Ayrık zamanlı PI, PID ve PIR kontrolörler ile baskın kutup bölgesi atama

Abstract

Bu çalışmada, kapalı çevrim sistemin zaman özelliklerinin istenen aralıkta kalması için baskın kutup bölgesi atama yöntemiyle ayrık zamanlı PI, PID ve PIR kontrolörlerin tasarlanması amaçlanmıştır. Öncelikle, kapalı çevrim sistemin baskın ve baskın olmayan kutuplarının konumlanmaları istenen bölgeler için sınır fonksiyonlarının belirlenmesi anlatılmıştır. Burada, sınır fonksiyonları için, baskın kutupların konumlanması istenen bölge ayrık zaman düzleminde sabit yarıçaplı iki çember ve sabit bir sönüm oranı eğrisi, kalan kutupların konumlanması istenen bölge ise sabit yarıçaplı bir çember kullanılır. Daha sonra, baskın kutup bölgesi atama probleminin çözüm yöntemi ayrık PI kontrolör için verilmiştir. Önerilen yöntem, kontrolörün bir parametresini sabitleyerek (𝐾𝑝 = 𝑘𝑝 ∗ ) ayrık PID ve PIR kontrolörler için genişletilmiştir. PIR kontrolörde ek olarak gecikme parametresi ℎ’nin pozitif bir tamsayı olarak seçilmesi ile tasarıma başlanır. Önerilen yöntem, iki sistem üzerinden ayrık PI, PID ve PIR kontrolörler için anlatılmıştır.

Keywords

• Kutup atama
• Baskın kutup bölgesi
• PI
• PID
• PIR
• Ayrık zaman düzlemi

Dominant pole region assignment with discrete time PI, PID and PIR controllers

Abstract

In this study, it is aimed to design discrete time PI, PID and PIR controllers with the dominant pole region assignment method in order to have time domain characteristics of the closed loop system in the desired interval. First of all, determination of the boundary functions for the regions where the dominant and non-dominant poles of the closedloop system are desired to be located are explained. Here, for the boundary functions, the region where the dominant poles are desired to be located are two circles of constant radius and a constant damping ratio curve in the discrete time domain, and the region where the remaining poles are desired to be located is a circle of constant radius. Then, solution method of dominant pole region assignment problem is given for discrete PI controller. The proposed method is extended for discrete PID and PIR controllers by fixing a parameter of the controller (𝐾𝑝 = 𝑘𝑝 ∗ ). In addition, the design starts with selecting the delay parameter ℎ as a positive integer in the PIR controller. The proposed method is demonstrated for discrete PI, PID and PIR controllers via two systems.

Keywords

• Pole assignment
• Dominant pole region
• PI
• PID
• PIR
• Discrete time domain

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