REVISITING BODE’S IDEAL LOOPS: INTEGRAL SQUARE ERROR OPTIMALITY OF BODE’S IDEAL LOOPS AND BODE’S IDEAL LOOP INVERSE CONTROLLER DESIGN

Yıl 2025, Cilt: 13 Sayı: 1, 202 - 220, 20.03.2025

Barış Baykant Alagöz , Furkan Nur Deniz , Cemal Keleş

https://doi.org/10.21923/jesd.1452157

Öz

Bode’s ideal loop models have been utilized in control system designs to obtain performance robustness for the Direct Current (DC) gain variations. However, effects of crossover frequency and fractional order on control optimality of Bode's ideal loop reference models have not been sufficiently discussed, and it may raise a question of whether a control system design based on Bode’s ideal loop reference model is optimal. In this regard, this study revisits Bode’s ideal loops to investigate Integral Square Error (ISE) optimality of Bode’s ideal loops. For this purpose, the ISE optimality of Bode’s ideal loop is theoretically investigated by using Parseval’s theorem, and an ISE optimality condition is suggested in terms of crossover frequency and fractional order. Then, a generic controller family, which achieves an exact matching with the characteristics of the ISE optimal Bode’s ideal loop, was implemented for inverse fractional-order control of a class of minimum phase fractional order plant models. The authors present a numerical experiment on an ISE optimal Bode’s ideal loop inverse (OBILI) controller, and the ISE optimality and performance robustness of the designed control system were investigated for closed-loop control of a heat furnace system model via Monte Carlo simulations.

Anahtar Kelimeler

Optimality, Robustness, Uncertain Systems, Control Design, Fractional Order Control, Bode’s Ideal Loop

BODE İDEAL DÖNGÜLERİNE YENİDEN BAKIŞ: BODE İDEAL DÖNGÜLERİNİN İNTEGRAL KARESEL HATA OPTİMALLİĞİ VE BODE İDEAL DÖNGÜ TERS KONTROLÖR TASARIMI

Öz

Bode ideal döngü modelleri, Doğru Akım (DA) kazanç değişimleri için performans dayanıklılığı elde etmek amacıyla kontrol sistemi tasarımlarında kullanılmıştır. Bununla birlikte, geçiş frekansı ve kesir derecenin Bode ideal döngü referans modellerinin kontrol optimalliği üzerindeki etkileri yeterince tartışılmamıştır ve bu, Bode ideal döngü referans modeline dayanan bir kontrol sistemi tasarımının optimal olup olmadığı sorusunu gündeme getirebilir. Bu bağlamda, bu çalışma, Bode ideal döngülerinin İntegral Karesel Hata (ISE) optimalliğini araştırmak için Bode ideal döngülerini yeniden ele almaktadır. Bu amaçla Bode ideal döngünün ISE optimalliği Parseval teoremi kullanılarak teorik olarak araştırılmış ve geçiş frekansı ve kesir derece açısından bir ISE optimallik koşulu önerilmiştir. Daha sonra, ISE optimal Bode ideal döngünün karakteristikleri ile tam bir eşleşme sağlayan bir genelleştirilmiş kontrolör ailesi, minimum faz kesir dereceli sistem modellerinin bir sınıfının ters kesir dereceli kontrolü için uygulanmıştır. Yazarlar, ISE optimal Bode ideal döngü ters (OBILI) kontrolörü üzerinde nümerik bir deney sunmuştur ve tasarlanan kontrol sisteminin ISE optimalliği ve performans dayanıklılığı, Monte Carlo simülasyonuyla bir ısı fırını sisteminin kapalı döngü kontrolü için araştırılmıştır.

Anahtar Kelimeler

Optimallik, Dayanıklılık, Belirsiz Sistemler, Kontrol Tasarımı, Kesirli Dereceli Kontrol, Bode’nin İdeal Döngüsü

Kaynakça

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