Bulanık Bilişsel Harita Tabanlı PID Kontrolör Tasarımı

Öz

Doğrusal oransal-integral-türev (PID) denetleyiciler sahip oldukları basit yapıları ve etkin performansları nedeniyle endüstriyel uygulamalarda en yaygın biçimde kullanılan denetleyicilerdir. Fakat, endüstriyel sistemlerin doğrusal olmayan karakteristikleri ya da sistem dereceleri arttıkça bu denetleyicilerin performansları düşmektedir. Bu nedenle, doğrusal PID denetleyicilerin performansını iyileştirmek için literatürde çeşitli doğrusal olmayan PID denetleyici modelleri önerilmiştir. Bu çalışmada bulanık bilişsel harita (BBH) tabanlı yeni bir doğrusal olmayan PID denetleyici tasarım yaklaşımı önerilmiştir. İki farklı BBH tabanlı PID denetleyici modeli sunulmuştur. İlk denetleyici modeli, hata, hatanın türevi ve hatanın integralinden oluşan üç girişli klasik paralel PID yapısında bir modeldir. İkinci model ise hata ve hatanın türevi olmak üzere iki girişten oluşan klasik bulanık PID yapısında bir kontrolör modelidir. Önerilen yöntemde, ilk olarak her bir giriş sinyali üyelik fonksiyonları kullanılarak bulanıklaştırılmaktadır. Daha sonra girişler ile çıkış arasındaki nedensel ilişkiler ağırlık parametreleri kullanılarak belirlenmektedir. Son olarak, bir aktivasyon fonksiyonu kullanılarak BBH çıkarımı gerçekleştirilmektedir. Bu nedenle, önerilen doğrusal olmayan PID modellerinde sırasıyla dört ve altı ayar parametresi bulunmaktadır. Önerilen BBH tabanlı PID denetleyici modellerinin performanslarını değerlendirmek için dördüncü dereceden doğrusal bir sistem üzerinde benzetim çalışmaları gerçekleştirilmiştir. Bu modellerin performanları, klasik PID denetleyici ve bulanık PID denetleyici performansları ile karşılaştırılmıştır. Karşılaştırma sonuçları, önerilen BBH tabanlı PID denetleyici modellerinin klasik PID ve bulanık PID denetleyicilerden daha üstün bir performans sağladığını göstermektedir.

Anahtar Kelimeler

• Bulanık bilişsel harita
• PID
• kontrol
• üyelik fonksiyonu

Fuzzy Cognitive Map Based PID Controller Design

Abstract

Linear proportional-integral-derivative (PID) controllers are the most widely used process controllers in industrial applications due to their simple structures and effective performances. However, performances of these controllers reduce as the nonlinear characteristics or the system orders of the industrial processes increases. Therefore, various nonlinear PID controller models are proposed in literature to improve the control performances of linear PID controllers. In this study, a new nonlinear PID controller design approach is proposed based on the fuzzy cognitive map (FCM) method. Two different FCM based PID controller models are introduced. The first controller model is in the conventional parallel PID structure with three inputs as the error, the derivative of the error, and the integral of the error. On the other hand, the second controller model is in the conventional fuzzy PID form with two inputs as the error and the derivative of the error. In the proposed method, each input signal is firstly fuzzified by using a membership function. Then, causal relationships between inputs and the output are determined by using weight parameters. Finally, the FCM inference is performed by using an activation function. Therefore, the proposed nonlinear PID controllers have four and six tuning parameters, respectively. Simulation studies are performed on a fourth order linear system in order to evaluate the performance of the proposed FCM based PID controller models. The performances of these controller models are compared with a conventional PID controller and a fuzzy PID controller. The comparison results show that the proposed FCM based PID controller models outperform the conventional PID and fuzzy PID controllers.

Keywords

• Fuzzy cognitive map
• PID
• Control
• Membership function

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