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

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

References

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