Ant colony based optimal PD control of an underactuated system: An experimental study

Öz

The inverted pendulum system (IP) is an underactuated, non-linear, unstable and complex-to-control system. In this study, the inverted pendulum system is modeled by taking into account the friction effects. A parallel PD controller, which controls the car position and pendulum angle, whose coefficients are adjusted with the help of the ant colony algorithm, is proposed for the control of the system. Depending on the ant colony algorithm, the ideal ratio and derivative coefficients were obtained with the help of the integral of the square of the error (ISE), the integral of the absolute value of the error (IAE), the integral of the absolute value of the error over time (ITAE) and the mean squared error (MSE) objective functions. The performance of the system has been compared with the classical PD controller by simulation and experimentally with the help of the coefficients found for the position and angle controllers. According to the results obtained, the rise time, settling time and overshoot values were reduced. In step reference, the response performance of the optimized parallel PD controllers is significantly increased.

Anahtar Kelimeler

• ant colony
• pd control
• inverted pendulum
• underactuated

Eksik tahrikli bir sistemin karınca kolonisi tabanlı optimal PD kontrolü: Deneysel bir uygulama

Öz

Ters sarkaç sistemi (IP) eksik tahrikli, doğrusal olmayan, kararsız ve kontrolü karmaşık bir sistemdir. Bu çalışmada ters sarkaç sistemi, sürtünme etkileri de dikkate alınarak modellenmiştir. Sistemin kontrolü için katsayıları karınca kolonisi algoritması yardımıyla ayarlanan araba konumunu ve sarkaç açısını kontrol eden paralel PD kontrolcüsü önerilmiştir. Karınca kolonisi algoritmasına bağlı olarak ideal oran ve türev katsayıları hatanın karesinin integrali (ISE), hatanın mutlak değerinin integrali (IAE), zamana bağlı olarak hatanın mutlak değerinin integrali (ITAE) ve ortalama karesel hata (MSE) amaç fonksiyonları yardımıyla elde edilmiştir. Sistemin performansı, konum ve açı kontrolcüleri için bulunan katsayılar yardımıyla klasik PD kontrolcü ile karşılaştırmalı bir şekilde benzetim ve deneysel olarak incelenmiştir. Elde edilen sonuçlara göre, yükselme zamanı, oturma zamanı ve aşma değerleri azaltılmıştır. Adım referansta, optimizasyonları sağlanan paralel PD kontrolcülerin cevap performansı önemli derecede arttırılmıştır.

Anahtar Kelimeler

• karınca koloni
• pd kontrol
• ters sarkaç
• eksik tahrikli

Kaynakça

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