Exact Controllability and Boundary Stabilization of Torsional Vibrations of an Internally Damped Flexible Space Structure

G. C. Gorain and S. K. Bose
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G. C. Gorain: S. N. Bose National Center for Basic Sciences
S. K. Bose: S. N. Bose National Center for Basic Sciences

Journal of Optimization Theory and Applications, 1998, vol. 99, issue 2, No 7, 423-442

Abstract: Abstract In this paper, we study the exact controllability and boundary stabilization of the torsional vibrations of a flexible space structure (such as a solar cell array) modeled by a rectangular panel, incorporating the material damping of the structure. The panel is hoisted at one end by a rigid hub and the other end is totally free. For the attachment of this hub on one side of the panel, the hub dynamics leads to a nonstandard boundary condition. To incorporate internal damping of the material, we assume Voigt-type viscoelasticity of the structure. Exact controllability theory is established using the Hilbert uniqueness method by means of a control torque applied only on the rigid hub of the panel. At the same time, uniform exponential energy decay rate is obtained directly for the solution of this problem.

Keywords: Exact controllability; Hilbert uniqueness method; boundary stabilization; internally damped wave equation; exponential energy decay; torsional vibrations; boundary control; adjoint system (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1021778428222

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