Control of Lorenz Chaotic System with Linear Feedback, High Gain, High Frequency and Model Predictive Control

Year 2021, Volume: 9 Issue: 2, 314 - 323, 28.05.2021

Murat Erhan Çimen Muhammed Ali Pala Ömer Faruk Boyraz Zeynep Garip Akif Akgül Mustafa Zahid Yıldız Ali Fuat Boz

https://doi.org/10.21541/apjes.805998

Abstract

There are many control methods for systems that have been developed and continued to be developed, linear or non-linear, time-varying or invariant. In this study, in the control of the nonlinear Lorenz Chaotic system, model predictive control method with integrator action, which has not been applied to this system before, is applied. In addition to this method, different nonlinear control methods were applied to the same system and the control of the Lorenz Chaotic system was realized. Feedback control, high gain control, high frequency control and model predictive control techniques are used in the selected control methods. In addition, the methods used were obtained mathematically and their advantages and disadvantages were revealed. As a result, it has been shown that this type of nonlinear control methods can control the Lorenz chaotic system, and then the advantages and disadvantages are discussed in the results section and information about future studies is given.

Keywords

Chaotic system, feedback control, high gain control, high frequency control, model predictive control

Lorenz Kaotik Sisteminin Doğrusal Geri Beslemeli, Yüksek Kazanç, Yüksek Frekans ve Model Öngörülü Kontrol ile Denetlenmesi

Abstract

Günümüze kadar gelişen ve geliştirilmeye devam edilen, doğrusal veya doğrusal olmayan, zamanla değişen veya zamanla değişmeyen sistemler için birçok kontrol yöntemleri bulunmaktadır. Bu çalışmada doğrusal olmayan Lorenz Kaotik sisteminin kontrolünde daha önceden bu sisteme uygulanmamış olan integratör içeren model öngörülü kontrol yöntemi uygulamıştır. Bu yöntemin yanı sıra aynı sisteme farklı doğrusal olmayan kontrol yöntemleri de uygulanarak Lorenz Kaotik sisteminin kontrolü gerçekleştirilmiştir. Seçilen kontrol yöntemlerinde geri beslemeli kontrol, yüksek kazanç kontrol, yüksek frekans kontrol ve model öngörülü kontrol teknikleri kullanılmıştır. Ayrıca kullanılan yöntemler matematiksel olarak elde edilmiş, avantaj ve dezavantajlarını ortaya konulmuştur. Sonuçta doğrusal olmayan bu tip kontrol yöntemlerinin Lorenz kaotik sisteminin kontrol edebildiği gösterilmiş ardından avantaj ve dezavantajları sonuçlar bölümünde tartışılmış ve ileriye yönelik çalışmalar hakkında bilgiler verilmiştir.

Keywords

Kaotik sistem, geri beslemeli kontrol, yüksek kazanç kontrolü, yüksek frekans kontrolü, model öngörülü kontrol

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