Analytical study of time-delayed feedback control of rectangular prisms undergoing subcritical galloping

In this study, time-delayed feedback control is investigated for an elastically mounted rectangular prism undergoing subcritical galloping in the transverse direction, when subjected to wind excitation. The mathematical model of the galloping system under consideration is established by using the quasi-steady aerodynamic theory. The control performance in terms of the galloping onset speed of the time-delayed displacement, velocity and acceleration feedback is investigated via linear stability analysis, respectively. Subsequently, the method of multiple scales is implemented for nonlinear analysis in order to derive the analytical expression of the vibration amplitude of the galloping system and determine the criticality curve that is the boundary of the subcritical and supercritical bifurcation regions. The results show that the hybrid objective of increasing the galloping onset speed, changing the Hopf bifurcation behavior from subcritical to supercritical and reducing the amplitude of limit-cycle oscillations can be achieved by means of delayed acceleration feedback. This study provides an analytical tool and procedure for time-delayed feedback control design of such a kind of flow–structure interaction system.