An Euler–Bernoulli beam equation under boundary control and delayed observation is considered. An observer–predictor based scheme is developed to stabilize the equation. On a time interval where the observation is available, the state is tracked by the observer; when the observation is not available due to the delay, the state is estimated by the predictor. The estimation is then used in propor...

This paper studies the basis property and the stability of a distributed system described by a nonuniform Euler–Bernoulli beam equation under linear boundary feedback control. It is shown that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state Hilbert space. The asymptotic distribution of eigenvalues, the spectrumdetermined growth condition,...

We model a exible robot arm supported at a prismatic joint so the length of (the relevant part of) the rod is variable | indeed, this variation in the length of the arm is taken to be the control action. The principal results are: exact controllability for the consideration of purely longitudinal vibrations (wave equation) and the existence of optimal controls in the more practically interestin...

The aim of this paper is to present some recent developments and hints for future researches in control inspired of flatness-based ideas. We explain how explicit trajectory parameterization, a property that is central for flat systems, can be useful for the control of various oscillatory systems (linear, nonlinear, finite and/or infinite dimension) of physical and engineering interests. Such pa...

In this paper, we proceed exploring the case of non-stationary helical flows Navier-Stokes equations for incompressible fluids with variable (spatially dependent) coefficient proportionality between velocity and curl field flow. Meanwhile, system (including continuity equation) has been successfully explored previously respect to existence analytical way presentation aforementioned type. The ma...

In this paper, we consider conformable equal width wave (EW) equation in order to construct its exact solutions. This plays an important role physics and gives interesting model define change waves with weak nonlinearity. The aim of paper is present new solutions EW equation. For purpose, use effective method called Improved Bernoulli Sub-Equation Function Method (IBSEFM). Based on the values s...

The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers. The micro-beam is suspended over a fixed substrate and undergoes the both piezoelectric and electrostatic actuation. The piezoelectric layers are poled through the thickness and equipped with surface electrodes. The equation governing the micro-beam deflection under electrostatic pressure is deriv...

This research presents a model of the avian vocal tract, implemented using classical waveguide synthesis and numerical methods. The vocal organ of the songbird, the syrinx, has a unique topography of acoustic tubes (a trachea with a bifurcation at its base) making it a rather unique subject for waveguide synthesis. In the upper region of the two bifid bronchi lies a nonlinear vibrating membrane...

In this paper we analyse a simple model of a digital communications channel. This model proves to be closely related to an iterated function system (IFS) related to the well-known Bernoulli convolution. We derive it from a randomly forced first-order ordinary differential equation. This allows the parameter of the Bernoulli convolution—the contraction rate, λ—to be related to the rate at which ...