Kontrol Teorisinde Sık Kullanılan Bazı Fonksiyonların Kesirli Dereceden Çeşitli Türevlerinin Farklı Yöntemlere Göre Hata Değerlendirilmesi

Abstract

Bu çalışma kesirli dereceden türev işlemlerinin farklı kontrol fonksiyonları ve farklı kesirli türev yöntemlerine göre bir analizi üzerinedir. Kontrol fonksiyonları olarak sıklıkla kullanılan birim basamak ve rampa fonksiyonları seçilmiştir. Kesirli dereceden türev hesaplaması için analitik yöntemlerin yanı sıra literatürde sıklıkla kullanılan Grünwald-Letnikov ve Riemann-Liouville yöntemleri tercih edilmiştir. Fonksiyonların farklı dereceden türevleri hesaplanarak analitik çözümle karşılaştırılmıştır. Elde edilen sonuçların hata değerlendirilmesi yapılmış ve ilgili eğrileri çizdirilmiştir.

Keywords

• Gama fonksiyonu
• kontrol teorisi
• kesirli dereceden türevli sistemler
• kesirli dereceden türev hesabı

Error Evaluation of Some Frequently Used Control Functions in Terms of Different Order Fractional Derivatives According to Several Calculation Methods

Abstract

This study is an analysis of the calculation of fractional order derivatives of some frequently used control functions according to the different calculation methods. A unit step and ramp functions are used as control functions which are often preferred to assess the system outputs. Besides analytical solutions, Grünwald-Letnikov and Riemann-Liouville methods are chosen as calculation procedures of fractional derivatives. Analytical solutions of functions at different orders are compared with different definitions methods for the same orders. Obtained results are analysed in terms of error values and relevant curves are plotted.

Keywords

• Gamma function
• control theory
• fractional order derivative systems
• fractional order derivative calculation

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