Linear Quadratic Optimal Control of an Inverted Pendulum on a Cart using Artificial Bee Colony Algorithm: An Experimental Study

Öz

This study presents a Linear Quadratic Optimal (LQR) controller design for an inverted pendulum on a cart using the Artificial Bee Colony (ABC) algorithm. Main design parameters of the linear quadratic regulator are the weighting matrices. Generally, selecting weighting matrices is managed by trial and error since there exists no apparent connection between these weights and time domain requirements such as settling time, steady state error, and overshoot percentage. In this study after deriving the mathematical models of the inverted pendulum on a cart and the DC motor, an LQR controller is designed using the ABC algorithm to determine weighting matrices to overcome LQR design difficulties. The comparison and experimental results justify that the ABC algorithm is a very efficient way to determine LQR weighting matrices in comparison with a method in literature. 

Anahtar Kelimeler

• Artificial bee colony algorithm,Linear quadratic regulator,Inverted pendulum

Yapay Arı Kolonisi Algoritması ile Bir Arabalı Ters Sarkacın Lineer Kuadratik Kontrolü: Deneysel Bir Çalışma

Öz

Bu çalışmada, Lineer Kuadratik Regülatör (LQR) ile bir ters sarkacın kontrolü için, Yapay Arı Kolonisi (ABC) optimizasyon algoritmasına dayalı bir metot önerilmiştir. LQR’ın temel tasarım parametreleri ağırlık matrisleridir. Ağırlık matrislerinin değerleri ile yüzde aşımı, yerleşme zamanı ve kararlı hal hatası gibi zaman uzayı performans kriterleri arasında doğrudan bir ilişki olmadığı için bu matrislerin seçimi genellikle deneme yanılma yöntemiyle gerçekleştirilmektedir. Bu çalışmada arabalı ters sarkaç ve bu mekanizmayı hareket ettiren DC motorun matematiksel modellerinin elde edilmesinin ardından sürü zekası temelli bir optimizasyon algoritması olan ABC algoritması kullanılarak bir LQR kontrolör tasarlanmıştır. Karşılaştırma ve deney sonuçları, ABC algoritmasının literatürde önerilen bir yöntem ile karşılaştırıldığında ağırlık matrislerinin belirlenmesinde daha etkin bir yol olduğunu göstermiştir.

Anahtar Kelimeler

• Yapay arı kolonisi algoritması,Lineer kuadratik regülatör,Ters sarkaç

Kaynakça

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