KESİR DERECELİ TEMEL TRANSFER FONKSİYON YAPILARI İÇİN YAKLAŞIK ANALİTİK ZAMAN CEVABI MODELİ

Bilgisayar teknolojilerindeki gelişmeler zor ve karmaşık hesaplamalar içeren kesirli matematik alanına olan ilgiyi arttırmıştır. Özellikle, gerçek sistemleri modellemedeki başarısı nedeniyle kontrol sistemleri alanında çokça yararlanılmaktadır. Pek çok çalışma yapılmasına rağmen karmaşık ve zor matematiği nedeniyle literatürde hala çözümsüz durumlar bulunmaktadır. Kontrol sistemleri alanında kullanımında karşılaşılan en büyük zorluk analitik çözüm eksikliğidir. Bu eksikliklerden biri kesir dereceli bir transfer fonksiyon için analitik zaman cevabı hesaplamasıdır. Bu nedenle, bu çalışmada bazı temel kesir dereceli transfer fonksiyon yapıları için yaklaşık analitik zaman cevabı fonksiyonları yani yaklaşık ters Laplace dönüşümlerini elde edebileceğimiz bir çözüm önerisi sunulmuştur. Bu temel çözümler, gelecekte büyük ve karmaşık kesir dereceli transfer fonksiyonların çözümünde temel taşı olacaktır. Çalışmada kesir dereceli transfer fonksiyonların hesaplamalarındaki başarısı sebebiyle Grunwald-Letnikov (GL) nümerik hesaplama metodu kullanılmıştır. Ayrıca, eğri uydurma hesaplamalarında ise en küçük kareler metodu kullanılmıştır. Sonuçlar örnek hesaplamalar ile desteklenmiştir.

Anahtar Kelimeler:

Kesir dereceli transfer fonksiyon, Zaman cevapları, Ters Laplace dönüşümü, Grunwald-Letnikov, Eğri uydurma

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