3 Serbestlik Dereceli Sistemin Yapay Zekâ Tabanlı LQR ve PID Kontrolcü Tasarımı

Year 2024, Volume: 6 Issue: 3

Engin Hasan Çopur , Hasan Hüseyin Bilgiç , Tarık Ünler

Abstract

Bu çalışmada 3 serbestlik dereceli eksik eyleyicili bir sistemin konum kontrolü gerçekleştirilmiştir. Geliştirilen yaklaşım ikili sarkaç tipi tepe vincinin üzerinde denenmiştir. İlk olarak sistemin matematiksel modeli doğrusal olmayan dinamikler dikkate alınarak Euler-Lagrange metodu ile elde edilmiştir. Benzetim çalışmalarında PID ve LQR kontrolcüleri kullanıldığından doğrusal olmayan model sistemin denge noktası etrafında doğrusallaştırılmıştır. Elde edilen doğrusal model kullanılarak PID ve LQR kontrolcülerinin parametreleri Yapay Arı Kolonisi Algoritması ile ayarlanmıştır. Optimizasyon sürecinde sistemin üç serbestliğindeki hatanın minimize edilmesi için geleneksel uygunluk fonksiyonlarından Zamansal mutlak hataların toplamı (Integral Time Absulate Error) fonksiyonu seçilmiştir. Ayrıca arabanın hassas hareketini sağlamak için amaç fonksiyonu birim basamak cevaplarını içerecek şekilde iyileştirilmiştir. Kontrolcü performansları benzetim ortamında yapılan çalışmalar ile denenmiştir. Sonuçlar tablo ve grafikler halinde sunulmuştur. Önerilen yaklaşım çok serbestlik dereceli ve eksik eyleyici sistemlerin kontrolünde kullanılabilir.

Keywords

Tepe Vinci, Yapay Zeka, LQR, PID, Yapay Arı Kolonisi Algoritması

Artificial Intelligence based LQR and PID Controller Design of 3 Degree of Freedom System

Abstract

In this study, the position control of a 3 DoF underactuated system is carried out. The developed approach is tested on a double pendulum overhead crane. Considering the nonlinear dynamics of the system, its mathematical model is first obtained by Euler-Lagrange model. Then, since PID and LQR controllers are used in the simulations, the nonlinear model is linearized around the equilibrium point of the system. Using the linear model, the parameters of LQR and PID controllers are tuned by Artificial Bee Colony Algorithm. In the optimization process, the Integral Time Absolute Error function is chosen from traditional fitness functions to minimize the error in each single-degree-of-freedom joint of the system. Additionally, to ensure the precise movement of the car, the objective function is improved in a way to include unit step response characteristics. The control performance is evaluated in the simulations. The results are presented in tables and graphs. The proposed approach can be used to control multi-degree of freedom underactuated systems.

Keywords

Gantry Crane, Artificial Intelligence, LQR, PID, Artificial Bee Colony Algorithm

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