Kayma Kipli Kontrol Yöntemiyle Newton-Leipnik Sisteminin Dinamik Analizi ve Sağlam Kaos Bastırılması

Öz

Bu çalışma, doğrusal olmayan dinamik sistemler çerçevesinde Newton-Leipnik kaotik sisteminin matematiksel analizini ve sağlam kontrolünü sunmaktadır. Sistem önce parametrik biçimde formüle edilir ve ardından kaotik özelliklerini ve parametreye bağlı davranışını belirlemek için zaman tepkileri, faz portreleri, Lyapunov üsleri ve çatallanma analizi yoluyla incelenir. Sonuçlar, kontrolsüz sistemin sınırlı ancak periyodik olmayan bir hareket, garip bir çekici yapı ve başlangıç ​​koşullarına belirgin bir duyarlılık sergilediğini, yani tamamen gelişmiş bir kaotik rejimi gösterdiğini doğrulamaktadır. Dinamik analizden sonra, kaotik salınımları bastırmak ve tüm durum değişkenlerini denge noktasına getirmek için bir kayma modu kontrol stratejisi tasarlanmıştır. Önerilen kontrolör, hem nominal hem de bozulmuş çalışma koşulları altında değerlendirilmiştir. Simülasyon sonuçları, kontrol yasasının sistemi hızla stabilize ettiğini, kaotik davranışı etkili bir şekilde ortadan kaldırdığını ve sınırlı kontrol çabasını koruduğunu göstermektedir. Sağlamlığı daha da değerlendirmek için, kapalı döngü tepkisi dürtüsel ve salınımlı bozulmalar altında test edilmiştir. Her iki durumda da, kontrolör kararlılığı korur ve bozulmadan sonra sistemi istenen çalışma bölgesine hızla geri döndürür. Elde edilen bulgular, kayma modlu kontrolün Newton-Leipnik kaotik sisteminin stabilizasyonu için güvenilir ve sağlam bir çözüm sağladığını ve önerilen çerçevenin, sağlam kaos bastırma ve doğrusal olmayan kontrol tasarımı üzerine gelecekteki çalışmalar için yararlı bir temel sunduğunu göstermektedir.

Anahtar Kelimeler

• Kaos analizi
• Kayma kipli kontrol
• Newton-Leipnik sistemi

Dynamical Analysis and Robust Chaos Suppression of the Newton-Leipnik System via Sliding Mode Control

Öz

This study presents the mathematical analysis and robust control of the Newton-Leipnik chaotic system within a nonlinear dynamical systems framework. The system is first formulated in parametric form and then examined through time responses, phase portraits, Lyapunov exponents, and bifurcation analysis in order to identify its chaotic characteristics and parameter dependent behavior. The results confirm that the uncontrolled system exhibits bounded but aperiodic motion, a strange attractor structure, and clear sensitivity to initial conditions, indicating a fully developed chaotic regime. Following the dynamical analysis, a sliding mode control strategy is designed to suppress chaotic oscillations and regulate all state variables to the equilibrium point. The proposed controller is evaluated under both nominal and disturbed operating conditions. Simulation results show that the control law rapidly stabilizes the system, effectively eliminates chaotic behavior, and maintains bounded control effort. To further assess robustness, the closed loop response is tested under impulsive and oscillatory disturbances. In both cases, the controller preserves stability and quickly restores the system to the desired operating region after perturbation. The findings demonstrate that sliding mode control provides a reliable and robust solution for the stabilization of the Newton-Leipnik chaotic system and that the proposed framework offers a useful basis for future studies on robust chaos suppression and nonlinear control design.

Anahtar Kelimeler

• Chaos analysis
• Sliding mode control
• Newton-Leipnik system

Kaynakça

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