A design template for globally stable nonlinear oscillators with multiple dynamics

Year 2024, Volume: 13 Issue: 4, 1192 - 1200, 15.10.2024

İsmail Öztürk

https://doi.org/10.28948/ngumuh.1458253

Abstract

In this study, a template is proposed for designing ordinary differential equation-based nonlinear oscillators. The template is a two-dimensional system with two control parameters and an energy function. By choosing the appropriate energy function, it is possible to obtain globally stable systems. These systems can be a gradient system, a Hamiltonian system, or a system with a stable limit cycle depending on the choice of control parameters. Hamiltonian and limit cycle cases can be used as a nonlinear oscillator for various applications. An example system is demonstrated by choosing a simple energy function and the obtained system is simulated to verify its dynamics. Hardware verification of the simulated system is performed with a field programmable gate array (FPGA) implementation.

Keywords

Nonlinear Oscillator, Gradient System, Hamiltonian System, Limit Cycle, FPGA

Çoklu dinamiklere sahip global kararlı lineer olmayan osilatörler için bir tasarım şablonu

Abstract

Bu çalışmada adi diferansiyel denklem tabanlı lineer olmayan osilatörlerin tasarımı için bir şablon önerilmektedir. Önerilen şablon iki adet kontrol parametresine ve bir adet enerji fonksiyonuna sahip iki boyutlu bir sistemdir. Uygun enerji fonksiyonu seçimi ile global olarak kararlı sistemler elde etmek mümkün olmaktadır. Bu sistemler farklı kontrol parametreleri için gradyan sistem, Hamilton sistemi veya kararlı bir limit çevrime sahip bir sistem olabilmektedir. Hamilton sistemi ve limit çevrim durumlarında sistem farklı uygulamalar için lineer olmayan osilatör olarak kullanılabilir. Basit bir enerji fonksiyonu seçimiyle örnek bir sistem elde edilip sistemin dinamikleri simülasyonlarla doğrulanmıştır. Simülasyonu yapılan sistemin donanımsal doğrulaması ise alanda programlanabilir kapı dizisi (FPGA) kullanılarak gerçekleştirilmiştir.

Keywords

Lineer Olmayan Osilatör, Gradyan Sistem, Hamilton Sistemi, Limit Çevrim, FPGA

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