Vibration Suppression of Flexible Beam with Delayed Boundary Feedback via Discrete-time Optimal Controller

Haraguchi, Masakazu; Hu, Haiyan

doi:10.1109/icma.2007.4303533

Cited by 1 publication

(1 citation statement)

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“…There exist many representative examples in the literature. The study of Ma and Butcher [7] investigated the stability of a continuum beam when delayed follower force is applied at its end; in the paper of Haraguchi and Hu [8], the vibration suppression of a continuum beam is studied in the presence of delayed control. In both cases, they used low DoF approximations since the PDE models with delayed boundary conditions were too complex for analytical approaches.…”

Section: Introductionmentioning

confidence: 99%

Exact stability chart of an elastic beam subjected to delayed feedback

Zhang

Stépàn

2016

Journal of Sound and Vibration

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a b s t r a c tThe stability of an elastic beam is studied when the beam is subjected to a longitudinal force governed by a feedback loop. The setup of the simplified mechanical model is motivated by a basic problem of electroacoustics. The corresponding governing equation is the 1D wave equation with delayed boundary conditions. By means of the D'Alembert solution, the system can be transformed into a delay differential equation of neutral type that includes two time delays. The intricate stability chart is constructed analytically in the parameter plane of the gain parameter and the ratio of the time delays. The complete chart extends the numerical results of the literature, while it also draws attention to the numerical difficulties of finite degree of freedom approximations and to the extreme sensitivity of the dynamics with respect to the time delay parameters of the system.

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Section: Introductionmentioning

confidence: 99%