In this paper the stability and control of a parametrically excited, rotating flexible beam is considered. The equations of motion for such a system contain time periodic coefficients. Floquet theory and a numerical integration are used to evaluate the stability of the linearized system. Stability charts for various sets of damping, parametric excitation, and rotation parameters are obtained. Several resonance conditions are found and it is shown that the system stability can be significantly changed due to the rotation. Such systems can be used as preliminary models for studying the flap dynamics and control of helicopter rotor blades and flexible mechanisms among other systems. To control the motion of the system, an observer based controller is designed via Lyapunov-Floquet transformation. In this approach the time periodic equations are transformed into a time invariant form, which are suitable for the application of standard time invariant controller design techniques. Simulations for several combinations of excitation and rotation parameters are shown.
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December 1998
Technical Papers
Stability and Control of a Parametrically Excited Rotating Beam
S. C. Sinha,
S. C. Sinha
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, AL 36849
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Dan B. Marghitu,
Dan B. Marghitu
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, AL 36849
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Dan Boghiu
Dan Boghiu
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, AL 36849
Search for other works by this author on:
S. C. Sinha
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, AL 36849
Dan B. Marghitu
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, AL 36849
Dan Boghiu
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, AL 36849
J. Dyn. Sys., Meas., Control. Dec 1998, 120(4): 462-470 (9 pages)
Published Online: December 1, 1998
Article history
Received:
September 5, 1996
Online:
December 3, 2007
Citation
Sinha, S. C., Marghitu, D. B., and Boghiu, D. (December 1, 1998). "Stability and Control of a Parametrically Excited Rotating Beam." ASME. J. Dyn. Sys., Meas., Control. December 1998; 120(4): 462–470. https://doi.org/10.1115/1.2801487
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