On the exponential decay of the Euler-Bernoulli beam with boundary energy dissipation

We study the asymptotic behavior of the Euler-Bernoulli beam which is clamped at one end and free at the other end. We apply a boundary control with memory at the free end of the beam and prove that the "exponential decay" of the memory kernel is a necessary and sufficient condition for the exponential decay of the energy.Comment: 13 page

Backstepping-Based Exponential Stabilization of Timoshenko Beam with Prescribed Decay Rate

This is an open access article under the CC BY-NC-ND license.In this paper, we present a rapid boundary stabilization of a Timoshenko beam with anti-damping and anti-stiffness at the uncontrolled boundary, by using PDE backstepping. We introduce a transformation to map the Timoshenko beam states into a (2+2) × (2+2) hyperbolic PIDE-ODE system. Then backstepping is applied to obtain a control law guaranteeing closed-loop stability of the origin in the H1 sense. Arbitrarily rapid stabilization can be achieved by adjusting control parameters. Finally, a numerical simulation shows that the proposed controller can rapidly stabilize the Timoshenko beam. This result extends a previous work which considered a slender Timoshenko beam with Kelvin-Voigt damping, allowing destabilizing boundary conditions at the uncontrolled boundary and attaining an arbitrarily rapid convergence rate

Frequency stabilization of an ultraviolet semiconductor disk laser

We report a tunable, narrow-linewidth UV laser based on intracavity second-harmonic generation in a red semiconductor disk laser. Single-frequency operation is demonstrated with a total UV output power of 26 mW. By servo-locking the fundamental frequency to a reference Fabry–Pérot cavity, the linewidth of the UV beam has been reduced to 16 kHz on short timescales and 50 kHz on a 1 s timescale, relative to the reference

Exponential stability of a class of boundary control systems

We study a class of partial differential equations (with variable coefficients) on a one dimensional spatial domain with control and observation at the boundary. For this class of systems we provide simple tools to check exponential stability. This class is general enough to include models of flexible structures, traveling waves, heat exchangers, and bioreactors among others. The result is based on the use of a generating function (the energy for physical systems) and an inequality condition at the boundary. Furthermore, based on the port Hamiltonian approach, we give a constructive method to reduce this inequality to a simple matrix inequality

Frequency stabilization in nonlinear micromechanical oscillators

Mechanical oscillators are present in almost every electronic device. They mainly consist of a resonating element providing an oscillating output with a specific frequency. Their ability to maintain a determined frequency in a specified period of time is the most important parameter limiting their implementation. Historically, quartz crystals have almost exclusively been used as the resonating element, but micromechanical resonators are increasingly being considered to replace them. These resonators are easier to miniaturize and allow for monolithic integration with electronics. However, as their dimensions shrink to the microscale, most mechanical resonators exhibit nonlinearities that considerably degrade the frequency stability of the oscillator. Here we demonstrate that, by coupling two different vibrational modes through an internal resonance, it is possible to stabilize the oscillation frequency of nonlinear self-sustaining micromechanical resonators. Our findings provide a new strategy for engineering low-frequency noise oscillators capitalizing on the intrinsic nonlinear phenomena of micromechanical resonators.Fil: Antonio, Dario. Argonne National Laboratory. Center for Nanoscale Materials; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Zanette, Damian Horacio. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: López, Daniel . Argonne National Laboratory. Center for Nanoscale Materials; Estados Unido

Boundary feedback stabilization of a flexible wing model under unsteady aerodynamic loads

This paper addresses the boundary stabilization of a flexible wing model, both in bending and twisting displacements, under unsteady aerodynamic loads, and in presence of a store. The wing dynamics is captured by a distributed parameter system as a coupled Euler-Bernoulli and Timoshenko beam model. The problem is tackled in the framework of semigroup theory, and a Lyapunov-based stability analysis is carried out to assess that the system energy, as well as the bending and twisting displacements, decay exponentially to zero. The effectiveness of the proposed boundary control scheme is evaluated based on simulations.Comment: Published in Automatica as a brief pape