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Gain-scheduled H∞ buckling control of a circular beam-column subject to time-varying axial loads

: Schäffner, Maximilian; Platz, Roland


Smart materials and structures : SMS 27 (2018), Nr.6, Art. 065009, 14 S.
ISSN: 0964-1726
ISSN: 1361-665X
Fraunhofer LBF ()
circular beam-column; time-varying axial load; gain-scheduled; H∞ buckling control

For slender beam-columns loaded by axial compressive forces, active buckling control provides a possibility to increase the maximum bearable axial load above that of a purely passive structure. In this paper, an approach for gain-scheduled ${{\mathscr{H}}} {\infty }$ buckling control of a slender beam-column with circular cross-section subject to time-varying axial loads is investigated experimentally. Piezo-elastic supports with integrated piezoelectric stack actuators at the beam-column ends allow an active stabilization in arbitrary lateral directions. The axial loads on the beam-column influence its lateral dynamic behavior and, eventually, cause the beam-column to buckle. A reduced modal model of the beam-column subject to axial loads including the dynamics of the electrical components is set up and calibrated with experimental data. Particularly, the linear parameter-varying open-loop plant is used to design a model-based gain-scheduled ${{\mathscr{H}}} {\infty }$ buckling control that is implemented in an experimental test setup. The beam-column is loaded by ramp- and step-shaped time-varying axial compressive loads that result in a lateral deformation of the beam-column due to imperfections, such as predeformation, eccentric loading or clamping moments. The lateral deformations and the maximum bearable loads of the beam-column are analyzed and compared for the beam-column with and without gain-scheduled ${{\mathscr{H}}} {\infty }$ buckling control or, respectively, active and passive configuration. With the proposed gain-scheduled ${{\mathscr{H}}} {\infty }$ buckling control it is possible to increase the maximum bearable load of the active beam-column by 19% for ramp-shaped axial loads and to significantly reduce the beam-column deformations for step-shaped axial loads compared to the passive structure.