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  • Yayın
    Adaptive backstepping approach for 2-DOF telescopes despite unknown wind disturbance
    (Institute of Electrical and Electronics Engineers Inc., 2019-07) Ünal, Ali Cem; Yılmaz, Cemal Tuğrul; Kararsız, Gökhan; Keskin, Onur; Yeşilyaprak, Cahit
    Small ground telescopes on the marked are widely used in many space observatories and scientific researches. There are three main problems in such telescopes; positioning of the focal point and the need of tuning for both different seasonal wind speeds and mass changes of the telescope arm. This study focuses on eliminating those problems for 2-DOF altazimuth configuration small telescopes. An adaptive controller is designed to create a set and forget system. The mathematical model of the telescope is derived based on RR type joint configuration. For a realistic approach, motor dynamics is considered in the mathematical model. The wind disturbance is modeled according to the Wind-Gust model which is a sum of sinusoidal with unknown amplitude, frequency and phase. The controller aims to cancel the effect of the disturbance on focal point of the telescope while positioning. The asymptotic stability is proven with the Lyapunov approach. The numerical study is illustrated to success of the proposed controller.
  • Yayın
    Nonlinear waves in a stenosed elastic tube filled with viscous fluid: Forced perturbed korteweg-de vries equation
    (Springer Science and Business Media, LLC, 2008) Tay, Kim Gaik; Demiray, Hilmi; Tiong, Ong Chee
    In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the propagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By introducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the smallness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.