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Research Papers

Boundary Control of Slender Beams Under Deterministic and Stochastic Loads

[+] Author and Article Information
K. D. Do

Department of Mechanical Engineering,
Curtin University,
Kent Street,
Bentley, WA 6102, Australia
e-mail: duc@curtin.edu.au

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 13, 2016; final manuscript received February 8, 2017; published online June 5, 2017. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 139(9), 091012 (Jun 05, 2017) (14 pages) Paper No: DS-16-1311; doi: 10.1115/1.4036071 History: Received June 13, 2016; Revised February 08, 2017

This paper first derives equations of motion of extensible and shearable slender beams with large motions under both deterministic and stochastic external loads. Boundary feedback controllers are then proposed to achieve almost surely globally practically asymptotic stability. The control design, well-posedness, and stability analysis are based on a Lyapunov-type theorem developed for a class of stochastic evolution systems (SESs) in Hilbert space.

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Figures

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Fig. 1

Beam boundary configuration (boundary control forces, ϕ1B and ϕ2B, and moment ϕ3B are provided by actuators at the top-end) and loading diagram: (a) boundary configuration and (b) loading diagram

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Fig. 2

Simulation results without any boundary controls

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Fig. 3

Simulation results with boundary controls

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