The response of a Duffing–van der Pol oscillator under delayed feedback control

Li, Xinye; Ji, Jinchen; Hansen, Colin H.; Tan, Chunxiao

doi:10.1016/j.jsv.2005.06.033

Cited by 72 publications

(37 citation statements)

References 13 publications

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“…Kakmeni et al [18] examined the strange attractors and chaos control in a Duffing-van der Pol oscillator with two external periodic forces. Li et al [19] considered the response of a doffing-van der Pol oscillator under delayed feedback control and found that unwanted multiple solutions can be prevented. It is also shown that coupled nonlinear state feedback control can be replaced by uncoupled nonlinear state feedback control.…”

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confidence: 99%

Arbitrary amplitude periodic solutions for parametrically excited systems with time delay

Maccari

2007

Nonlinear Dyn

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Periodic solutions for parametrically excited system under state feedback control with a time delay are investigated. Using the asymptotic perturbation method, two slow-flow equations for the amplitude and phase of the parametric resonance response are derived. Their fixed points correspond to limit cycles (phaselocked periodic solutions) for the starting system. In the system without control, periodic solutions (if any) exist only for fixed values of amplitude and phase and depend on the system parameters and excitation amplitude. In many cases, the amplitudes of periodic solutions do not correspond to the technical requirements. On the contrary, it is demonstrated that, if the vibration control terms are added, stable periodic solutions with arbitrarily chosen amplitude and phase can be accomplished. Therefore, an effective vibration control is possible if appropriate time delay and feedback gains are chosen.

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confidence: 99%

Arbitrary amplitude periodic solutions for parametrically excited systems with time delay

Maccari

2007

Nonlinear Dyn

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“…1 The model describing the nonlinear state feedback control system delayed feedback control are relatively rare and they focused on the single degree of freedom [11,17]. It is well known that the appropriate choice of feedback gains and time delays can enhance the performance of vibration reduction.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Analysis of vibration suppression of master structure in nonlinear systems using nonlinear delayed absorber

Chen

Chung

et al. 2014

Int. J. Dynam. Control

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In this paper, a nonlinear delayed absorber is proposed by a delayed feedback loop and is utilized to absorb or suppress the vibration of a two-degree-of-freedom nonlinear system when the primary resonance and the 1:1 internal resonance occur simultaneously. To explain analytically mechanism of performance of the absorber, an integral equation method is provided to obtain the second order approximation and the amplitude equations. As a result, the feedback gain and time delay which make the amplitude of the main system equal to zero can be derived analytically. Optimal working conditions of the system are extracted from the time delay-response curves, the force-response curves and the frequency-response curves. In the illustrative example, the appropriate choice of feedback gains and time delays can reduce the amplitude of the main system by more than 98 % in comparison with the amplitude with no time delay. All analytical predictions are in excellent agreement with the numerical simulations.

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“…and the bilinear form as (20) where C * is the dual space of C, φ ∈ C, and ψ ∈ C * . Suppose that q 1 (θ ) and q 2 (θ ) are the eigenvectors corresponding to the eigenvalue λ 1 = iβ, and satisfy…”

Section: Centre Manifold Reduction and Poincaré Normal Formmentioning

confidence: 99%

Non-resonant response, bifurcation and oscillation suppression of a non-autonomous system with delayed position feedback control

Wang

Zhang

2007

Nonlinear Dyn

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The maglev system with delayed position feedback control is excitated by the deflection of flexible guideway and resonant response may take place. This paper concerns the non-resonant response of the system by employing centre manifold reduction and method of multiple time scales. The dynamical model is presented and expanded to the third-order Taylor series. Taking time delay as its bifurcation parameter, the condition with which the Hopf bifurcation may occur is investigated. Centre manifold reduction is applied to get the Poincaré normal form of the nonlinear system so that we can study the relationship between periodic solution and system parameter. At first, the non-resonant periodic solution of the normal form is calculated based on the method of multiple time scales. Then the bifurcation condition of the free oscillation in the solution is analyzed, and we get the conditions with which the free oscillation has maximum and minimum values. The relationship between external excitation and the periodic solution is also discussed in this paper. Finally, numerical simulation results show how system and excitation parameters affect the system response. It is shown that the existence of the free oscillation and the amplitude of the forced oscillation can be determined by time delay and control parameters. So felicitously selecting them can suppress the oscillation effectively.

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The response of a Duffing–van der Pol oscillator under delayed feedback control

Cited by 72 publications

References 13 publications

Arbitrary amplitude periodic solutions for parametrically excited systems with time delay

Arbitrary amplitude periodic solutions for parametrically excited systems with time delay

Analysis of vibration suppression of master structure in nonlinear systems using nonlinear delayed absorber

Non-resonant response, bifurcation and oscillation suppression of a non-autonomous system with delayed position feedback control

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