Bifurcation Stabilization with Local Output Feedback

Gu, Guoxiang; Chen, Xiang; Sparks, Andrew G.; Banda, Siva S.

doi:10.1137/s0363012997320924

Cited by 58 publications

(37 citation statements)

References 11 publications

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“…Using the multiple scales method, they demonstrated that appropriate choices of the feedback gains and the time delay are possible for better vibration control. Bifurcation stabilization with local output feedback was treated by Gu [11] and Hy and Zh [12] considered controlled mechanical systems with time delays and, in particular, primary resonance and subharmonic resonance of a harmonically forced Duffing oscillator with time delay (stabilization of periodic motion and applications to active chassis of ground vehicles were discussed). Local bifurcation control was applied by Ji [13] to a forced one-degree-of-freedom nonlinear system, while Zhu et al [14] applied a new stochastic averaging method to predict the response of a Duffing-van der Pol oscillator under both external and parametric excitation of wide-band stationary random processes.…”

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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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“…In [6-91, state feedback is used and in [2], static output feedback is used. We have not seen any paper that uses dynamic output feedback.…”

Section: Control Of Rotating Stall In Axial Flow Compressorsmentioning

confidence: 99%

Bifurcation suppression of nonlinear systems via dynamic output feedback and its applications to rotating stall control

Chen

Qin

Mei

2005

J. Control Theory Appl.

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This gaper deals with the problems of bifurcation suppression and bifurcation suppression with stability of nonlinear systems. Necessary conditions and sufficient conditions for bifurcation suppression via dynamic output feedback are presented; Sufficient conditions for bifurcation suppression with stability via dynamic output feedback are obtained. As an application, a dynamic compensator,which guarantees that the bifurcation point of rotating stall in axial flow compressors is stably suppressed, is constructed.

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“…Using the multiple scales method, they demonstrated that appropriate choices of the feedback gains are possible for better vibration control. Bifurcation stabilization with local output feedback was treated by Gu [18] that considered in particular stabilization of periodic motion in the primary and subharmonic resonance of a harmonically forced Duffing oscillator with time delay. Oueni et al [19] considered a nonlinear active vibration absorber coupled with the plant through userdefined cubic nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

Vibration control by nonlocal feedback and jerk dynamics

Maccari

2010

Nonlinear Dyn

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Jerk dynamics is used for a new method for the suppression of self-excited vibrations in nonlinear oscillators. Two cases are considered, the van der Pol equation and nonlinear oscillator with quadratic and cubic nonlinearities. A nonlocal control force is introduced in such a way to obtain a third order nonlinear differential equation (jerk dynamics). Using the asymptotic perturbation method, two slow flow equations on the amplitude and phase of the response are obtained, and subsequently the performance of the control strategy is investigated. The feedback gains are connected with the stability and response of the system under control. Uncontrolled and controlled systems are compared and the appropriate choices for the feedback gains are found in order to reduce the amplitude peak of the self-excitations. Numerical simulation confirms the validity of the new method.

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Bifurcation Stabilization with Local Output Feedback

Cited by 58 publications

References 11 publications

Arbitrary amplitude periodic solutions for parametrically excited systems with time delay

Arbitrary amplitude periodic solutions for parametrically excited systems with time delay

Bifurcation suppression of nonlinear systems via dynamic output feedback and its applications to rotating stall control

Vibration control by nonlocal feedback and jerk dynamics

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