Analytical Design of PI Controllers for Second Order plus Time Delay Systems

Year 2019, Cilt:7 Sayı:2 (2019) (Özel Sayı), 27 - 37, 30.03.2019

Bilal Şenol

https://doi.org/10.29130/dubited.474280

Abstract

Analytical
design scheme of a Proportional Integral controllers for the stability and
performance of second order plus time delay systems is presented in this paper.
The method proposed in the study achieves general computation equations for
mentioned systems. Inspired from the Bode’s ideal transfer function
characteristics, gain crossover frequency and phase margin specifications are
considered for the system. Then, these specifications are used to obtain the
parameters of the controller. Analytically derived formulas by the proposed
method are tested with existing plants in the literature and the results are
illustrated graphically. It is shown that the tuning method satisfies desired gain
crossover frequency and phase margin specifications.

Keywords

Second Order Plus Time Delay Plant, PI Controller, Bode’s ideal loop

İkinci Derece Zaman Gecikmeli Sistemler için PI Denetleyicilerin Analitik Tasarımı

Abstract

Bu
çalışmada ikinci dereceden zaman gecikmeli sistemlerin kararlılığı ve
performansı için oransal integral denetleyicilerin analitik tasarımı
verilmiştir. Çalışmada önerilen yöntem söz konusu sistemler için
genelleştirilmiş hesaplama eşitliklerini elde etmektedir. Bode’nin ideal
transfer fonksiyonunun karakteristiklerinden esinlenerek, kazanç kesim frekansı
ve faz payı şartları göz önüne alınmıştır. Daha sonra, bu şartlar denetleyicinin
prametrelerini elde etmek için kullanılmıştır. Önerilen yöntemle analitik olan
türetilen formüller literatürde var olan sistemler üzerinde test edilmiş ve
sonuçlar grafiksel olarak sergilenmiştir. Parametre ayarlama yönteminin istenen
kazanç kesim frekansı ve faz payı şartlarını sağladığı gösterilmiştir.

Keywords

İkinci Derece Zaman Gecikmeli Sistem, Oransal Integral Denetleyici, Bode’nin İdeal Çevrim

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