Adaptive vibration control using a virtual-vibration-absorber controller

A control algorithm emulating a dynamic vibration absorber (DVA) is developed for a flexible structure subject to harmonic disturbances of uncertain frequency. The virtual vibration absorber is mathematically equivalent to a passive DVA, but its stiffness, inertia and damping coefficient are adjustable by software. Stiffness of the virtual spring is tuned according to the phase difference between the acceleration of the primary body and the displacement of the virtual mass. The adaptation algorithm consists of a phase detector with a low-pass filter, similar to that found in a phase-locked loop. Both undamped and damped vibration absorbers are developed; the former has the advantage of cleaner vibration neutralization while the latter has a smoother stiffness adaptation. Adaptation rate of the virtual stiffness is analyzed in detail. The effectiveness of the proposed method is confirmed by simulations and real-time experiments.