Devre Teorisinden Esinlenerek Dinamik Sistemlerin Niteliksel Davranışı Üzerine Bir Paradigma

Year 2025, Volume: 30 Issue: 2, 699 - 707, 31.08.2025

Muzaffer Ateş , Muhammet Ateş

https://doi.org/10.53433/yyufbed.1617145

Abstract

Bu makalede, elektriksel bir modele sahip sıvı mekanik tank sisteminin nitel analizini ele alıyoruz. Prototip aşamasında, bu tür modeller ilk nükleer reaktörlerin inşa süreci gibi daha esnektir. Bu dinamik sistemin matematiksel modeli doğrusal olmayan ve zamanla değişendir. Burada, herhangi bir matematiksel yaklaşım olmaksızın benzersiz sonuçlar bulmak için fiziksel ilkeler ve mühendislik özellikleri kullanılacaktır. Sistemin enerji fonksiyonu sezgisel fiziksel ilkelerle oluşturulmuştur. Sistem ayrıca geri bildirim kontrol yasalarıyla ve onlarsız olarak tartışılacaktır. Sistemin denge noktasının küresel asimptotik kontrol edilebilirliği belirlenecektir. Literatür bize seviye kontrolünün altıya kadar birkaç çoklu tankla çalıştığını göstermektedir. Bunları tanklarla farklı bir teorik bakış açısıyla tank olarak genelleştiriyoruz. Hazır sistem ve aday Lyapunov fonksiyonu burada kullanılmayacak; çalışma bunları inşa ederek yürütülecektir. Kontrol mekanizmasının etkinliği hem teorik analiz hem de simülasyonla belirlenecektir. Önerilen algoritmaya göre, tanklardaki sıvı seviyelerinin ölçümü sistemin herhangi bir yerinde, topluca veya ayrı ayrı volt cinsinden yapılabilir. Algoritma açıktır, çok zaman alıcı değildir ve çözüm maliyeti pahalı değildir. Ayrıca teorik tahminlerimizi doğrulayan bazı simülasyonlar da sunulmuştur.

Keywords

Kararlılık , Lyapunov , Pasiflik , PD kontrol , Sıvı seviye kontrolü

A Paradigm on the Qualitative Behavior of Dynamical Systems Inspired by Circuit Theory

Abstract

In this paper, we consider the qualitative analysis of a liquid mechanical tank system with an electrical model. In the prototype phase, such models are more flexible like the construction process of the first nuclear reactors. The mathematical model of this dynamic system is nonlinear and time-varying. Here, physical principles and engineering specifications will be used to find unique results without any mathematical approximation. The energy function of the system is constructed with intuitive physical principles. The system also will be discussed with and without feedback control laws. Global asymptotic controllability of the equilibrium point of the system will be determined. The literature presents us, the level control works with a few multi-tanks up to six. We generalize those with tanks from a different theoretical perspective. The readymade system and candidate Lyapunov function will not be used here; the study will be conducted by constructing them. The effectiveness of the control mechanism will be determined by both theoretical analysis and simulation. According to the proposed algorithm, the measurement of liquid levels in tanks can be made in volts anywhere in the system, collectively or individually. The algorithm is clear, not large time-consuming and the solution cost is not expensive. Some simulations are also presented that validate our theoretical predictions.

Keywords

Liquid level control , Lyapunov , Passivity , PD control , Stability

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