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Remarks on an Optimal Linear Control Design Applied to a Nonideal and an Ideal Structure Coupled to an Essentially Nonlinear Oscillator

[+] Author and Article Information
Fábio Roberto Chavarette

 UNESP-Rio Claro, State University of São Paulo, C.P. 178, Rio Claro, São Paulo 13500-230, Brazilfabioch@rc.unesp.br

José Manoel Balthazar1

 UNESP-Rio Claro, State University of São Paulo, C.P. 178, Rio Claro, São Paulo 13500-230, Braziljmbaltha@rc.unesp.br

Jorge L. P. Felix

 UNESP-Rio Claro, State University of São Paulo, C.P. 178, Rio Claro, São Paulo 13500-230, Braziljorgelpfelix@yhaoo.com.br

1

Corresponding author.

J. Comput. Nonlinear Dynam 5(2), 024501 (Feb 11, 2010) (8 pages) doi:10.1115/1.4000829 History: Received October 10, 2008; Revised August 12, 2009; Published February 11, 2010; Online February 11, 2010

This paper considers a nonlinear dynamics of a particular structure coupled (or uncoupled) to an essentially nonlinear oscillator. We used an optimal linear control design to reduce the amplitude of oscillations and to expand energy consumption, for both ideal and nonideal mathematical models.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of an oscillator attachment coupled to an essentially nonlinear oscillator: (a) ideal; (b) nonideal

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Figure 2

(a) Phase portrait and (b) fast Fourier transform (FFT) both for ideal structure coupling

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Figure 3

(a) Phase portrait and (b) FFT both for nonideal structure coupling

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Figure 4

Stability diagram for (a) ideal and (b) nonideal structures

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Figure 5

Controlled ideal structure coupling: (a) time history x1, (b) time history x3, (c) time history energy, (d) phase plane, (e) controlled time history x1, and (f) controlled time history x3; the parameters are λ1=0.025, λ2=0.075, ε1=0.25, and ε2=0.25 (periodic); ε2=−1.3 (chaos) and γ=0.15; the initial conditions are x1(0)=0, x2(0)=2.0, x3(0)=0, and x4(0)=0(14)

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Figure 6

Controlled nonideal structure coupling (a) time history x1, (b) time history x2, (c) time history energy, (d) phase plane, (e) controlled time history x1, and (f) controlled time history x3; the parameters are λ1=0.025, λ2=0.075, ε1=0.25, ε2=0.25 (periodic), ε2=−1.3 (chaos), q1=0.10, q2=0.30, b=5, and γ=0.15; the initial conditions are x1(0)=0, x2(0)=2.0, x3(0)=0, and x4(0)=0(14)

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Figure 7

Time history of the energy consumption: (a) uncontrolled system; (b) controlled system

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