Bulanık Bilişsel Harita Tabanlı PD Kontrolörler Kullanılarak Ters Sarkaç Sisteminin Stabilizasyonu

Öz

Yumuşak hesaplama yöntemleri doğrusal olmayan sistemlerin modellenmesi ve kontrolünde sıklıkla kullanılan yöntemlerdir. Buna karşın, yumuşak hesaplama yöntemlerinden biri olan bulanık bilişsel harita yöntemi, kontrol uygulamalarında ana kontrolör olarak nadiren kullanılmaktadır. Bu çalışmada bulanık bilişsel harita tabanlı PD kontrolör yapısı önerilmiş ve bu yöntem doğrusal olmayan, kararsız ve eksik tahrikli bir sistem olan ters sarkaç sisteminin stabilizasyonu için kullanılmıştır. Önerilen kontrolör hata ve hatanın değişimi olmak üzere iki adet giriş değişkenine sahiptir. Önerilen PD kontrolör yapısında, kesin değerlere sahip girişler bulanık bilişsel harita hesaplama sürecinde değerlendirilebilmek için bulanıklaştırılmaktadır. Ardından bulanıklaştırılmış bu girişler ile kontrolör çıkışı arasındaki nedensel ilişkiler ağırlıklandırma parametreleri kullanılarak tanımlanmaktadır. Son olarak ise bir aktivasyon fonksiyonu kullanarak sisteme uygulanacak kesin çıkış değeri elde edilmektedir. Bulanıklaştırma işlemi için kullanılan üyelik fonksiyonlarının yapıları ve ayrıca aktivasyon fonksiyonun yapısı, önerilen bulanık bilişsel harita tabanlı PD kontrolörün doğrusal olmayan karakteristiğini belirlemektedir. Önerilen kontrolör bir çıkış kazancı ve iki ağırlık parametresi olmak üzere üç adet ayar parametresine sahiptir. Önerilen bulanık bilişsel harita tabanlı PD kontrolörün etkinliğini ve dayanıklılığını göstermek için ters sarkaç sistemi üzerinden benzetim çalışmaları gerçekleştirilmiştir. Ayrıca önerilen PD kontrolörün performansı geleneksel yapıdaki PD kontrolör performansı ile karşılaştırılmıştır. Tüm kontrolör parametreleri genetik algoritma kullanılarak belirlenmiştir. Karşılaştırma sonuçları göstermiştir ki önerilen bilişsel harita tabanlı PD kontrolör geleneksel PD kontrolörden daha iyi bir kontrol performans göstermektedir.

Anahtar Kelimeler

• Bulanık bilişsel harita
• Üyelik fonksiyonu
• Doğrusal olmayan sistem
• Ters sarkaç
• PD kontrol
• Stabilizasyon

Stabilization of Inverted Pendulum System Using Fuzzy Cognitive Map Based PD Controllers

Abstract

Soft computing techniques are frequently used in modeling and control applications of nonlinear systems. However, the fuzzy cognitive map method, which is one of the soft computing techniques, is rarely used in control applications as a main controller. In this study, a fuzzy cognitive map based PD controller structure is introduced and used for the stabilization of an inverted pendulum system which is a nonlinear, unstable, and under-actuated system. The proposed controller has two inputs which are the error and the change of error. In the proposed PD controller structure, the crisp input values are fuzzified to be handled in a fuzzy cognitive map process. Then, causal relationships between fuzzified inputs and a control output are defined by using weight parameters. Finally, the crisp control output value which will be applied to the system is obtained by using an activation function. The types of membership functions used for the fuzzification process and the activation function determine the nonlinear characteristics of the proposed fuzzy cognitive map based PD controller. The proposed controller has three tuning parameters which are one output gain and two weight parameters. To show the effectiveness and robustness of the proposed fuzzy cognitive map based PD controller, simulation studies are performed on an inverted pendulum system. Additionally, the performance of the proposed controller is compared with a PD controller. All controller parameters are determined by using a genetic algorithm. Comparison results indicate that the proposed fuzzy cognitive map based PD controller shows better control performance than the classical PD controller.

Keywords

• Fuzzy cognitive map
• Membership function
• Nonlinear system
• Inverted pendulum
• PD control
• Stabilization

Kaynakça

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