Arabalı Ters Sarkaç Sisteminin Dengelenmesi için Farklı Oransal-Türevsel Denetim Tabanlı Bulanık Üyelik Fonksiyonlarının Başarımlarının İncelenmesi

Yıl 2022, Cilt: 38 Sayı: 3, 483 - 499, 30.12.2022

Ahmet Gani , Hasan Rıza Özçalık

Öz

Bu çalışmada, arabalı bir ters sarkaç (TS) sisteminin oransal-türevsel denetim tabanlı farklı üyelik fonksiyonlu (MF) bulanık denetleyiciler kullanılarak dengelenmesi amaçlanmıştır. Bu amaçla araba yatay konumda (çizgisel konum) arzu edilen yörüngeyi takip ederken, sarkacın da dikey konumda (açısal konum) dengede kalması sağlanmıştır. Tasarlanan denetim sistemine ait benzetim çalışmaları Matlab/Simulink ortamında yapılmış olup sarkacın dikey ve arabanın yatay konum denetimi için elde edilen başarım değerleri ayrı ayrı verilmiştir. Benzetim çalışmasından edilen denetim başarım değerleri incelendiğinde sarkacın dikey konumu için yükselme zamanı, yerleşme zamanı ve aşım bakımından üçgen bulanık üyelik fonksiyonunun gauss bulanık üyelik fonksiyonuna göre sırasıyla %8, %4.35 ve %7.7 oranlarında iyileştirme yaptığı görülmüştür. Benzer şekilde arabanın yatay konumu için de yükselme zamanı, yerleşme zamanı ve aşım bakımından üçgen bulanık üyelik fonksiyonunun (ÜF) gauss bulanık ÜF’ye göre sırasıyla %3.8, %3 ve %30 oranlarında daha iyi denetim başarımına sahip olduğu görülmüştür. Sarkacın dikey konum ve arabanın yatay konum denetimi için tüm denetim başarım değerleri analiz edildiğinde üçgen bulanık ÜF’nin gauss bulanık ÜF’ye göre daha tatmin edici sonuçlar verdiği açıkça görülmüştür.

Anahtar Kelimeler

Arabalı Ters Sarkaç, Oransal-Türevsel Denetim, Farklı Bulanık üyelik fonksiyonları

The Investigation of Performances of Different Proportional-Derivative Control Based Fuzzy Membership Functions in Balancing the Inverted Pendulum (IP) System on Cart

Öz

The present study aims to balance an inverted pendulum (IP) system on cart using fuzzy controllers with different membership functions (MFs) based on proportional-derivative control. To this end, the cart was designed to track an intended trajectory in a horizontal (linear) position, while the IP was balanced in a vertical (angular) position. The designed controller system was simulated in Matlab/Simulink, and performance rates were measured for the IP’s vertical position and the cart’s horizontal position. The obtained simulation results demonstrated that triangular fuzzy membership function (MF) improved rise time, settling time and overshoot for the IP’s vertical position by 8%, 4.35% and 7.7%, respectively, compared to gaussian fuzzy MF. Similarly, for the cart’s horizontal position, triangular fuzzy MF improved rise time, settling time and overshoot by 3.8%, 3 and 30%, respectively, compared to gaussian fuzzy MF. When all performance rates are analyzed in terms of the IP’s vertical position and the cart’s horizontal position, it was found that triangular fuzzy MF displayed a more satisfactory performance compared to Gaussian fuzzy MF.

Anahtar Kelimeler

Inverted Pendulum on Cart, Different Fuzzy Membership Functions, Proportional- Derivative Control

Kaynakça

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