One position sensor, a bilinear observer, and quadratic, observer-based feedback to a parametric actuator asymptotically stabilize n-modes of a flexible system. Using a perturbation approach, the transient and forced response of a controlled mode are approximated. The decay rate and resonance amplitude are related to the control gains, initial conditions, and forcing amplitude. A forced spillover instability is discovered that can destabilize uncontrolled modes with insufficient damping. A control bound is determined, based on the damping coefficients and frequencies of the modes, that prevents this instability. Experiments on a tension-controlled, pinned-pinned beam demonstrate that parametric control provides substantially faster transient decay and constrained response at resonance.
Parametric Control of Flexible Systems
C. D. Rahn,
C. D. Rahn
Department of Mechanical Engineering, Clemson University, Clemson, SC 29643
C. D. Mote, Jr.
Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA 94720
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Rahn, C. D., and Mote, C. D. (July 1, 1994). "Parametric Control of Flexible Systems." ASME. J. Vib. Acoust. July 1994; 116(3): 379–385. https://doi.org/10.1115/1.2930439
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