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Research Papers

Anticontrol of Chaos Reduces Spectral Emissions

[+] Author and Article Information
Cristina Morel

 École Supérieure d’Électronique de l’Ouest (ESEO), 4 rue Merlet de la Boulaye, 49009 Angers, Francecristina.morel@eseo.fr

Radu Vlad

 Technical University of Cluj-Napoca, 103-105 Boulevard Muncii, 400641 Cluj-Napoca, Romaniaradu.constantin.vlad@mis.utcluj.ro

Jean-Yves Morel

 University of Angers, 4 Boulevard Lavoisier, 49100 Angers, Francejean-yves.morel@univ-angers.fr

J. Comput. Nonlinear Dynam 3(4), 041009 (Sep 02, 2008) (6 pages) doi:10.1115/1.2960463 History: Received April 20, 2006; Revised January 18, 2008; Published September 02, 2008

Switch-mode power supplies usually emit electromagnetic interferences at the switching frequency and its harmonics. Inducing chaos in these systems has recently been suggested as a means of reducing these spectral emissions, yet at the expense of aggravating the overall magnitude of the ripple in the output voltage. We propose here a new nonlinear feedback, which induces chaos and which is able at the same time to achieve a low spectral emission and to maintain a small ripple in the output. The design of this new and simple controller is based on the propriety that chaotified nonlinear systems present many independent chaotic attractors of small dimensions.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

dc-dc buck converter with feedback anticontrol. The values of the fixed parameters are taken from Refs. 2,16: L=20mH, C=47μF, R=22Ω, c1=8.4, Vref=11.3V, VL=3.8V, VU=8.2V, T=400μs, and E=16V.

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Figure 2

The periodic output voltage v(t) of the buck converter with the control law vc1(t) of Eq. 1 (70mV ripple)

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Figure 3

Power spectrum of the output voltage v(t) with the control law vc1(t) of Eq. 1

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Figure 4

The maximum of the power spectrum of the output voltage v(t) obtained with the control law vc3(t) of Eq. 7c2 and ω2

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Figure 5

Slow dynamics of δ(t): example of sine function g(t) and the anticontrol of chaos state feedback u(x(t))

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Figure 6

A chaotic attractor of the buck converter of Eqs. 3,4,12 and with the control law vc2(t) of Eq. 13 (c2=2V and ω2=100rad∕V)

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Figure 7

Fast dynamics of δ(t): example of sine function g(t) and the anticontrol of the chaos state feedback u(x(t))

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Figure 8

Independent chaotic attractors of the buck converter of Eqs. 3,4,12 obtained for c2=18V and ω2=100rad∕V with the control law vc2(t) of Eq. 13

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Figure 9

Attractor diagram as function of c2 with different initial conditions

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Figure 10

A chaotic attractor of the buck converter of Eqs. 3,4,12 and with the control law vc2(t) of Eq. 13 (c2=18V and ω2=100rad∕V)

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Figure 11

Output voltage v(t) obtained for c2=18V and ω2=100rad∕V with the control law vc2(t) of Eq. 13 (30mV ripple)

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Figure 12

Power spectrum of the output voltage v(t) obtained with the control law vc2(t) of Eq. 13 and with the parameters c2=18V and ω2=100rad∕V(min(maxFFT)=0.7V2∕Hz)

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Figure 13

The maximum Lyapunov exponent of the modified buck converter of Eqs. 3,4,12 in function of c2 with ω2=100rad∕V

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Figure 14

Output voltage ripple as function of c2 and ω2

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Figure 15

Output voltage ripple as function of c2 and ω2

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