Balanced calibration of resonant piezoelectric RL shunts with quasi-static background flexibility correction

Resonant passive–active vibration absorber with integrated force feedback control

“…As demonstrated in [25,26] the influence of spill-over from nonresonant modes can be represented by the extended modal representation…”

“…Resonant vibration absorbers are effectively calibrated using the balanced concept of equal modal damping [26,28]. It is a pole-placement approach where the coefficients of the quartic character- …”

“…For the pure passive absorber the inertia in H q (ω) = −ω 2 m q is realized by a mechanical inerter element, while for the active realization the control equation G q (ω) = −ω 2 m q contains a double integration of the measured absorber force, which might be sensible to actuator saturation from low-frequency sensor input [29]. The calibration of the stiffness-based absorber follows the equal modal damping procedure outlined in [28] for a family of resonant control formats and in [26] for piezoelectric damping with RL (resistive-inductive) shunt circuits. The characteristic equation is obtained from the denominator of the frequency response function u s /f e ,…”

“…Therefore, the calibration procedure in [26] is conveniently applied with the two stiffness ratios ν and α as given system parameters, and with ω d and ζ q determined by the calibration procedure,…”

“…For the present stiffness-based absorber the stiffness ratio ν is chosen with respect to a desired level of supplemental damping ζ des . According to [26] the stiffness ratio ν should therefore be determined as…”