Control of amplitude and frequency of lim it cycles in nonlinear oscillatory systems

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Journal of Vibration and Shock ›› 2009, Vol. 28 ›› Issue (6) : 90-92,1.

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SHEN Jian-he1,2, CHEN Shu-hui1
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Abstract

The multiple scales method was used to calculate the normal forms of dynamical systems near the Hopf bifurcation point and the analytical formula regarding the amplitude and frequency of the controlled limit cycles and the
feedback gains was obtained. Thus, the control of amplitude and frequency of limit cycleswas realized by choosing the suitable feedback gains. A three-dimensional system was chosen as an illustrated example. The efficiencies of some linear or nonlinear state feedback controllers were discussed and compared. The obtained analytical conclusions were verified bynumerical simulations.

Key words

limit cycles / amplitude contro / l frequency control

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SHEN Jian-he;CHEN Shu-hui(. Control of amplitude and frequency of lim it cycles in nonlinear oscillatory systems[J]. Journal of Vibration and Shock, 2009, 28(6): 90-92,1