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TECHNICAL PAPERS

A Global Control Strategy for Efficient Control of a Braille Impact Hammer

[+] Author and Article Information
Jenny Jerrelind

Division of Vehicle Dynamics, Royal Institute of Technology, SE-100 44 Stockholm, Swedenjennyj@kth.se

Harry Dankowicz

Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

J. Vib. Acoust 128(2), 184-189 (May 11, 2005) (6 pages) doi:10.1115/1.2159033 History: Received March 10, 2004; Revised May 11, 2005

A combined control scheme relying on feedback-based local control in the vicinity of periodic system responses and global control based on a coarse-grained approximation to the nonlinear dynamics is developed to achieve a desirable dynamical behavior of a Braille printer impact hammer. The proposed control methodology introduces discrete changes in the position of a system discontinuity at opportune moments during the hammer motion while the hammer is away from the discontinuity, thereby exploiting the recurrent contacts with the discontinuity to achieve the desired changes in the transient dynamics. It is argued that, as the changes in the position of the discontinuity affect the motion only indirectly through changes in the timing and state at the subsequent contact, the control actuation can be applied over an interval of time during the free-flight motion as long as it is completed prior to contact. A forced, piecewise smooth, single-degree-of-freedom model of a Braille impact hammer is used to illustrate the methodology and to yield representative numerical results.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic model of the Braille printer impact hammer

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Figure 2

Approximated current pulse (2)

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Figure 3

Bifurcation diagram of the steady-state response of the impact hammer to a periodic current pulse under variations in lag time Tlag. Here, the gray curves indicate the shift of the periodic-trajectory bifurcation curves under variations in the position of the back stop, σ.

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Figure 4

The backward-in-time images of trajectories based at initial conditions at the front stop with strong (high impact velocity) and weak (low impact velocity) impacts under the free-flight flow. Here, the dots refer to the location of periodic system responses.

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Figure 5

Dynamic response of the impact hammer under reference feedback only. Here, the desired impact pattern 0-1-1-0-0-0-0-0-1-1-1 governs the switch between the appropriate values of xref and the associated gain parameter values. Specifically, panels (a) and (d) depict the time evolution of the hammer velocity including discrete points representing the velocity at the Poincaré section (Panel (a)) and the velocity at the impact with the front stop (Panel (d)). Panels (b) and (c) show the time evolution of θ and σ, respectively, including discrete points representing their values upon leaving the Poincaré section, i.e., after the imposition of g̃control.

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Figure 6

Dynamic response of the impact hammer under the combined control scheme. Here, the desired impact pattern 0-1-1-0-0-0-0-0-1-1-1 governs the switch between the appropriate values of xref and the associated gain parameter values. Specifically, panels (a) and (d) depict the time evolution of the hammer velocity including discrete points representing the velocity at the Poincaré section (panel (a)) and the velocity at the impact with the front stop (panel (d)). Panels (b) and (c) show the time evolution of θ and σ, respectively, including discrete points representing their values upon leaving the Poincaré section, i.e., after the imposition of g̃control.

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