of a 4D Hyperchaotic System With Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 24/2 (April 2024), 465-475. https://doi.org/10.35414/akufemubid.1379669.
JAMA İlten E. Synchronization of a 4D Hyperchaotic System with Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2024;24:465–475.
MLA İlten, Erdem. “Synchronization of a 4D Hyperchaotic System With Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 24, no. 2, 2024, pp. 465-7, doi:10.35414/akufemubid.1379669.
Vancouver İlten E. Synchronization of a 4D Hyperchaotic System with Active Disturbance Rejection Control and Its Optimization via Particle Swarm Algorithm. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2024;24(2):465-7.
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