Araştırma Makalesi
Yıl 2025,
Cilt: 11 Sayı: 1, 219 - 239, 30.06.2025
Öz
In this study, the control of 21 chaotic systems with different characteristics and dynamics was achieved using five different control methods: classical PID, Direct Feedback Control, Passive Control ve Sliding Mode Control. A graphical user interface was designed using MATLAB/SIMULINK and the Graphical User Interface Toolbox. Through 84 different applications, performance metrics such as settling time, steady-state error, and maximum overshoot were compared based on the applied control method, aiming to determine the control technique that delivers the best performance for the selected chaotic system. The results were presented with detailed data in tables for thorough analysis.
Anahtar Kelimeler
Kaynakça
- N. Wang, C. Li, H. Bao, M. Chen and B. Bao, "Generating Multi-Scroll Chua’s Attractors via Simplified Piecewise-Linear Chua’s Diode," IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 66, No. 12, pp. 4767-4779, 2019, doi:10.1109/TCSI.2019.2933365.
- J. Gleick, Chaos: Making a New Science. New York, NY, USA: Penguin, 2008.
- G. Chen and S. Dong, “From Chaos to Order: Perspectives, Methodologies, and Applications”. Singapore: World Scientific, 1998.
- E. Ott, C. Grebogi, and J. A. Yorke, "Controlling chaos", Phys. Rev. Lett., Vol. 64, No. 11, pp. 1196–1199, Mar. 1990, doi: https://doi.org/10.1103/PhysRevLett.64.1196.
- G. Chen, T. Ueta, “Yet another chaotic attractor”, Int J Bifur Chaos Vol.9, No.7,pp.1465-1466, 1999, doi:10.1142/S0218127499001024.
- Q. Lai, B. Norouzi, F. Liu, “Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors, Chaos, Solitons & Fractals,Vol. 114, pp. 230-245, 2018, doi: https://doi.org/10.1016/j.chaos.2018.07.011.
- Xiong, L., Qi, L., Teng, S. “A simplest Lorenz-like chaotic circuit and its applications in secure communication and weak signal detection”. Eur. Phys. J. Spec. Top. Vol.230, pp.1933–1944, 2021, doi: Eur. Phys. J. Spec. Top. (2021) 230:1933–1944 https://doi.org/10.1140/epjs/s11734-021-00177-y.
- J. Hou and S. Ma, "Chaos Control in a Class of Fractional-order Stochastic Lorenz System," 2012 Fifth International Workshop on Chaos-fractals Theories and Applications, Dalian, China, pp. 241-244, 2012, doi: 10.1109/IWCFTA.2012.58.
- H. Nijmeijer and H. Berghuis, "On Lyapunov control of the Duffing equation," IEEE Trans. Circuits Syst. I, vol. 42, no. 8, pp. 473–477, Aug. 1995, doi: 10.1109/81.404059.
- R. Saravanan, O. Narayan, K. Banerjee, J. K. Bhattacharjee, “Chaos in periodically forced Lorenz System”, Physical Review A, Vol.31, pp.520-522, 1984, doi: https://doi.org/10.1103/PhysRevA.31.520.
- Z. Cangtao, C.H. Lai, M.Y. Yu, “Chaos, bifurcation and periodic orbits of the Lorenz–Stenflo system”, Phys Scr, Vol.55, pp. 394-402, 1997, doi: 10.1088/0031-8949/55/4/003.
- S. Yan, J. Wang, L Li, “Analysis of a new three-dimensional jerk chaotic system with transient chaos and its adaptive backstepping synchronous control”, Integration, Vol. 98, 102210, 2024, doi: https://doi.org/10.1016/j.vlsi.2024.102210.
- R.P. Borase, D.K. Maghade, “A review of PID control, tuning methods and applications”. Int. J. Dynam. Control, Vol. 9, pp.818–827, 2021, doi:10.1007/s40435-020-00665-4.
- C. Novara, L. Fagiano, M. Milanese, “Direct feedback control design for nonlinear systems”, Automatica, Vol.49, No.4, pp. 849-860, 2013, doi:https://doi.org/10.1016/j.automatica.2013.01.002.
- D. Qi, G. Zhao and S. Yunzhong, "Passive control of Chen chaotic system," Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788), Vol.2, pp. 1284-1286, China, 2004, doi:10.1109/WCICA.2004.1340844.
- L. Caina and C. Baotong, "Passive Control of Uncertain Linear Systems with Time-Varying Delay in States," 2006 Chinese Control Conference, Harbin, China, 2006, pp. 16-20,
- J. M. Nazzal, A. N. Natsheh, “Chaos control using sliding-mode theory”, Chaos, Solitons & Fractals, Vol.33, No. 2, pp.695-702, 2007, doi:10.1016/j.chaos.2006.01.071.
- R. K. Moghaddam; M. Rabbani, "Back‐Stepping Sliding‐Mode Control," in Methods of Developing Sliding Mode Controllers: Design and Matlab Simulation , IEEE, pp.123-149, 2025.
