Amplitude modulation control method for bursting dynamics under time-delayed feedback. (December 2022)

• Record Type: Journal Article
• Authors: Yu, Yue; Wang, Ning; Chen, Zhenyu
• Is Part Of: Journal of vibration and control. Volume 28:Number 23/24(2022)
• Page Start: 3550
• Page End: 3558
• Publication Date: 2022-12
• Subjects: Bursting dynamic -- vibration control -- Hopf bifurcation -- time delay -- critical manifold; Vibration -- Periodicals; Damping (Mechanics) -- Periodicals; 620.3
• DOI: 10.1177/10775463211035934
• Languages: English
• ISSNs: 1077-5463

Abstract

Time-delayed feedback control is one of the important active control methods for complex dynamical behaviors in nonlinear systems. Yet its relationship and effectiveness on multiple time scale dynamics need to be further explored. As a purpose to gain insight into such complexity, we investigate the effectiveness of amplitude modulation in controlling (suppressing or enhancing) bursting oscillations in a classical mechanical oscillator with time-delayed feedback. It is shown how the presence of delay can change the amplitude of the singular cycle oscillations, or suppress them altogether. The results are compared to the conventional periodic perturbation method. In many cases, the amplitudes of periodic solutions under delayed feedback are easier to satisfy the technical requirements. If the delayed feedback is added, stable periodic bursting can be easily accomplished. Therefore, we demonstrate that an effective vibration modulation for bursting dynamics is possible if appropriate time delay and feedback gains are chosen.