Sezai TOKAT, İbrahim EKSİN, Müjde GÜZELKAYA

Koordinat dönüşümüne dayalı zamanla değişen doğrusal kayma yüzeyi

Bu çalışmanın amacı, kayma yüzeyi tasarımı için yeni bir yöntem geliştirmektir. Yeni yaklaşımlar; birisi kayma yüzeyinin kendisi, diğeri ise doğal olarak kayma yüzeyine dik olan bir koordinat ekseninde geliştirilmiştir. Daha sonra, kontrol kuralı Lyapunov kararlılık koşulu uygulanarak düzenlenmiştir. Önerilen yeni kayma yüzeyi bulanık mantık kontrol, yakın komşuluk ve fonksiyon atama yaklaşımları kullanılarak zamanla değişen bir parametre yardımı ile ayarlanmıştır. Elde edilen yöntemlerin analizi parametre belirsizlikleri ile sınır değerli dış bozuculara sahip ikinci derece sistem modeli üzerinde koşturulan benzetimlerle yapılmıştır. Çeşitli başarım ölçütleri kullanılarak önerilen yöntemin ulaşma zamanının azaltılmasının, bozuculara karşı dayanıklılık, yumuşak faz düzlemi yörünge hareketi gibi olumlu iyileştirmeler sağladığı gözlenmiştir.

Coordinate transformation based time-varying linear sliding surface

The aim of this study is to propose new approaches for on-line tuning of the linear sliding surface in the sliding mode controllers. The new approaches are developed for a class of second order systems on a new coordinate axes that one of which is the classical sliding surface and the other one is naturally chosen to be orthogonal to it. The control law is then modified accordingly by applying the Lyapunov stability condition. The adjustment of the linear sliding surface defined in the new coordinate axes is achieved by tuning a new parameter using three different methods. First, an adaptive sliding surface with a rotation scheme is constructed by interpreting the classical delta neighborhood approach. Next, the rotation process is achieved by using a fuzzy tuning mechanism that uses the new coordinates as its input variables and generates an incremental change in the new parameter value as an output. Thirdly, a time-varying function is used for defining the new parameter. Numerical simulations are performed on a second order system model with parameter uncertainties and bounded external disturbance. The new approaches are compared with the sliding mode controller having a constant sliding surface and two sliding mode controllers having a continuously time-varying sliding surface. Results have shown improved performances of the proposed approaches in terms of a decrease in the reaching and settling times, robustness to disturbances and smooth phase plane trajectory.

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