Lagrangian description of electrical circuit model of a reluctance type accelerator system is introduced. The effectiveness of the general purpose magnetostatic finite element analysis (FEA) tools on the introduced model is demonstrated. Electrical equivalent circuit model of the system lays out many properties of the system in terms of voltage, current, power or energy distributions of electrical components, and also electrical equivalent of the mechanical components, in an easily perceivable form. These type of actuators are simple mechanisms when they are in steady state. However, when they are in transient, their dynamics may become very complex. The aim of the study is to show how this approach allows many researchers without the full electromagnetic background, to model and understand the dynamics of the reluctance type linear or rotary motor or actuators whether they are saturated or not. To exhibit the validity of the proposed model and solution of dynamic behaviors with FEA, it is verified on a basic capacitor discharge type driver circuit including the electromagnetic accelerator coil and projectile.

A novel swing-up algorithm for an inverted pendulum under a restricted cart track length is introduced. The algorithm achieves the swing-up task by means of a control law that uses a finite input set. The algorithm neither knows nor uses values of cart and pendulum masses, or pendulum length. In the swing-up process, it self-learns a weight that is used in normalizing the energy injected to the pendulum. This weight makes it possible for the algorithm to determine the number of sampling periods needed to reach the upright equilibrium state. Also, by predicting the multi-step ahead cart position, it gives rise to a control law that keeps the cart within the track and makes the pendulum reach the neighbourhood of the upright equilibrium state in a smooth manner. The validity and robustness of the swing-up algorithm are verified through laboratory experiments.

A novel algorithm, called the edge determination algorithm, for exact computation of the frequency response of a linear interval system is proposed. The algorithm formulates candidate curves for the frequency response boundaries as cubic Bezier curves. The edge determination algorithm operates on the cubic Bezier control points of these curves to obtain those, or their parts, that are on the frequency response boundaries. It presents the frequency response boundaries as an array whose entries are the cubic Bezier control points of the curves on the boundaries. Examples for two different cases are presented to illustrate the mechanics and validity of the algorithm.

No abstract

Bir ters sarkaç sisteminin faz portresinin oluşturulmasında kübik Bezier eğrisi formülasyonu kullanılmıştır. Sonlu sayıda elde edilen deneysel yörünge verileri kullanılarak, araç ve sarkaç kütlelerinin, sarkaç boyunun ve sürtünme katsayı değerlerinin bilinmediği durumlarda deneysel olarak elde edilenlerin dışındaki yörüngelerin yüksek doğrulukla çıkarılabilmesi sağlanmıştır. Deney yapılmadan hesaplanan yörüngelerin elde edilmesinde içiçe geçmiş Bezier eğrileri kullanılarak verimli bir hesaplama yapılabildiği gösterilmiştir. Verilen keyfi başlangıç şartları için, system dinamiği modelinin bilinmemesi durumunda, deneysel verilerden kübik Bezier eğrisi formülasyonu ile elde edilen yörüngeler, model dinamiği bilgisi ile hesaplanan yörüngelerle yüksek doğrulukla uyuşmaktadır. Makalede sunulan örnek çalışma, kübik Bezier eğrileri ile hesaplama yaklaşımının doğrusal interpolasyon ile elde edilebilecek değerlere göre çok daha yüksek yaklaşıklık performansı gösterdiğini doğrulamaktadır.