- Kaynak Dosyalar, https://drive.google.com/file/d/1jw8Jqq73CoCobUflzSd7ta7kMrkcOyQo/view?usp=sharing (Erişim Tarihi: 21.05.2025)
Yıl 2025,
Cilt: 11 Sayı: 1, 219 - 239, 30.06.2025
Öz
Bu çalışmada, farklı özelliğe ve dinamiğe sahip 21 kaotik sistemin, klasik PID, Doğrudan Geri Beslemeli Kontrol, Pasif Kontrol ve Kayan Kipli Kontrol gibi 4 farklı kontrol yöntemi ile her bir sistemin kontrolü sağlanmıştır. Bu çalışmada, MATLAB/SIMULINK ve Grafik Kullanıcı Ara Birim araç kutusu ile bir kullanıcı ara birimi tasarlanmış ve 84 farklı uygulama gerçekleştirilerek uygulanan kontrol yöntemine göre oturma zamanı, kalıcı durum hatası, maksimum aşma gibi sonuçlar birbiriyle karşılaştırılarak seçilen kaotik sisteme en iyi performansa sahip kontrol yönteminin bulunması amaçlanmıştır. Elde edilen sonuçlar tablolar yardımı ile incelenebilmesi için ayrıntılı veriler içerecek şekilde sunulmuştur.
Anahtar Kelimeler
Kaynakça
- N. Wang, C. Li, H. Bao, M. Chen and B. Bao, "Generating Multi-Scroll Chua’s Attractors via Simplified Piecewise-Linear Chua’s Diode," IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 66, No. 12, pp. 4767-4779, 2019, doi:10.1109/TCSI.2019.2933365.
- J. Gleick, Chaos: Making a New Science. New York, NY, USA: Penguin, 2008.
- G. Chen and S. Dong, “From Chaos to Order: Perspectives, Methodologies, and Applications”. Singapore: World Scientific, 1998.
- E. Ott, C. Grebogi, and J. A. Yorke, "Controlling chaos", Phys. Rev. Lett., Vol. 64, No. 11, pp. 1196–1199, Mar. 1990, doi: https://doi.org/10.1103/PhysRevLett.64.1196.
- G. Chen, T. Ueta, “Yet another chaotic attractor”, Int J Bifur Chaos Vol.9, No.7,pp.1465-1466, 1999, doi:10.1142/S0218127499001024.
- Q. Lai, B. Norouzi, F. Liu, “Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors, Chaos, Solitons & Fractals,Vol. 114, pp. 230-245, 2018, doi: https://doi.org/10.1016/j.chaos.2018.07.011.
- Xiong, L., Qi, L., Teng, S. “A simplest Lorenz-like chaotic circuit and its applications in secure communication and weak signal detection”. Eur. Phys. J. Spec. Top. Vol.230, pp.1933–1944, 2021, doi: Eur. Phys. J. Spec. Top. (2021) 230:1933–1944 https://doi.org/10.1140/epjs/s11734-021-00177-y.
- J. Hou and S. Ma, "Chaos Control in a Class of Fractional-order Stochastic Lorenz System," 2012 Fifth International Workshop on Chaos-fractals Theories and Applications, Dalian, China, pp. 241-244, 2012, doi: 10.1109/IWCFTA.2012.58.
- H. Nijmeijer and H. Berghuis, "On Lyapunov control of the Duffing equation," IEEE Trans. Circuits Syst. I, vol. 42, no. 8, pp. 473–477, Aug. 1995, doi: 10.1109/81.404059.
- R. Saravanan, O. Narayan, K. Banerjee, J. K. Bhattacharjee, “Chaos in periodically forced Lorenz System”, Physical Review A, Vol.31, pp.520-522, 1984, doi: https://doi.org/10.1103/PhysRevA.31.520.
- Z. Cangtao, C.H. Lai, M.Y. Yu, “Chaos, bifurcation and periodic orbits of the Lorenz–Stenflo system”, Phys Scr, Vol.55, pp. 394-402, 1997, doi: 10.1088/0031-8949/55/4/003.
- S. Yan, J. Wang, L Li, “Analysis of a new three-dimensional jerk chaotic system with transient chaos and its adaptive backstepping synchronous control”, Integration, Vol. 98, 102210, 2024, doi: https://doi.org/10.1016/j.vlsi.2024.102210.
- R.P. Borase, D.K. Maghade, “A review of PID control, tuning methods and applications”. Int. J. Dynam. Control, Vol. 9, pp.818–827, 2021, doi:10.1007/s40435-020-00665-4.
- C. Novara, L. Fagiano, M. Milanese, “Direct feedback control design for nonlinear systems”, Automatica, Vol.49, No.4, pp. 849-860, 2013, doi:https://doi.org/10.1016/j.automatica.2013.01.002.
- D. Qi, G. Zhao and S. Yunzhong, "Passive control of Chen chaotic system," Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788), Vol.2, pp. 1284-1286, China, 2004, doi:10.1109/WCICA.2004.1340844.
- L. Caina and C. Baotong, "Passive Control of Uncertain Linear Systems with Time-Varying Delay in States," 2006 Chinese Control Conference, Harbin, China, 2006, pp. 16-20,
- J. M. Nazzal, A. N. Natsheh, “Chaos control using sliding-mode theory”, Chaos, Solitons & Fractals, Vol.33, No. 2, pp.695-702, 2007, doi:10.1016/j.chaos.2006.01.071.
- R. K. Moghaddam; M. Rabbani, "Back‐Stepping Sliding‐Mode Control," in Methods of Developing Sliding Mode Controllers: Design and Matlab Simulation , IEEE, pp.123-149, 2025.
- Kaynak Dosyalar, https://drive.google.com/file/d/1jw8Jqq73CoCobUflzSd7ta7kMrkcOyQo/view?usp=sharing (Erişim Tarihi: 21.05.2025)
Toplam 19 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Devreler ve Sistemler |
| Bölüm | Makaleler |
| Yazarlar | |
| Erken Görünüm Tarihi | 27 Haziran 2025 |
| Yayımlanma Tarihi | 30 Haziran 2025 |
| Gönderilme Tarihi | 21 Mayıs 2025 |
| Kabul Tarihi | 12 Haziran 2025 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 11 Sayı: 1 |
