Fractional Order PID Controller Design Using Reference Model on Inverted Pendulum System

Year 2023, Volume: 15 Issue: 2, 804 - 819, 14.07.2023

Mehmet Serhat Can , Emrah Sürücü

https://doi.org/10.29137/umagd.1298311

Abstract

The proportional Integral Derivative (PID) controller has three basic parameters: Proportional gain (Kp), Integral gain (Ki) and Derivative gain (Kd). In a conventional PID controller, integral and derivative operators are integer order. The researchers proposed a fractional order PID (PIλDµ) controller by using the fractional integral and derivative operators instead of the integer order integral and derivative operators in the traditional PID controller because it improves the control performance. The PIλDµ controller has an additional fractional integrator degree (λ) and fractional derivative degree (µ). In this study, the focus is on the design of a fractional-order PID controller according to a reference model in the time domain. Bode's ideal transfer function was used as the reference model. It is aimed to obtain PIλDµ parameters by minimizing the error between the time domain response of Bode's ideal transfer function model and the output of the system to be controlled by using the optimization method. Genetic Algorithm (GA) optimization was used as the optimization method. The study was carried out as a simulation study on an inverted pendulum system with a single-input multiple-output (SIMO) structure.

Keywords

Fractional order PID controller, model reference design, inverted pendulum, single input multi output system.

Ters Sarkaç Sisteminde Referans Model Kullanarak Kesir Dereceli PID Denetleyici Tasarımı

Abstract

Oransal İntegral Türev (PID) denetleyicisinin üç temel parametresi vardır: Oransal kazanç (Kp), İntegral kazanç (Ki) ve Türev kazancı (Kd). Geleneksel bir PID denetleyicide, integral ve türev operatörleri tamsayı derecelidir. Araştırmacılar, kontrol performansını iyileştirdiği için geleneksel PID denetleyicideki tamsayı sıralı integral ve türev operatörleri yerine kesirli integral ve türev operatörlerini kullanarak kesir dereceli PID (PIλDµ) denetleyici önermişlerdir. PIλDµ denetleyici, ek bir kesirli entegratör derecesine (λ) ve kesirli türev derecesine (µ) sahiptir. Bu çalışmada, zaman domeninde referans modele göre kesir dereceli PID denetleyici tasarımı üzerinde durulmuştur. Referans model olarak Bode'nin ideal transfer fonksiyonu kullanılmıştır. Optimizasyon yöntemi kullanılarak Bode'nin ideal transfer fonksiyon modelinin zaman domeni yanıtı ile kontrol edilecek sistemin çıkışı arasındaki hata minimize edilerek PIλDµ parametrelerinin elde edilmesi amaçlanmıştır. Optimizasyon yöntemi olarak Genetik Algoritma (GA) optimizasyonu kullanılmıştır. Çalışma, tek girişli çoklu çıkış (SIMO) yapısına sahip ters sarkaç sistemi üzerinde simülasyon çalışması olarak gerçekleştirilmiştir.

Keywords

Kesir dereceli PID denetleyici, model referans tasarım, ters sarkaç, tek girişli çoklu çıkış sistem.

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