Fractional Order PI Control Design in V-domain According to Minimum Angle Pole Placement Method and Investigation of Robust Control Performance

Abstract

Since fractional dynamic system models can represent real-life systems more accurately, interest in fractional order system models and fraction order control has increased. This study presents fractional order PI controller design according to minimum angle pole placement method in v-field that was used for stability analysis of fraction order system models, and the effects of different target minimum angle values on the robust control performance of these designs are considered. For this purpose, fractional order PI controller designs were carried out for selected three different target angle values according to minimum angle pole placement in v-domain. Here, genetic algorithm is used to place the minimum angle system poles to the specified target angles and thus fractional order PI controller coefficients were optimized. In this study, two illustrative design examples are demonstrated, and fractional order PI control system designs, which place minimum angle system poles to selected target points in the stability region, are obtained in these examples. The robust stability performance of the PI controller designs obtained for different target angle configurations were examined by changing gain coefficient of plant functions. According to findings obtained, the target angle regions that provide robust control performance, have been investigated.

Keywords

• Fractional order PI control
• roboust control performance
• v-field design
• iso-damping property

V-alanında Minimum Açılı Kutup Yerleşimi Yöntemine Göre Kesir Dereceli PI Denetçi Tasarımı ve Dayanıklı Kontrol Performansının Bir İncelenmesi

Öz

Kesir dereceli dinamik sistem modelleri gerçek hayatta kullanılan sistemleri daha doğru bir şekilde temsil edilebilmesi nedeni ile kesir dereceli sistem modellerine ve kesir dereceli kontrole olan ilgi artırmıştır. Bu çalışma kesir dereceli sistem modellerinin kararlılık analizi için kullanılan v-alanı içerisinde, minimum açılı kutup yerleştirme yöntemine göre kesir dereceli PI denetçi tasarımlarını sunmaktadır ve farklı hedef açı değerlerinin bu tasarımların dayanıklı kontrol performansına etkileri incelenmektedir. Bu amaçla, kesir dereceli PI denetçi tasarımları seçilen üç farklı hedef açı değeri için v-alanında kutup yerleştirme yöntemine göre gerçekleştirilmiştir Burada, minimum açılı sistem kutuplarının belirlenmiş hedef açılara yerleştirilmesi için genetik algoritma kullanılmış ve böylece kesir dereceli PI denetçi katsayıları optimize edilmiştir. Bu çalışmada iki örnek uygulama gösterilmekte ve bu örnek uygulamalarda kararlılık bölgesi içerisinde seçilen hedef noktalara minimum açılı sistem kutuplarının yerleştiren kesir dereceli PI denetçi tasarımları elde edilmiştir. Elde edilen PI denetçi tasarımları için plant fonksiyonlarının kazanç katsayısı değiştirilerek farklı hedef açı konfigürasyonları için elde edilen kontrol sistemlerinin dayanıklı kontrol performansları incelenmiştir. Elde edilen bulgulara göre dayanıklı kontrol performansı sağlayan hedef açı bölgeleri araştırılmıştır.

Anahtar Kelimeler

• Kesir dereceli PI denetçi
• dayanıklı kontrol performansı
• v-alanı tasarımı
• iso-damping özelliği

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