Ters Sarkaç Sistemi için Meta Sezgisel Algoritmalara Dayalı PID Denetleyici Ayarlama Yaklaşımı

Öz

Oransal integral türev kontrolörleri olarak da bilinen PID kontrolörleri, sistem çıkışlarını düzenlemek için sıklıkla kullanılır. PID parametre ayarlarının sistem performansı üzerinde önemli bir etkisi vardır. Bu parametrelerin belirlenmesinde kullanılan çeşitli yöntemler mevcut olup bu yöntemlerin dezavantajları bulunmaktadır. Bu olumsuzlukların üstesinden gelmek için meta sezgisel optimizasyon algoritmaları kullanılmıştır. Bu çalışmada ters sarkaç sisteminin doğrusallaştırılmış matematik modeli elde edilmiştir. Sistemin doğrusal modeline Ziegler-Nichols metodu uygulanarak kontrolcü parametreleri elde edilmiştir. Daha sonra ters sarkaç sisteminin PID kazanç parametreleri, parçacık sürüsü optimizasyonu (PSO), sinüs kosinüs optimizasyonu (SCA) ve gri kurt optimizasyonu (GWO) olmak üzere üç farklı meta sezgisel optimizasyon yöntemiyle ayarlanmıştır. Meta sezgisel optimizasyon algoritmalarıyla kontrol parametrelerinin ayarlanması sonucu PID kontrolcünün performansında önemli ölçüde artış meydana geldiği görülmüştür. Bu çalışmada PSO, SCA ve GWO yöntemlerinin uygulanması sonucu mutlak hata integrali uygunluk fonksiyonundan elde edilen sonuçlar karşılaştırılmıştır. PSO, SCA ve GWO metotlarının yakınsama grafikleri elde edilmiş olup GWO algoritmasının yakınsama hızı uygulanan diğer iki yönteme göre daha hızlı sonuç vermiştir.

Anahtar Kelimeler

• Ters sarkaç
• PID parametrelerinin ayarlanması
• Meta sezgisel optimizasyon
• Parçacık sürü optimizasyonu
• Sinüs kosinüs optimizasyon algoritması
• Gri kurt optimizasyon algoritması.

Metaheuristic Algorithms Based PID Controller Tuning Approach for Inverted Pendulum System

Abstract

Proportional, integral, derivative (PID) controllers, also known as proportional integral derivative controllers, are frequently used to regulate system outputs. PID parameter settings have a significant impact on system performance. There are various methods used to determine these parameters, and these methods have disadvantages. To overcome these drawbacks, metaheuristic optimization algorithms have been used. In this study, a linearized mathematical model of the inverted pendulum system was obtained. Controller parameters were obtained by applying the Ziegler-Nichols method to the linear model of the system. Then, the PID gain parameters of the inverted pendulum system were tuned by three different metaheuristic optimization methods which are particle swarm optimization (PSO), sine cosine optimization (SCA), and gray wolf optimization (GWO). It has been observed that the performance of the PID controller has increased significantly because of adjusting the control parameters with metaheuristic optimization algorithms. In this study, the results obtained from the integrated absolute error (IAE) fitness function as a result of the application of PSO, SCA and GWO methods were compared. Convergence graphs of PSO, SCA and GWO algorithms were obtained, and the convergence speed of the GWO algorithm was faster than the other two methods applied.

Keywords

• Inverted pendulum
• PID parameters tuning
• Metaheuristic
• Particle swarm optimization
• Sine cosine optimization algorithm
• Gray wolf optimization algorithm.

Kaynakça

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