Bifurcations in a controlled system with softening stiffness: The Virtual Mechanical System control law for nonlinear vibration control

This study investigates the control of an impulsively excited one-degree-of-freedom (DOF) oscillator with softening stiffness, modelled with an arctangent characteristic. The goal is to control the host system’s vibrations by transferring the vibrational energy to an active controller. To this end, a Virtual Mechanical System (VMS) control law is implemented. This law is characterised by controller dynamics, which describe the behaviour of a mechanical system coupled to the host system skew-symmetrically in the velocities and having stiffness identical to that of the host system. The hypothesis is that this similarity and unique coupling facilitate energy transfer. By using the Complexification-Averaging (CxA) technique and examining the slow flow dynamics wrt. fixed points, bifurcations and impulsive orbits, the conditions for energy transfer are uncovered, enabling tuning of the controller.

Recommended citation: Sarah Geykens, Jasper Juchem, Kevin Dekemele and Mia Loccufier. "Bifurcations in a controlled system with softening stiffness: The Virtual Mechanical System control law for nonlinear vibration control." Nonlinear Dynamics (2025): 1-19.
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