Feedback Control of the T Chaotic System

Öz

In this study, the chaotic behavior of the T system is shown by analyzing Lyapunov exponents, Kaplan-Yorke dimension and equilibrium points. Also, the chaos control of T system showing chaotic behavior under certain parameters is investigated via linear feedback control. Routh-Hurwitz criterion is used to provide the condition of stability of the controlled system around the equilibrium points. The feedback gain is calculated to control the T chaotic system with single state feedback, then the same calculations repeated for the control of the system with two and three state feedback. The controller designed by calculating the feedback coefficients using the Routh-Hurwitz criterion is added to the T chaotic system. It is shown by phase portraits how the change of the feedback gains affects the control of the system. The design and implementation of the controller is quite simple. Due to the simple structure of the controller, the controller hardware is low and realized conveniently. Simulation results show that the controlled system with the application of feedback control converges to zero and other equilibrium points.

Anahtar Kelimeler

• Chaotic T system
• chaos control
• feedback control
• Routh-Hurwitz Method

T Kaotik Sisteminin Geri Besleme ile Kontrolü

Öz

Bu çalışmada, T sisteminin kaotik davranışı Lyapunov üstelleri, Kaplan-Yorke boyutu ve denge noktaları analiz edilerek gösterilmiştir. Daha sonra belirli parametreler altında kaotik davranış gösteren T sisteminin doğrusal geri beslemeli kontrol yardımıyla kontrolü araştırılmıştır. Denge noktaları etrafında kontrol edilen sistemin kararlılığını sağlamak için Routh-Hurwitz kriteri kullanılmıştır. T kaotik sistemini tek durum değişkeni geri besleme ile kontrol etmek için geri besleme katsayısı hesaplanmış daha sonra iki ve üç durum geri besleme ile sistemin kontrolü için aynı işlemler tekrarlanmıştır. Routh-Hurwitz kriteri kullanılarak geri besleme katsayıları hesaplanarak tasarlanan kontrolör T kaotik sistemine eklenmiştir. Kontrollü sistemde geri besleme katsayısı değişiminin sistemin kontrolünü nasıl etkilediği faz portreleri ile gösterilmiştir. Doğrusal geri beslemeli kontrolörün tasarlanması ve uygulanması oldukça basittir. Kontrolör basit yapıya sahip olduğundan donanımsal olarak maliyeti düşüktür ve pratik olarak gerçeklenmesi kolaydır. Geri beslemeli kontrolün uygulanmasıyla kontrollü sistemin sıfır ve diğer denge noktalarına yakınsadığı bilgisayar benzetim çalışmalarıyla gösterilmiştir.

Anahtar Kelimeler

• Kaotik T sistemi
• kaos kontrolü
• geri beslemeli kontrol
• Routh-Hurwitz kriteri

Kaynakça

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