PID Controller Design Based on Reference Model in Fractional Order Control Systems

Year 2017, Volume: 1 Special Issue, 52 - 58, 25.12.2017

Tufan Doğruer Ali Yüce Nusret Tan

Abstract

In
the modeling of physical systems, fractional order systems are known to perform
a more successful modelling than integer order systems. In this paper, PID
controller design was performed according to a reference model for a fractional
order system. The main purpose of the study is to obtain PID controller
parameters according to a desired time response in the output signal. It is
aimed to obtain the optimum PID parameters by minimizing the error between the
reference model and controlled system. Integral performance criteria were used
to minimize the error. The reference model is a transfer function of a second
order system. This transfer function has two parameters that
need to be set. These parameters are natural frequency (ω_n) and damping ratio (ζ). By
setting these two parameters, desired unit step response curve can be obtained. PID
controller parameters were obtained by optimization method. Optimization
describes problem-solving processes in a systematic way by minimizing or
maximizing a real function and placing values in the function. PID
controller parameters are obtained by optimizing according to model transfer
functions. By applying the calculated PID controller
parameters to the fractional order control system, the unit step responses are
obtained. The success of the optimization method can be
seen from the graphs obtained and from the given tables.

Keywords

PID Controller, Optimization, Fractional order systems

Kesir Dereceli Kontrol Sistemlerinde Referans Modele Dayalı PID Kontrolör Tasarımı

Abstract

Fiziksel
sistemlerin modellenmesinde, kesir dereceli sistemler tamsayı dereceli
sistemlere göre daha başarılı bir modelleme gerçekleştirebilmektedir.
Çalışmada, kesir dereceli bir sistem için referans bir modele göre PID
kontrolör tasarımı gerçekleştirilmiştir. Çalışmanın temel amacı, çıkış
sinyalinde istenen bir zaman cevabına göre PID kontrolör parametrelerini elde
etmektir. Referans model ile denetlenen sistem arasındaki hata minimize
edilerek optimum PID parametrelerinin elde edilmesi amaçlanmıştır. Hatayı
minimize etmek için sıklıkla integral performans kriterleri kullanılır.
Referans olarak alınan sistem ikinci mertebeden bir sistemin transfer
fonksiyonudur. Bu transfer fonksiyonu ayarlanması gereken iki parametreye
sahiptir. Bu parametreler doğal frekans (ω_n)
ve sönüm oranıdır (ζ). Bu iki parametre ayarlanarak istenilen birim basamak
cevap eğrisi elde edilebilir. PID kontrolör parametrelerinin elde edilmesi
optimizasyon yöntemiyle gerçekleştirilmiştir. Optimizasyon bir gerçel
fonksiyonu minimize ya da maksimize etmek amacı ile fonksiyona değerler
yerleştirerek sistematik bir şekilde problem çözüm işlemlerini tanımlar. Bu
model transfer fonksiyonlarına göre optimizasyon işlemi gerçekleştirilerek, PID
kontrolör parametreleri elde edilebilir. Bulunan PID kontrolör parametrelerinin
kesir dereceli kontrol sistemine uygulanmasıyla, denetlenen sistem çıkışında
birim basamak cevapları elde edilir. Optimizasyon yönteminin başarısı elde
edilen grafiklerden ve oluşturulan tablolardan görülmektedir.

Keywords

PID Kontrolör, Optimizasyon, Kesir dereceli sistemler

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