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TECHNICAL PAPERS

A Nonlinear State-Space Model of a Resonating Single Fiber Scanner for Tracking Control: Theory and Experiment

[+] Author and Article Information
Quinn Y. J. Smithwick

Dept. of Aeronautics & Astronautics, University of Washington, Seattle, WA 98195;Dept. of Mechanical Engr., University of Washington, Seattle, WA 98195;Human Interface Technology Lab, University of Washington, Seattle, WA 98195

Per G. Reinhall

Dept. of Mechanical Engr., University of Washington, Seattle, WA 98195

Juris Vagners

Dept. of Aeronautics & Astronautics, University of Washington, Seattle, WA 98195

Eric J. Seibel

Dept. of Mechanical Engr., University of Washington, Seattle, WA 98195;Human Interface Technology Lab, University of Washington, Seattle, WA 98195

J. Dyn. Sys., Meas., Control 126(1), 88-101 (Apr 12, 2004) (14 pages) doi:10.1115/1.1649974 History: Received August 21, 2003; Online April 12, 2004
Copyright © 2004 by ASME
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References

Figures

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Resonating Single Fiber Scanner and Experimental Setup
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Scan Patterns with z and y components
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Coordinate systems for a base excited cantilever x,y and z are the inertial coordinates; t is the time; s is the undeformed arc length (material coordinate); ξ, η, ζ are the principle axes of the beam’s cross section at position s;Dξ,Dη,Dζ are the principle stiffnesses; βy=DζDη and βγ=Dξ/Dη;u(s,t),v(s,t), and w(s,t) are the components of the displacement of the centroid at an arbitrary location s along the inertial axes x,y and z respectively, and g denotes the acceleration due to gravity. F and Ω are the constant amplitude and frequency of the base motion. All variables are nondimensionalized using the constrained length of the beam L and the characteristic times L2m/Dη where m is the mass per unit length. The following assumptions are made: (a) the cross-section dimensions b and h and material properties are uniform, (b) the distributed torsional moments of inertia of the beam are negligible, (c) the dissipation of energy due to internal friction, resistance and relative motion between the beam and its support system can be modeled by a viscous damper having the coefficient c.3
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Resonating Fiber Profile and Theoretical Mode Shape
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z-Raster frequency response curves for 2,4,6,8,10 Volts—Theory vs. Experiment
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y-Raster frequency response curves for 2,4,6,8,10 Volts—Theory vs. Experiment
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Spiral scan frequency response curves for 2,4,6,8,10 Volts—Theory vs. Experiment
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Propeller scan frequency response curves for 2,4,6,8,10 Volts—Theory vs. Experiment
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Piezotube Frequency and Amplitude Response. a) Frequency Response 0-10,000 Hz. b), c) Amplitude and Phase Frequency Response near fiber resonance, d) Amplitude Response near fiber resonance, e) scaling factor vs amplitude
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Frequency Response Plots with and without Centripetal Acceleration and Linear Response
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Spiral Scan Frequency Response with and without aerodynamic damping
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Amplitude and phase angle of describing function N for backlash of width 2b and input amplitude A. (18, pg. 179, figures 5.17, 5.18).

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