Aydin, Ahmet KaanHaider, Md ZulfiqurÖzkan Özer, Ahmet2025-01-222025-01-222024-12-17Aydin, Ahmet Kaan, Md Zulfiqur Haider, and Ahmet Özkan Özer. "A New Semi-Discretization of the Fully Clamped Euler-Bernoulli Beam Preserving Boundary Observability Uniformly". IEEE Control Systems Letters 8 (2024): 2955-60. https://doi.org/10.1109/LCSYS.2024.3519379.https://doi.org/10.1109/LCSYS.2024.3519379http://hdl.handle.net/11603/37425This letter extends a Finite Difference model reduction method to the Euler-Bernoulli beam equation with fully clamped boundary conditions. The corresponding partial differential equation (PDE) is exactly observable in the energy space with a single boundary observer in arbitrarily short observation times. However, standard Finite Difference spatial discretization fails to achieve uniform exact observability as the mesh parameter approaches zero, with minimal observation time potentially depending on the filtering parameter. To address this, we propose a Finite Difference algorithm incorporating an averaging operator and discrete multipliers, leveraging Haraux’s theorem on the spectral gap to ensure uniform observability. This approach eliminates the need for artificial viscosity or Fourier filtering. Our method achieves uniform observability for arbitrarily small times with dual observers-the tip moment and average tip velocity-mirroring results from mixed Finite Elements applied to the wave equation with homogeneous Dirichlet boundary conditions, where dual controllers converge to the single controller of the PDE model [Castro, Micu-Numerische Mathematiik’06]. Our reduced model is applicable to more complex systems involving Euler-Bernoulli beam equations.6 pagesen-US© 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Finite difference methodsBoundary conditionsFinite element analysisaverage operatoreuler-bernoulli beamObservabilityUniform observabilityEigenvalues and eigenfunctionsFilteringStandardsfinite differencesdiscrete multipliersFourier seriesViscosityMathematical modelsText