Doğrusal Olmayan Manyetik Levitasyon Sisteminin Kontrolü için PID ve LQR Kontrolcülerinin Performans Karşılaştırılması

Abstract

Manyetik Levitasyon Sistemi (MLS), düşük enerji tüketimi ve minimum sürtünme gibi avantajlarından dolayı mühendislik alanında güncel bir çalışma haline gelmiştir. MLS'ler doğrusal olmayan kararsız sistemlerdir. Yapının karmaşıklığı ve kontrollerin zorluğu nedeniyle bu sistemler üzerinde birçok gelişmiş kontrol teorisi uygulanabilmekte ve kontrolörlerin performansı değerlendirilebilmektedir. Bu makalede, MATLAB ortamında matematiksel olarak modellenen MLS üzerinde, Oransal–İntegral–Türev (PID) ve Lineer-Quadratic Regulator (LQR) denetleyici yöntemleri uygulanmıştır. Bulunan sonuçlarda denetleyici performansları karşılaştırılmıştır. PID ve LQR kontrol yöntemlerinin MLS için uygulanabilirliği konusunda elde edilen sonuçlar değerlendirilmiştir. Ayrıca kontrolörlerin sistem performansı bakımından beş parametre ile karşılaştırılmıştır. Bunlar yükselme zamanı, yerleşme zamanı, maksimum aşma, aşma ve kararlı durum hatasıdır. LQR kontrolör, PID kontrolöre kıyasla büyük bir kararlılık ve homojen yanıt üretmiştir.

Keywords

• Magnetic Levitation System
• PID Control
• LQR Control

Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System

Abstract

Magnetic Levitation System (MLS) has become a current study in the field of engineering due to its advantages such as low energy consumption and minimum friction. MLSs are nonlinear unstable systems. Due to the complexity of the structure and the difficulty of the controls, many advanced control theories can be applied on these systems and the performance of the controllers can be evaluated. In this article, Proportional-Integral-Derivative (PID) and Linear-Quadratic Regulator (LQR) controller methods are applied on MLS mathematically modeled in MATLAB environment. Controller performances were compared in the results found. The results obtained on the applicability of PID and LQR control methods for MLS were evaluated. In addition, the system performance of the controllers was compared with five parameters. These are rise time, settling time, maximum overshoot, overshoot and steady-state error. LQR controller produced great stability and homogeneous response compared to PID controller.

Keywords

• Magnetic Levitation System
• PID Control
• LQR Control
• Non-linear System Control

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