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TECHNICAL PAPERS

Limit Cycle Behavior of Smart Fluid Dampers Under Closed Loop Control

[+] Author and Article Information
Neil D Sims

Department of Mechanical Engineering, The University of Sheffield, Mappin St, Sheffield S1 3JD, United Kingdomn.sims@sheffield.ac.uk

J. Vib. Acoust 128(4), 413-428 (Apr 01, 2005) (16 pages) doi:10.1115/1.2212444 History: Received May 21, 2004; Revised April 01, 2005

Semiactive vibration dampers offer an attractive compromise between the simplicity and fail safety of passive devices, and the weight, cost, and complexity of fully active systems. In addition, the dissipative nature of semiactive dampers ensures they always remain stable under closed loop control, unlike their fully active counterparts. However, undesirable limit cycle behavior remains a possibility, which is not always properly considered during the controller design. Smart fluids provide an elegant means to produce semiactive damping, since their resistance to flow can be directly controlled by the application of an electric or magnetic field. However, the nonlinear behavior of smart fluid dampers makes it difficult to design effective controllers, and so a wide variety of control strategies has been proposed in the literature. In general, this work has overlooked the possibility of undesirable limit cycle behavior under closed loop conditions. The aim of the present study is to demonstrate how the experimentally observed limit cycle behavior of smart dampers can be predicted and explained by appropriate nonlinear models. The study is based upon a previously developed feedback control strategy, but the techniques described are relevant to other forms of smart damper control.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 12

Experimental and analytical limit cycle behavior. —, limit cycle: linear analysis; –∙–∙, limit cycle: nonlinear analysis; —, experimental force velocity data (scaled); (a) 5Hz±2mm, 5kNs∕m; (b) 5Hz±2mm10kNs∕m; (c) 10Hz±4mm, 2kNs∕m; (d) 10Hz±4mm4kNs∕m; (e) 15Hz±2mm, 2kNs∕m; (f) 15Hz±2mm4kNs∕m

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Figure 9

Experimental and simulated response, 15Hz, ±2mm, D=4kNs∕m, B=0.3, G=0.0015. (a) Experimental, (b) simulated, (c) time-force histories; (d) simulated phase-space trajectory and fixed points.

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Figure 10

Experimental and simulated response, 15Hz, ±2mm, D=4kNs∕m, B=0.5, G=0.002. (a) Experimental (b) simulated, (c) time-force histories (d) Simulated phase-space trajectory and fixed points.

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Figure 11

Experimental and simulated response, 15Hz, ±2mm, D=4kNs∕m, B=0.8, G=0.0025. (a) Experimental; (b) simulated; (c) time-force histories; (d) simulated phase-space trajectory and fixed points.

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Figure 1

Damper test facility. (a) General configuration; (b) damper attachment.

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Figure 2

Experimental results from the MR damper. 10Hz, ±4mm. Closed loop response. (a) Controllable viscous damping; (b) increased controller gain causing undesirable closed loop behavior.

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Figure 4

Model validation. —, model response; ⋯, experimental response. --- applied velocity -∙-∙- applied current (a) Sinusoidal mechanical excitation, constant current (0, 0.2, 0.4, 0.6, 0.8, 1.0A). (b) Filtered-random mechanical excitation, sinusoidal input current. (c) Time history of the result shown in (b).

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Figure 5

Control concept. (a) Basic concept; (b) modified to account for symmetry of MR behavior; (c) emulating a controllable viscous damper—the gain D controls the viscous damping rate.

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Figure 6

Linearization process. (a) Linearization of the model—physical significance. (b) Linearization about the operating point x2. (c) Linearized block diagram.

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Figure 7

Phase-space analysis for constant velocity. G=0.015, FR=500N, velocity ẋ2=0.05m∕s. (a) B=0.3, ζ1=0.3, ζ2*=1, ω1=2421rad∕s, ω2=868rad∕s, stable focus; (b) B=0.4, ζ1=0.04, ζ2*=1, ω1=2593rad∕s, ω2=1918rad∕s, stable focus; (c) B=0.5, ζ1=−0.1, ζ2*=1, ω1=2909rad∕s, ω2=2460rad∕s, unstable focus; (d) the same as (c) with different initial conditions.

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Figure 8

Fixed point stability for increasing velocity amplitude, B=0.5, G=0.002, D=2kNs∕m, and 4kNs∕m

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