Modelling of PID and LQR Controller for Stability and Position Control in Double Inverted Pendulum System

Abstract

Nowadays, stability of the inverted pendulum system is an up-to-date topic in which researchers working on control systems compare control theories and methods. The inverse pendulum systems are unstable and nonlinear systems in terms of controllability. Due to the complexity of the structure and the difficulty of the control process, many advanced control theories can be applied on these systems to improving the performance of the controllers. In this study, PID and LQR controller methods were applied on a double inverted pendulum modeled in MATLAB environment and their controller performances were compared. The results via experimental studies were evaluated on the applicability of PID and LQR control methods.

Keywords

• Double inverted pendulum
• PID controller
• LQR controller
• Control systems

Çift Ters Sarkaç Sisteminin Kontrolü için PID ve LQR Kontrolcü Tasarımlarının Modellenmesi

Öz

Günümüzde, ters sarkaç sisteminde denge sağlama özellikle kontrol sistemleri üzerine çalışma yapan araştırmacıların kontrol teori ve yöntemlerini kıyasladıkları güncel bir konudur. Ters sarkaç sistemi kontrol edilebilirlik açısından kararsız ve doğrusal olmayan sistemler arasında yer almaktadır. Yapısının karmaşıklığı ve kontrollerinin zorluğu nedeniyle birçok ileri düzey kontrol teorisi bu sistemler üzerinde uygulanarak kontrolcülerin performansları üzerinde değerlendirme yapılabilmektedir. Bu çalışmada, PID ve LQR kontrolcü yöntemleri MATLAB ortamında matematiksel olarak modellenen bir çift eklemli ters sarkaç üzerinde uygulanmış ve kontrolcü performansları karşılaştırılmıştır. PID ve LQR kontrol yöntemlerinin uygulanabilirliği üzerinde elde edilen sonuçlar değerlendirilmiştir.

Anahtar Kelimeler

• Çift eklemli ters sarkaç
• PID kontrolcü
• LQR kontrolcü
• kontrol sistemleri

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