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TECHNICAL PAPERS

A Stochastic Averaging Approach for Feedback Control Design of Nonlinear Systems Under Random Excitations

[+] Author and Article Information
O. Elbeyli, J. Q. Sun

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716

J. Vib. Acoust 124(4), 561-565 (Sep 20, 2002) (5 pages) doi:10.1115/1.1501084 History: Received August 01, 2001; Revised May 01, 2002; Online September 20, 2002
Copyright © 2002 by ASME
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References

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Figures

Grahic Jump Location
The steady state PDF of the response amplitude with c1=−1, c3=1/3, k1=2 and k3=8. (-⋅-⋅) the controlled response via stochastic averaging, (—) Monte Carlo simulation of the controlled system, (---) Rayleigh approximation of the controlled system, (⋯) uncontrolled system response.
Grahic Jump Location
Variation of the expected response amplitude E[a,(t)] with control gains k1 and k3. (—) k1=0, (---) k1=2, (-⋅-⋅) k1=8, (⋯) k1=12.
Grahic Jump Location
Variation of the expected response amplitude E[a,(t)] with control gains k1 and k3. (—) k3=0, (---) k3=2, (-⋅-⋅) k3=8, (⋯) k3=12.
Grahic Jump Location
Variation of the mean square of the response amplitude E[a,(t)2] with control gains k1 and k3. (—) k1=0, (---) k1=2, (-⋅-⋅) k1=8, (⋯) k1=12.
Grahic Jump Location
Variation of the mean square of the response amplitude E[a,(t)2] with control gains k1 and k3. (—) k3=0, (---) k3=2, (-⋅-⋅) k3=8, (⋯) k3=12.
Grahic Jump Location
Transient response of the mean square E[a(t)2] with c1=−1, c3=13, k1=2 and k3=8. (---) response via Rayleigh pdf approximation, (—) the averaged response via Monte Carlo simulation, (-⋅-⋅) the uncontrolled response, (⋯) the steady state response level with stochastic averaging.
Grahic Jump Location
The steady state PDF of the response amplitude with the worst case design of the control gains k1=5 and k3=913. (—) the PDF for the system with c1=c1min and c3=c3min, (⋯) the simulated transient response for the system with c1=−1 and c3=3, (---) the simulated averaged response for the system with c1=−2 and c3=13.
Grahic Jump Location
Transient responses of the mean square E[a(t)2] with k1=5 and k3=913. (---) the simulated averaged transient response with the worst case parameters c1=c1min and c3=c3min, (⋯) the simulated average transient response for the base case c1=c1max and c3=c3max, (—) the steady state response via stochastic averaging with c1=c1max and c3=c3max, (-⋅-⋅) the steady state response via stochastic averaging with c1=c1min and c3=c3min.

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